Arimaa/Print version

Arimaa is a two-player abstract strategy board game that can be played using the same equipment as chess.

Note: current version of this book can be found at http://en.wikibooks.org/wiki/Arimaa

Table of Contents

1. Overview
2. Playing The Game
3. Introduction to Tactics
4. Introduction to Strategy
5. Camel Hostage
6. Other Hostages
7. Frames
8. Trap Control
9. Distribution of Force
10. Rabbit Advancement
11. Elephant Blockade
12. Relative Value of Pieces
13. Advanced Tactics
14. Setup
15. Race Positions
16. Trap Attacks
17. Lone Elephant Attacks
18. Sample Games
19. Arimaa Challenge History
20. Glossary
21. Resources
22. GNU Free Documentation License

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Overview

Arimaa (pronounced uh-ree-muh) is a two-player board game invented by Omar Syed, a computer engineer trained in artificial intelligence. After Garry Kasparov was defeated by the chess computer Deep Blue, Syed wanted to create a game that could be played on a chessboard using chess pieces, but which could not be won by sheer calculating power. Syed thought that a large branching factor was the key, but soon realized that this would not automatically favor humans, who would need to anticipate a position a few turns ahead. While teaching his young son a simplified version of chess, Syed began to see a solution; if movement was limited but each turn allowed for multiple steps, a game could be both high-branching and playable. After much experimenting, Syed came up with a game which, like chess, used a 1-1-2-2-2-8 distribution of pieces. Conceptually, Syed's new game was much simpler than chess, yet the branching factor dwarfed that of chess. For a human or machine, imprecise planning would be key. The name Arimaa is derived from that of Syed's son Aamir.

Arimaa's first computer test was the Zillions of Games engine, which was designed to competently play any game it was given the rules to. As Syed expected, Zillions was an easy opponent. On November 20, 2002, Syed published the rules for Arimaa and announced a $10,000 prize, available annually until 2020, for the first bot to defeat a top human player in a "Challenge" match. David Wu's bot Sharp claimed the prize in 2015.

United States Patent number 6,981,700 for Arimaa was filed on the 3rd of October 2003, and granted on the 3rd of January 2006. Omar Syed also holds a trademark on the name "Arimaa". Syed has released an experimental license called "The Arimaa Public License", with the declared intent to "make Arimaa as much of a public domain game as possible while still protecting its commercial usage". Items covered by the license are the patent and the trademark.

Arimaa can be played online at the arimaa.com gameroom. Face-to-face, it might be played using a chess set, since each Arimaa piece corresponds to a chess piece. In 2009, Z-Man Games began producing a commercial Arimaa set. Only one face-to-face tournament has taken place, but various events have been hosted online:

• The World Championship is an annual tournament for human players. This tournament has taken various formats, and has lasted as many as fourteen rounds. Jean Daligault was the world champion six times from 2007 to 2014, and then Mathew Brown was champion six times from 2015 to 2023.
• From 2004 to 2015, the Computer Championship matched the top Arimaa bots in an elimination tournament. David Fotland's program Bomb placed first each year from 2004 to 2008, even though Fotland didn't update it after 2005. Stronger bots emerged in 2009; from then on, there was no one dominant bot until David Wu's Sharp went undefeated in 2015.
• The Arimaa Challenge took place following the Computer Championship. At first, the winning bot played an eight-game match against a lone human defender. The format evolved: from 2007 onward, the top two bots were available to play during a "screening" period. A human could play two games against each of these two bots; the bot with the better record in those matches advanced to the Challenge, where it faced three ultimate human defenders, who were selected beforehand and hadn't played in the screening. If this bot could win best-of-three matches against all three human defenders, its developer would win the $10,000 prize. Humans dominated until 2015, when Sharp defeated Jean Daligault, Lev Ruchka, and Mathew Brown.

After DeepMind's AlphaZero mastered Go, Chess, and Shogi simply by playing itself, neural networking Arimaa bots were developed. Rusty_Zero is currently the top bot, with an Elo rating near 3000.

External links

A collection of articles by the game creator and top bot developers

Playing The Game

Rules

Like classic chess, Arimaa is played on an 8×8 grid. The two players, Gold and Silver, control sixteen pieces each (listed in descending order of strength):

Piece	Elephant	Camel	Horse	Dog	Cat	Rabbit
Number	1	1	2	2	2	8
Symbols

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The players begin by setting up their pieces however they choose on their home rows. Highlighted are the four trap squares.

If Arimaa is played using a chess set, the pieces may be represented by the king, queen, knights, bishops, rooks, and pawns respectively. Unlike their chess counterparts, however, Arimaa pieces move only in cardinal directions, and step one square at a time. The relative strength of each piece lies in its power to push, pull, or immobilize weaker enemy pieces. There are four trap squares on which a piece can potentially be lost — these are the squares designated as c3, f3, c6, and f6 when classified by rank and file.

The game begins with an empty board. Gold arranges his pieces on the first and second ranks, in whatever configuration he chooses — Arimaa pieces do not have fixed starting positions. Silver then arranges her pieces on the seventh and eighth ranks.

A piece steps from square to square. Rabbits can step left, right, or forward. All other pieces can step left, right, forward, or backward. Diagonals have no place in the rules of Arimaa.

A turn (or move) consists of one to four steps. The steps in a turn can be used on four different pieces, all on the same piece, or any combination. After the setup phase is completed, the players alternate turns with Gold going first.

A player may not pass a turn, and must always make a net change to the position. Thus one cannot, for example, move the same piece forward and backward and leave it at that. Furthermore, a turn may not result in a position identical to one which the same player has created twice before.

The game's main objective is to get a rabbit across the board; the opponent's home rank is the goal line.

Freezing

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The second diagram portrays a position which could occur later in a game.

A piece which is adjacent to a stronger enemy piece is frozen, unless it is also adjacent to a friendly piece. While frozen, a piece may not be moved by its owner. The silver elephant on d5 freezes the gold horse on d6. The frozen gold horse itself freezes a silver rabbit on e6, but the rabbit would be unfrozen if the f7 dog stepped west. The dogs on a6 and b6 do not freeze each other, as they are of equal strength.

Pushing and pulling

A piece can pull or push a weaker enemy piece which is next to it, provided an empty square allows for the necessary movement.

In a pull, a piece steps onto an adjacent empty square and drags the weaker enemy piece onto the square from which it came. The silver elephant on d5 could step east, west, or south and pull the gold horse from d6 to d5. In a push, the weaker enemy piece is moved onto an adjacent empty square, and the piece which pushed it moves onto the square it had occupied. The gold elephant on d3 could push the silver rabbit on d2 to e2 and then occupy d2. A push or pull uses two steps, since two pieces are moved.

Note that the rabbit on d2 can't be pushed to d1, c2, or d3, because those squares are already occupied. Remember also that a piece can only push or pull a weaker enemy piece — for example, a dog may dislodge an enemy rabbit or cat, but not a dog, horse, camel, or elephant. Although a rabbit may not retreat toward its home row, it can nonetheless be pushed or pulled in that direction. For example, the gold rabbit on g3 could not itself step back to g2, but the silver horse could take a step right and then pull it down.

A piece may not push and pull simultaneously — for example, the gold elephant could not dislodge the d2 and c3 rabbits in one move. No push can occur if there is no empty square for a piece to be pushed onto, and no pull can occur if there is no empty square for the pulling piece to step onto. Strong pieces can sometimes be limited by teams of weaker pieces.

A frozen piece can be pushed or pulled by the opponent. A non-frozen piece can also be pushed or pulled — an adjacent friendly piece does not protect against this. For example, the d1 cat does not protect the c1 cat from being pushed to b1 or pulled to c2. Whether a piece is frozen is unrelated to whether it can be dislodged.

Captures

In Arimaa, a capture can only occur on a trap square. A piece which enters a trap square is removed from the board unless there is a friendly piece next to that trap. The silver elephant could capture the gold horse by pushing it from d6 to c6. The silver rabbit on c3 is still alive because of the c4 rabbit and c2 horse — the c3 trap has two silver defenders. If all friendly defenders left or got dislodged, a piece still on a trap square would be lost.

A piece may voluntarily step into a trap square, even if it is lost thereby. The second step of a pulling maneuver may be completed, even if the pulling piece is lost on the first step. For example, Silver to move could step the silver horse from f2 to f3, losing the horse, and still pull the gold rabbit from f1 to f2 as part of the horse's move.

End of the game

An Arimaa game cannot end in a draw. There are three different ways to win:

• Goal: Gold wins by moving a gold rabbit onto the eighth rank, and Silver wins by moving a silver rabbit onto the first rank. As the principal object of the game, goal is normally how a game is won.
• Elimination: One can win by capturing the last remaining enemy rabbit.
• Immobilization: One can win by creating a position that leaves the opponent with no legal move. This could involve a large blockade.

If one side's move directly brings about a winning condition for the opponent, the opponent wins, except under these rare circumstances:

• If a move brings about goal or elimination for both sides, the one who made the move wins.
• Goal or elimination wins the game even if one's pieces are technically left immobilized. Immobilization is only checked at the start of a turn.
• If a rabbit is dislodged onto its goal line and then dislodged off within the same turn, as occurred on 83g of this game, the game continues.

Setting up

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Gold has used the classic 99of9 setup; Silver has switched the dogs and cats.

The finer points of initial piece placement will be explored later, but a beginner just needs a flexible setup that denies the opponent an easy attack plan. Strong pieces start in the front row, as they must take the lead in clearing a path for a rabbit to goal.

In the diagram at right, Gold has chosen a classic symmetric setup. The elephant is placed in the center so that it can quickly reach any part of the board. The camel is placed in the center as well, so that it could defend either home trap and potentially punish an enemy horse advance on either wing. Rabbits are kept out of the center; since rabbits can't retreat, a rabbit pulled up in the middle might block its own friendly pieces. For the same reason, rabbits are not placed directly behind the traps.

The gold horses will quickly step forward, to assert control of Gold's home traps; one horse or the other might then advance in hopes of creating a threat. Beginning back and center, the gold dogs may soon move up. The gold cats might stay in place for a while, guarding the traps from behind and thus protecting other gold pieces from a quick capture at home.

Since Silver goes second, she can take Gold's setup into account when deciding on her own. Note that the silver elephant is not placed directly opposite the gold elephant. If both elephants started on the same file, Gold could advance his elephant four squares and temporarily fence in the silver elephant.

Silver has also used a symmetric setup, only switching the dogs and cats. Gold has chosen "cats behind the traps, dogs back", while Silver has used "dogs behind the traps, cats back". The pieces guarding their home traps from behind are potentially vulnerable to capture themselves — Silver stands to lose a dog in the opening if she's not careful. As long as another silver piece is next to the trap, however, a dog behind that trap strengthens Silver's control of it, since dogs cannot be pushed aside by enemy dogs. A dog might later advance through the trap and be replaced by a cat or rabbit.

A player who uses a non-symmetric setup may intend to move quickly on one wing.

Notation

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One can play Arimaa without learning the standard notation for moves. For brevity's sake, however, examples will sometimes use the notation rather than spell out each individual step.

Each step is notated as ⟨piece⟩⟨initial square⟩⟨direction⟩.

• ⟨piece⟩ is a single letter:
  • E for Elephant
  • M for caMel
  • H for Horse
  • D for Dog
  • C for Cat
  • R for Rabbit
  Upper case is used for the gold pieces, and lower case for the silver pieces.
• ⟨initial square⟩ is a two-character square name as in chess notation (e.g. e4).
• ⟨direction⟩ can be n, e, s, or w for north, east, south, or west. This is always from Gold's point of view. In addition, the special direction x indicates that the piece is captured.

Suppose Gold is to move in the diagram. The false protection capture of the silver elephant is described as Mb4e db3n cd3e ec3x Hd4s. The northeastern goal is Eg7s rh7w Rh6n Rh7n, or equivalently, Eg7s rh7w Rh6nn. Consecutive steps by the same piece may be condensed, with only the initial square given.

When an actual game is cited, a turn is referred to by a number and "g" (gold) or "s" (silver). 1g and 1s are the setups, 2g is Gold's first regular turn, and 2s is Silver's first regular turn.

While this notation may seem verbose, each step must be accounted for with no ambiguity.

Introduction to Tactics

A tactic is a narrow plan. The most basic tactics involve a one-turn goal or capture. When the opponent has thousands of options, it is difficult to precisely plan beyond the current turn. Some moves, however, might severely limit the opponent's viable options. One facing an immediate goal threat must stop the goal or else lose the game. A capture threat may leave the opponent with only a few ways to avoid a substantial disadvantage. One creating a threat might thus have a response planned for any possible countermove by the opponent.

Tactics can be offensive or defensive; a defensive tactic may slow things down considerably. When nothing big is imminent, plans may be more general, with each side aiming for a strong long-term position. This gets out of tactics and into strategy.

Goal

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Each side to move has a one-turn goal on each wing.

At left, the gold rabbit on b5 can step to victory via b6, c6, c7, and c8. The rabbit is never frozen, as it is always next to the b7 cat or c5 dog; the dog also allows the rabbit to move through the c6 trap. The rabbit will theoretically be frozen once it reaches c8, but Gold will have won regardless.

With friendly support, a rabbit one or two ranks from the goal line might reach goal even if its path is blocked. If the gold cat on h7 moves to h6 while pulling the silver rabbit from g7 to h7, the gold rabbit on g6 can step to goal. The gold camel on f6 is lost when the rabbit advances, but reaching goal is worth any sacrifice. Beginners often incline more toward pushing than pulling, but a push is ineffectual here. If the gold cat pushes the silver rabbit, the cat will be on g7, blocking its own rabbit with only two steps remaining.

Near a depleted goal line, an enemy rabbit is a constant threat. By pushing the b3 horse to c3, the silver camel would occupy b3 and unfreeze the b2 rabbit, which could then step to victory via a2 and a1. Occasionally a rabbit can be unblocked and unfrozen with one pull. Silver to move could slide the silver elephant from g3 to f3, pulling the gold rabbit from g2 to g3; the newly unfrozen f2 rabbit could then step to the vacated g2 and then to g1, winning the game. The silver elephant is lost on the third step, but that doesn't matter since Silver has won. With the f2 rabbit beginning the turn blocked and frozen, this one-turn goal is easy to overlook.

Goal defense

In the above position, each side to move can win the game, but pretend that Silver does not have a one-turn goal and thus must defend. There are a few ways to stop each gold goal individually, but Silver has only four steps to stop both. To block the eastern goal, Silver must close the path to g8 without opening a different one-turn goal path. This could be accomplished by stepping the h8 cat to g8, leaving three steps for the western defense. In those three steps, the b4 camel or d6 horse could capture the c5 dog and freeze the b5 rabbit. If Silver had only two steps for western defense, the b5 rabbit could be pushed west, or the goal path could be blocked.

Suppose Gold had to stop Silver's goals. The simplest solution is Ee3nww Rh1w, which would freeze and threaten the silver camel while also keeping the f2 rabbit frozen, since unfreezing it would no longer be worth an elephant sacrifice by Silver. If Gold had only two steps for western defense, he could either move his elephant onto c3 or use the c2 horse to push the rabbit west.

Goal threat

Even if a goal can be stopped, a one-turn goal threat will force the opponent to use up steps on defense, unless he has a one-turn goal of his own. After the opponent defends goal, one can either press the goal threat further or take advantage of any new weakness resulting from the goal defense. One should always be aware of possible goal paths on both sides, so as not to be caught off guard or miss an opportunity. On the other hand, one should be cautious about advancing rabbits, which can never step backward.

One-turn capture

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Gold to move has one-turn captures in c6, f6, and f3; Silver to move has a one-turn capture in c3.

With Gold to move in the position at right, the gold elephant can take two steps west and then push the b6 dog into the c6 trap. Since there is no other silver piece next to the trap, this captures the silver dog, in one turn.

One can sometimes push aside an obstructing piece to get at a vulnerable piece. With Gold to move, the g6 camel can push the g7 cat to h7; now on g7, the gold camel can push the f7 horse to f6, capturing it in a turn where one piece pushed two different enemy pieces.

A piece on a trap square will be captured if its sole defender is dislodged. Silver to move could step her elephant two squares west and then push or pull the b3 dog, capturing the c3 horse.

The g3 dog can capture the g2 cat by pushing it west and then north. Alternatively, the dog could move through the trap and pull the cat along; with the gold horse on e3, a gold piece can move through f3. A third way to capture the cat would be to pull it to g3 and then push it into f3; the dog would move north and then south. A pull-push in which a single piece moves an enemy piece two squares is known as a flip.

Capture defense

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Sometimes, the best way to stop a capture is to move the threatened piece. The silver elephant protects the b3 cat from capture in c3, but neither piece needs to be tied down. The silver elephant could step west and thereby unfreeze the b3 cat, which could then step to a3 and then to a4.

Other than that, stationing one's elephant next to a trap square is the simplest capture defense. Since an elephant can't be dislodged, no friendly piece can be captured in that trap until the elephant chooses to leave. At left, no gold piece can be captured in c6, and no silver piece can be captured in c3, unless the respective elephant moves away.

A non-elephant can sometimes defend a trap alone, but must then keep a constant eye on all enemy pieces stronger than itself. The opponent may lose something if he moves his elephant, but if he captures more than he lost, it was worth it.

Two non-elephant pieces can defend a trap together; this is called mutual protection. At left, Silver has defended the c6 trap with a dog on b6 and a rabbit on c7. Even if the gold elephant started on b5, it could not immediately capture anything in c6; when a trap has two defenders, any single attacker would need more than four steps to dislodge one defender and capture the other. Gold could at most dislodge the dog to set up a capture threat for the following turn, but then Silver could add another defender, such as the d7 horse.

A capture can sometimes be blocked. A phalanx blocks the gold camel from g7, and thus the f7 horse is currently safe even though it is Silver's only direct defender of the f6 trap. In other cases, one might block a capture by pushing an enemy piece into the capture path.

One counter-intuitive way to block an enemy's path is to station a friendly piece on a trap square in front of another friendly piece. Gold has stuffed c3; the silver elephant could push the gold cat to d3, but that would temporarily give the c3 trap two gold defenders, preventing any capture in Silver's final two steps. Occupying c3 only works because no silver piece immediately threatens the c2 dog; if it were dislodged with the cat still on c3, the cat would be lost.

The f2 dog allows the g3 camel to safely step into the f3 trap, and then capture the gold horse with a pull. Gold to move could prevent this with He3sn df2w Df1n, a pull-and-replace that would give the trap a second gold defender.

If defending a trap is not feasible, threatened pieces might scatter away from it. It may not be possible to get every piece to safety, but even delaying captures may buy time to make progress elsewhere. One scattering pieces away from a home trap should try to block the goal line, as enemy rabbits can easily advance toward an undefended trap.

More capture patterns

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Although not immediately obvious, a one-turn capture is possible in each trap.

It is easy to become too confident about one's defense. In the northwest, the two silver defenders will not prevent a capture in c6, as Gold has a stronger piece next to each. If the gold elephant pushes the silver dog from b6 to c6, the newly unfrozen gold cat can then push the silver rabbit off of c7, capturing the dog. If Gold prefers to capture the rabbit instead, he can pull the dog away and then push the rabbit into c6. This situation, where two defenders do not prevent a one-turn capture, is known as false protection. Such a capture is only possible if there are two attackers, each adjacent to a weaker defender.

In the northeast, the silver camel cannot push the gold dog into the trap, since the horse is in the way. However, Silver can play a split capture: the camel pushes the dog to g6, then the horse pulls the dog into the trap.

In the southwest, Gold has ensured that the b3 horse cannot be pushed. Gold has overlooked another possibility, however; after pushing aside the b4 rabbit, the silver elephant can pull the gold horse to b4, capturing the gold camel on c3.

In the southeast, the f3 dog can step east or west, leaving three steps for the f4 horse to enter the trap square and pull the gold dog from f2 to f3, capturing it. If instead a gold piece were on f3, Silver wouldn't have a one-turn capture there.

The fork

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The gold elephant has forked the silver dog between the c3 and f3 traps.

The fork threatens a single piece with capture in two different traps. On 62g of this game, Gold forked the silver dog between c3 and f3. The dog could not escape, and Silver did not have time to defend both traps, as the e4 rabbit threatened goal and could not be frozen in place. Silver must use at least one step to defend goal, and thus concede the dog.

Generally speaking, a solid fork is most likely to occur between the forker's home traps; any other fork would tend to be easier to escape. From the start of the game, each side must be wary of allowing the opposing elephant to flip a piece into the centre, as that can lead to a strong fork. As defenses thin, forks become a greater potential threat in all areas of the board.

The fence

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The silver horse on c4 has been fenced in; Silver to move can't save it.

The fence is a less common offensive tactic. A piece is brought next to a trap, and hemmed in on two sides. Even if unfrozen from the fourth side, the piece could only step into the trap. On 14g of this game, Gold fenced the silver horse next to the c3 trap. Silver is to move, but can't save the horse. The silver elephant could step to c5 (incidentally capturing the gold rabbit in c6), but the unfrozen silver horse couldn't then escape, as its only available move would be suicide. Silver can't defend the trap, as no silver piece can reach d3, c2, or b3 in four steps; gold pieces block the silver elephant from doing so.

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plan window

Problem: Silver to move and win material

Solution: ef4nw Hg5w hg6s blocks the gold elephant out of e6, fences the gold horse on f5, and clears g6 so that the f6 rabbit can step east. The gold elephant can still pull the e6 dog, capturing the f6 rabbit, but in any event Silver can capture the fenced horse.

4 3 2 1 a b c d e

A fence may be valuable even if the fenced piece can be defended. At right, the silver elephant can go to d3 to defend the horse, but Gold can then frame the horse with hc4s Ed4w Hb4s. In other cases, one might keep the fenced piece in place as a hostage, and perhaps blockade the trap square to stop the piece from moving through it. A frame or hostage is worthwhile only if it results in a whole-board advantage, which is usually a strategic rather than tactical issue.

Limitations of tactics

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Gold to move can avoid any capture.

Tactics alone can't accomplish much, if the opponent understands basic threats and defenses. Early in this game, a gold horse and camel both appeared to be at risk, but Gold went on to win without losing a single piece until the end.

The next thing to learn is basic long-term strategy, which can help one get a whole-board advantage and overwhelm the opponent's defenses.

Introduction to Strategy

Strategy is focused on long-term positions. A threat may create an advantage which can gradually be built upon, even if no captures happen for a while.

Direct goal

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If he is not distracted by a camel or dog capture opportunity, Gold to move can easily stop the silver goal and threaten the advanced silver rabbit with capture. (Game)

The ultimate object of Arimaa is to get a friendly rabbit to goal. If the opponent pays any attention to defense, an early goal is unlikely. It is difficult to directly tear a hole into a well-defended goal line, as pushes and pulls can be blocked. Until there is a substantial opening in the goal line, a rabbit advance should not be regarded as progress toward a goal. A quick rabbit advance may be costly, since an advanced rabbit can never retreat. Defending a rabbit from capture is often untenable, as an elephant has more important things to do, and any other defender could be captured itself.

Capture

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Because the gold elephant was decentralized, Silver was able to fork a gold dog. (Game)

Capture threats are important, whether or not they lead to actual captures. A piece is captured only when it is on a trap square with no friendly piece beside it; there are many ways to prevent a capture. If nothing else, an elephant can camp out beside a trap where there is a threat; since nothing can dislodge an elephant, its friendly pieces can never be captured in a trap it stays next to.

Often, the key to progress is to make strong threats around two different traps. The enemy elephant can only defend one trap, and any other defender or rescuer could itself be at risk.

The simplest double threat is a fork between one's home traps. If a piece can be flipped in the center, it may be doomed to such a fork. This is one of many reasons both elephants might stay near the center. Although any piece can unfreeze a friend, an elephant can do so without putting itself at risk.

A rabbit near the center could be an easy target for a fork, since rabbits can't retreat homeward. This is one reason rabbits often do not begin in the middle. A piece dragged up on the edge would only be threatened in one trap. Many such pulls are not worth the time they use up.

Hostages

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In this game, the silver camel was taken hostage.

In the diagram, Gold has taken the silver camel hostage, threatening to capture it in c3 if the silver elephant leaves. The c4 cat could not defend the hostage alone, as the cat could itself be captured if the trap had no other silver defender. Since an elephant beside its home trap could normally pull a non-elephant enemy piece into the trap, this type of hostage can only be defended by an elephant or by a team of well-placed weaker pieces. A solid camel hostage will make the forces asymmetrical: with the gold elephant holding the silver camel hostage and the silver elephant defending it, the gold camel is the strongest free piece. Until something changes, there is not even a threat to a gold horse. With the gold camel and horse both active in the east, Gold might soon overload Silver's defenses. Having the strongest free piece is a large advantage, if that piece is well-positioned and supported by other pieces.

Without a strong alignment, holding a hostage can be costly. An elephant deadlock at one's home trap is a potential space disadvantage, since the opponent can safely advance pieces toward the deadlocked trap, but the home elephant is not available to ensure safe advances of its own friendly pieces. A home hostage-holder often can't easily leave, as the former hostage might then team up with its elephant to force captures in the trap, clearing space for a goal. In fact, the defending elephant often has better prospects for leaving; its friendly pieces might swarm the trap and soon defend it independently. That could be a devastating turn of events for a hostage-holder, as the enemy elephant might become the strongest free piece. To prevent an easy rotation by the defender, a hostage-holder should usually have an additional strong piece standing guard.

Given such costs, one must be selective about hostage-taking. Generally speaking, it is no good for an elephant to hold a horse hostage while the enemy camel is elsewhere. Conversely, it is usually fine for an elephant to defend a horse hostage held by the enemy elephant, as the defending elephant might hope to rotate out, or trade its horse for the enemy camel if that camel advances.

A camel could take a horse hostage, but a hostage-holding camel might be vulnerable to the "defending" elephant. To maintain a hostage position, a non-elephant hostage-holder may need supporting pieces. A solid horse-by-camel hostage can be quite effective, however, if the hostage-holder's own elephant is free.

Attacking

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Silver has taken control of the c3 trap, creating a large problem for Gold.

If a piece cannot be taken as a strong hostage, it can safely advance along with its elephant. If the enemy camel can be cut off from one wing, a horse might quickly advance on that wing. In the game shown, the silver horses advanced with impunity because the gold camel was far away. Silver was not worried about the gold elephant taking a horse hostage, as this would not have given Gold an advantage.

To own a trap square is to be safe from capture therein while the opponent is not. A trap attack entails an attempt to gain ownership of an away trap and thus threaten several quick captures. Here, Silver has a strong attack on c3, where he can clean up unless the gold elephant moves to c4, which would leave the a6 dog to be captured in c6. An elephant can usually defend against a trap attack, but then will not be available elsewhere.

Seeing his overall weakness in the west, Gold looked east and counterattacked f6, but this was too late; Silver captured two gold pieces in c3 and then forced a rabbit through to goal. Even had the gold elephant defended c3, Gold's long-term prospects would have been bleak; more silver pieces could have advanced in the west, and the silver elephant likely could have gone elsewhere while the gold elephant remained stuck defending against an attack which would otherwise result in a quick goal by Silver. A strong trap attack will create a space advantage, capture threats, and potential goal threats. Had Gold attacked f6 sooner, a capture race might have ensued.

Home and away games

There are two basic plans: try to take control of an away trap, or threaten enemy pieces in one's home traps. Since rabbits can't retreat, they can in principle be pulled out gradually. Rabbit pulling was once routine, but fell out of favor as trap attacks caught on. One who simply chases and drags pieces may quickly find a home trap under siege, and may even face a goal threat from a pulled rabbit. Homeward pulling has its place, but should perhaps not be one's main strategy.

Instead of thinking in terms of home and away play, one should think about the whole board. For a while, any possible move could be met with a solid defense or counterattack. The object is to attain the stronger overall position.

Piece mobility

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The gold camel could be unfrozen from above or from below. (Game)

The elephants are extremely important, but cannot do everything at once. A recurring theme in Arimaa strategy is elephant mobility. Sometimes an elephant gets blockaded, but more often it is restricted by the cost of leaving a particular area. Before getting into a position that will require one's elephant to stay put, one must consider the enemy elephant's situation. If one elephant is even slightly more free than the other, this can snowball, since it affects how free other pieces are.

In the opening, camel mobility is of first concern. If a camel becomes stuck against the edge, even in home territory, the effect may be similar to that of a camel hostage. Sometimes a horse quickly advances on a flank, potentially threatening attack but also providing a way of escape for a friendly piece which might get stuck below it. Rabbits may likewise advance on the edges to keep stronger pieces mobile. When the camel is in the middle, a dog or cat might advance one row ahead and act as a linchpin, so that the camel can immediately retreat if it is pulled forward.

Strategy vs. tactics

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Gold has a far superior board, but will lose the game unless he immediately occupies b2. (Game)

Though strategy is vital, tactics should be considered first. A goal wins the game regardless of the rest of the board; a strong position may mean nothing if one forgets to defend goal. Beyond that, one must watch for hanging pieces and false protection. If a player is careless in this regard, the opponent might quickly gain ground.

Camel Hostage

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To capitalize on this camel hostage, Gold must create a threat in the east.

The position at right is a basic example of a camel hostage. If the silver elephant left the trap, Gold could capture the silver camel by flipping or pulling it onto c3. For now, Silver can only defend with the elephant; any other silver defender could itself be captured in c3, unless there were two weaker silver defenders securely in place, which would require some work.

If Silver ever abandons her camel, the gold elephant should then pull it into the trap, finishing on c4 or d3, near the action. It is thus important that the gold cat remain on c2. The silver camel is not held on b3, as Gold must occupy that square to keep shared trap control and thus avoid losses at home. Gold does not occupy d3, as any gold piece on that square could be pulled away and perhaps threatened with capture.

For now, Gold's elephant is tying up Silver's elephant and camel both, leaving Gold's camel unopposed as the strongest free piece. The silver camel obviously can't defend any trap, and the silver elephant can only defend one trap at a time. The gold camel is thus a grave threat in the east.

Use of free pieces

Gold now wants to create a second threat and force Silver to make a tough choice. In preparation, Gold has wisely advanced a horse ahead of his camel; until the silver elephant comes east, a gold horse cannot be threatened there. A material exchange is possible if Silver moves her elephant east and blocks the gold elephant's path to e6 or f5. A horse-for-camel trade would be acceptable for Gold, but an even camel trade would waste the hostage.

Advanced horses can also protect weaker pieces. To defend the camel hostage, the silver elephant need only finish each turn on c4, d3, or c2; the silver elephant could thus dart around the trap and perhaps dislodge a small gold piece, which might then be delivered to c6 or f6. The gold horses are prepared to defend those traps. The western gold horse must keep some distance from the silver elephant, to avoid being frozen on c5 and then captured in two steps.

Gold could now attack the f6 trap, but if he wants to play it safe, he can keep his camel at home and use the eastern gold horse to drag weaker pieces down for capture in f3 (remember, rabbits can't retreat homeward). As long as the silver elephant defends the silver camel, horses are the strongest silver pieces which could defend f3, but that would be difficult with the gold camel right there; any capture threat at f3 would likely overload Silver. With nothing to stop the gold camel and horse in the east, several silver pieces could ultimately be lost there; the silver elephant will have to come east at some point.

Silver to move could easily trade her camel for a horse: if the silver elephant moves to b6, and the silver camel is then captured, Silver can pull the gold horse from a6 into c6, capturing it in return. The silver elephant could then go wherever it was needed. The loss of a camel for a horse is nothing compared to what Silver could have soon faced if she didn't move her elephant. Alternatively, Silver could play hb5ws Da2e ma3s, unfreezing and burrowing her camel so that it could not be captured in one turn. This is an option only because Gold has left b2 empty; gold pieces on a1, a2, and b2 would form a phalanx, fencing in any a3 hostage. Burrowing the camel would not free it, but would buy Silver time, as Gold would then need two turns just to reestablish a solid camel hostage, this time with the camel on b2.

Gold to move can stop Silver from doing either of those things. To fence in the silver camel, Gold could simply advance the b1 rabbit to b2, but a better option would be to slide the a2 dog to b2, the a1 rabbit to a2, and the b1 rabbit to a1; that way, the dog isn't blocked in. On the fourth step, the a6 horse could move to a7, precluding an immediate camel-for-horse trade.

Multi-piece defense

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With the silver elephant free, this camel hostage is no longer an advantage for Gold.

When the opponent has the strongest free piece, this must be changed before he can capitalize. When the gold camel is active, the silver elephant must not perpetually defend a hostage. Fortunately, it might not need to. With the silver elephant on e3, silver pieces can safely advance in the east. This often allows one to rotate the elephant out of hostage defense, replacing it with two weaker defenders supported by other friendly pieces. Elephant rotation may turn the tables, as the hostage-holding elephant often cannot afford to leave the trap. On 63s of this game, the silver elephant became the strongest free piece; the gold elephant was restricted by capture threats as well as goal threats. Gold could temporarily retake e3 or f4 with a pull-and-replace, but Silver could punish such a move.

A nearby strong piece can strengthen a hostage position. A gold horse or camel might have pulled a silver dog away from the trap, making elephant rotation more difficult for Silver.

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Gold has just freed his elephant, but still has a fight ahead.

On 28g of this game, Gold completed an elephant rotation just in time. Silver had a strong attack in the southwest, but the silver strength concentrated there made the northeastern rotation easier for Gold. Gold had no goal threat and no piece on f6, so the silver elephant had some degree of freedom. Meanwhile, Silver's western goal threat remained formidable; Gold's elephant rotation hardly sealed the game.

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This hostage position makes the eastern gold horse the strongest free piece.

On 13g of this game, Gold held the silver camel hostage and was strong on both wings, yet could not force a capture in c3 or f3. The well-placed silver elephant prevented any capture in f3, while also protecting the silver horses from the gold camel.

Who has the strongest free piece now? If the gold elephant left the c3 trap, Silver would soon wipe out Gold's southwestern forces. If the silver elephant went north, the gold camel might soon dismantle Silver's defense of c3. The silver camel obviously isn't free, and the gold camel can't go anywhere without quickly being confronted by the silver elephant, which would be free to follow the camel north. The silver horses are not free, as they are defending the silver camel and each other. The western gold horse is not totally free, as it is stopping a potential Silver swarm of c3, which could give the silver elephant more freedom.

The eastern gold horse is currently the strongest free piece; Gold can soon create an away threat that will force captures somewhere. The gold camel should stay in place for now, but the f2 dog could advance and be replaced by a cat or rabbit. The silver elephant might then go north and make multiple captures, but Gold could more than make up for that by moving his camel west. Even if both silver horses escaped, Gold could capture the silver camel and minimize his own losses, as Silver would have lost time getting her horses to safety.

This example and the next show that an elephant not directly defending a hostage can still be restricted by it. An elephant rotation does not always free the elephant; it may just tie up more material in the hostage position.

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Each side currently has an elephant, camel, horse, and dog tied up in this hostage position.

After the gold elephant rotated out of hostage defense in this game, it still had to protect the pieces defending f6. Each time the silver camel returned north, the gold elephant went north also, so as to protect its northeastern army. If Silver now keeps her camel in place and moves the c2 horse east, that horse will be the strongest local piece and can work toward a goal threat. If the h5 rabbit advances, the h7 horse may advance behind it and join the southeastern attack. Silver would have done better not to have a horse blocked in to begin with, as that weakens a hostage-holder's position.

Of these four examples, the first camel hostage was quite weak, the second was not quite strong enough, the third was strong, and the fourth was somewhat unclear, though by 21s Silver appeared to have stronger goal prospects. If the defender can free his elephant in time to mitigate a second threat, he will likely have the advantage. The hostage-holder will usually have the advantage if he can create a strong second threat while the enemy elephant remains on defense. If both elephants and camels are tied up, the side with the most active horse may have the advantage.

Camel hostage value

A hostage-holder wants to create a second threat that will overload the opponent. The defender usually wants to free his elephant, preferably without giving up the hostaged piece. If the defender aims for an elephant rotation, the two sides will likely advance pieces on opposite wings. The outcome of such a race will depend on the initial positions of the pieces. For Gold, a camel hostage will tend to be worthwhile if two strong gold pieces are already on the non-hostage wing, and Silver is not well-developed on the hostage wing. Ideally, the free camel and a friendly horse will work together on the non-hostage wing, and the other friendly horse will guard against a potential elephant rotation on the hostage wing. There are other possibilities, but the free pieces are always key, and there is limited time to maneuver them. If the hostage-holder cannot soon create a second threat, the hostage may be weak.

If Silver is not well-positioned for an elephant rotation, she might abandon her camel and seek compensation elsewhere. While creating a second threat, a camel hostage-holder will likely expose a friendly horse to capture; the hostage value is thus related to the value of a horse-for-camel trade. A camel is estimated to be worth a horse and cat as an initial trade, so one might say that a solid camel hostage is worth a cat. This should be kept in mind if one has to choose whether to take a hostage or do something else.

If Silver is well-positioned for a quick elephant rotation, a hostage might be of negative value for Gold. The purpose of a camel hostage is to tie down the enemy elephant and camel, thus freeing one's own camel and/or horse to attack. If the enemy elephant quickly becomes free while one's own elephant remains effectively stuck, this has backfired badly.

If the hostage-holder does not have an advantage in free pieces, a hostage may be of negative value even if the defender is not poised for an elephant rotation. Being advanced and centralized, the defending elephant might eventually join an attack on the non-hostage wing. If such an attack threatens goal, the opponent might not have time to capture the camel.

Rotation strength

4 3 2 1 a b c d	This is typical of a successful elephant rotation; a team of silver pieces has freed the silver elephant and cornered the gold elephant. The a4 rabbit ensures that the silver dog could step right back to c4 were it pulled to b4. The c3 rabbit blockades the trap; if c3 were clear, the gold elephant could push the horse to e3, perhaps threatening it in f3 if the overall position allowed for that. The gold elephant could try to go around c3, but this would free the silver camel to attack the goal line, and Silver would likely have time to defend against any threat in f3. If a gold horse or camel is nearby, Gold might hope to reassert ownership of c3, but the silver elephant could likely thwart and perhaps punish such a move.
4 3 2 1 a b c d	Here a gold rabbit blockades the trap. Unable to step backward, the rabbit is stuck on c3 as long as b3, d3, and c4 are occupied. Silver could flip the rabbit out and threaten it in c6, but might prefer to keep the trap blocked and do something on the other wing. Silver does not yet have a strong goal threat on this wing, so Gold has some flexibility. Gold could push the camel to b1, burying the hostage and clearing b3 for a different piece. This is a possible advantage of holding a hostage on b2 rather than a3.
4 3 2 1 a b c d	If the silver elephant left, the gold horse might occupy c4 or d3, and any nearby silver piece would be at risk. To rotate out her elephant, Silver must either blockade both c4 and d3 or remove the gold horse from the area. Silver might consider flipping the gold horse away, but Gold could occupy d2 and e3 to prevent this.
4 3 2 1 a b c d	The trap is clear, but the gold elephant can't move through it, as the trap currently has no other gold defender. The silver elephant has left the quadrant, but may still be nearby; how free it is depends on the rest of the board. If Gold could displace the silver dog or horse, the silver elephant might have to return to the trap to prevent catastrophic losses. Once again, the a4 rabbit ensures that the silver dog could return to c4 if pulled to b4. The a2 and b2 gold rabbits are also key to Silver's position; if Gold could clear b2, the silver horse would not be safe on c2, from where it could be pulled to b2. That would give Gold a double hostage and also allow a gold defender to occupy c2. If the silver horse and dog are safe, this is a strong position for Silver. If either piece can be displaced, however, this could soon become a strong position for Gold, especially if the silver elephant is far away. If Gold could occupy d3, he might then clear b2 via Eb3e Rb2nn Ec3w, though in this case the camel could then push the a2 rabbit to b2, frustrating Gold's plans for a cleanup. To be safe, Silver might blockade b4.
5 4 3 2 1 a b c d	A hostage held by a c2 elephant alters the usual alignment, since c2 is typically held by a weak piece. With the gold elephant on c2, b3 may be vulnerable. Here the gold horse may not be able to stop an elephant rotation, as Silver could occupy b3 and b4 if the gold horse stepped east. A hostage held behind the trap may therefore be weak, especially if the opponent is well-developed on the wing. If d3 and d2 were unoccupied, the gold elephant could move to d3 and pull the silver camel to d2 as a central hostage. This is a possible advantage of holding a hostage behind a trap, but the opponent can usually block such a maneuver.

Other hostage patterns

Double hostage

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A double hostage is stronger than a simple camel hostage.

On 16g of this game, the gold elephant took a double hostage. With three strong silver pieces tied up, Silver's options are quite limited. Unless Gold is reckless, Silver cannot hope to abandon the hostages and remotely make up for a camel and horse loss. With Gold's large advantage in free pieces, elephant rotation would also be quite difficult for Silver. Neither hostage can escape; the g2 horse is frozen, and the silver camel is blocked by a phalanx.

A silver piece on g4 could weaken this double hostage; if the silver elephant then left, any capture the gold elephant could make would land it on a square other than g3, so the second hostage could escape or be defended again after an exchange. Realizing that Silver could complicate things by stepping the g5 cat south, Gold should take care not to expose his camel to quick capture, as he might only get an even camel trade which would free and strengthen the southeastern silver horse. Silver might then have a formidable goal threat.

High hostage

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Gold has an unstable but valuable high hostage. (Game)

A high hostage is held on the fourth or fifth rank, allowing the hostage-holding elephant to remain centralized. This pattern is tricky to maintain, as multiple squares must be blocked to keep the hostage in place. The silver camel is a high hostage here; a gold horse and a phalanx of rabbits keep the camel frozen, but b4 is not secure in the long term. If Silver eventually unfreezes his camel from the side, the gold horse could then be lost in c6, so this might become a risky hostage position for Gold. It may be easier to hold a high hostage on a depleted board, as Silver did in this endgame.

Central hostage

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A central hostage may face capture threats in two different traps.

A central hostage is held on the d- or e-file. If the hostage-holder has good control of both home traps, a central hostage might turn into a fork: Silver can play ed6s Md7s cc8s df6e, and Gold cannot defend both c6 and f6. This hostage position is more tactical than strategic; Silver gave up a horse to trap the gold camel. If a capture cannot soon be forced, a central hostage may be worth little more than an ordinary hostage.

Other Hostages

Horse-by-elephant hostages

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As long as her elephant remains in the northeast, Silver can do little other than pull a gold rabbit on the a-file.

As with a camel hostage, a horse or smaller piece hostage will be effective only if it gives the hostage-holder a usable advantage in free pieces. This is usually not the case when an elephant holds a horse hostage, as occurred in this opening. Silver's alignment is poor; the gold elephant is a far greater threat to the silver camel than is the silver elephant to the gold camel. Gold would gladly trade his horse for the silver camel, which if it came east would be at risk in both c3 and f3. If a silver horse advanced first, it could be threatened by the gold camel. If the silver elephant simply left the f6 trap, Gold would have a strong attack which might decimate Silver's eastern forces.

For now, the gold elephant is better placed on e6 than on f5. If e6 and e7 were clear, the silver elephant could pull the gold horse onto e7 and then perhaps fork it between traps. That is a possible advantage of positioning a hostage-holder behind the trap.

In some cases, a horse-by-elephant hostage might be converted to a frame or passed off to the camel. If Silver were better positioned for that, it would be urgent for Gold to prevent a solid frame or horse-by-camel hostage, which could free the silver elephant while the gold elephant remained stuck defending the horse.

Gold should be prepared to go after an aggressive silver piece or clean up in the east, but if Silver plays gingerly, Gold might swarm the f6 trap and rotate out his elephant.

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Gold cannot save both horses.

While a horse-by-elephant hostage is usually a bad long-term strategy, it may be an effective tactic if the hostage-holder can make a quick second threat. In this opening, Silver threatened both gold horses, and Gold did not have time to defend both traps.

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Dogs will likely decide this game.

A horse-by-elephant hostage may be effective on a depleted board. In this endgame, such a hostage tied up the three strongest remaining pieces. Up two-to-one in dogs, Silver can dominate the rest of the board. If a second gold horse or dog remained, this hostage would likely be weak.

Horse-by-camel hostages

The camel is usually the piece that should fight an enemy horse long term. This may lead to a horse-by-camel hostage, which could be very strong or very weak. The "defending" elephant can usually dislodge a hostage-holding camel, at least temporarily; what happens next depends on what other pieces are nearby. If the hostage can be held without the direct support of the friendly elephant, the hostage-holder may have a large elephant mobility advantage.

5 4 3 2 1 a b c d e

These diagrams illustrate different horse-by-camel hostage configurations, with Gold holding such a hostage in the southwest. A gold piece is always on a4, to keep the gold camel mobile if it is pulled to b4. In the first diagram, the b2 cat allows for capture of the hostage if the silver elephant goes to b4. Gold should leave d3 clear, so that the camel could finish that capture on d3 rather than c4, where it would then be at risk in c6. The b2 cat and empty d3 square indirectly protect Gold on the b-file; if the silver elephant could afford to step west and begin the next turn on b4, things could quickly turn around. As things stand, this may be a solid hostage position for Gold, whose own elephant is the strongest free piece for the time being.

Without a gold piece securely on a4, the hostage would be weak. With ec4we Mb3n ha3e, Silver could have her elephant on c4 and her horse on b3; if the gold camel were frozen on b4, Silver would have strong capture threats in c3, and could also flip the gold camel to c5 with a threat to capture it in c6. The a4 square is thus crucial to such a hostage position, and Gold does well to have a horse on that square, as a weaker piece could be pulled away more easily.

5 4 3 2 1 a b c d e

In the second diagram, the hostage horse is on b2 rather than a3; this has implications if the camel is dislodged. For instance, if the silver elephant moved to b4, it would then threaten to capture the camel due to false protection. On the other hand, a hostage on b2 could be pushed to b1 if the camel needed to back away from the elephant. The camel might then move the hostage to c1, or back to b2 when feasible.

5 4 3 2 1 a b c d e

In the third diagram, the hostage is held behind the trap. On c2, the gold camel is less exposed and thus perhaps easier to support. A camel-held hostage behind the trap can thus be strong, if the area is reasonably well-fortified and the opposing army is not well-developed on the wing.

In all of these cases, the defender should consider bringing in more pieces if possible. In the last example, Silver could own the trap if she could take b3 in addition to d3. In the first, the silver camel might displace Gold's linchpin horse.

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Gold has no good way to break this hostage.

When a camel holds a hostage behind a trap, the defender might be no better off if he pushes the camel away. In this game, Gold's 13g left him even more vulnerable in the west, where Silver then advanced a horse and dog. When the gold elephant left f7, the silver camel retook the hostage. When an elephant goes to a corner to try to free a hostage, there is also a risk that both pieces will get blockaded.

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Silver's horse-by-camel hostage allows silver dogs to control an away trap.

By tying up the gold elephant and horse while other strong pieces were tied up in the west, Silver's horse-by-camel hostage at right enabled silver dogs to control f3. This led to a 29-turn win.

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Gold holds a camel hostage in the east, and a double hostage in the center.

In this game, Gold's central horse-by-camel hostage allowed him to defend goal in the west, as no additional silver piece could reach the southwestern corner. This would be a strong position for Silver if he could displace the gold camel, but Gold to move can blockade c3 and perhaps move toward a northwestern goal threat. With the southern forces tying each other down, the western gold horse is the strongest free piece; the silver elephant must stay beside c3, and cannot freeze the gold horse in place. One way or another, this horse can soon accomplish something.

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Blocked by his own rabbits, Gold cannot easily displace the silver camel or horse.

After 15s of this game, Silver in effect had a strong horse-by-camel hostage, despite the proximity to the gold elephant and camel. Advanced gold rabbits shielded the silver camel and horse. Silver kept e7 and f7 occupied, so that the gold rabbit could not get off of f6 and threaten goal.

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Silver's development allows the silver camel to hold a hostage from a5.

After 17s of this game, the hostage-holding camel was itself on a5, and supported by silver pieces which had advanced further. Gold could unfreeze and move his horse, but couldn't really threaten the silver camel. Gold might advance more pieces toward c6, but that could further weaken his own home defense.

Cat and dog hostages

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Silver does not have an ideal alignment, but may eventually overload Gold.

A smaller piece may also make a valuable hostage, if its elephant is the only piece which can defend it. In this game, the silver camel held a gold dog hostage behind c6. The silver elephant is free to pull gold pieces toward f6. The gold elephant can't defend both traps.

However, Silver's situation is less than ideal, for a few reasons. The silver camel does not currently threaten either gold horse. Even if the gold elephant leaves the c6 trap, Silver will have to clear space for the dog capture. Gold is well-developed in the east, and might create a double-threat on that wing. A dog-by-camel hostage is not ideal, but may still give the hostage-holder an elephant mobility advantage.

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Gold's dog-by-horse hostage allowed the gold camel to safely advance to g6.

In this game, Gold's early dog-by-horse hostage allowed for an elephant-camel attack on f6. An early camel advance would often result in a camel hostage, but the southeastern hostage gave Gold time to advance his camel and support it with rabbits.

Frames

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The gold elephant is pinned to the horse framed on c6.

A piece held on a trap square, securely surrounded on three sides, has been framed. In this game, Silver framed a gold horse on c6; a phalanx stops the framed horse from pushing onto c7. The gold elephant is pinned: if it takes one step, the framed horse will disappear.

A pinned piece is more stuck than a hostage defender, which can at least move between key squares or otherwise step away during a turn. Here, it would be pointless for the pinned gold elephant to break the phalanx; even flipping the d7 rabbit would instantly lose the framed horse. If a pinned piece abandons a framed piece, the framer won't even use up a turn making the capture, since the piece is already gone. This strength of frames is balanced by the high material cost of maintaining them.

When possible, a framer should rotate out strong pieces, replacing them with the weakest ones which can reliably hold the frame. If the a5 horse moves to c5, the silver elephant will be the strongest free piece, although it may not be totally free if Silver wants to avoid an even horse trade.

Even if elephant rotation is not feasible, a framer will often have a mobility advantage. Gold would instantly lose the framed horse if he moved his elephant, whereas Silver could move his elephant at no cost other than giving up the frame. It would thus be risky for the gold camel to advance, whereas the silver camel is already in Gold's home territory.

A frame is broken when a framing piece is dislodged. A frame might be broken from the side or from behind, but here Silver can likely prevent either maneuver. With the gold elephant pinned, the gold camel is the only piece that could dislodge a silver horse, but Silver could likely stop such an intrusion in the west. Gold might instead aim to break the c7 phalanx; with the gold elephant immobile, this would require a gold piece to advance and begin a turn active on e7 or d8. If this piece could pull away a rabbit, the c6 horse could then push its way out. Silver can strengthen the phalanx by sliding the d7, c7, b7, and a7 pieces east.

A frame's value depends on each side's free pieces. This frame should be very strong once the silver elephant rotates out. By contrast, a breakable frame may backfire on the framer, since the formerly framed piece could become an attacker. On a depleted board, a horse frame may not be worth the material it uses, as the framer could become thin on the other wing. A dog or cat frame could be wasteful at any juncture; a framer must always weigh the cost of keeping material tied up in the frame.

Elephant position

When a frame is already in place, it is too late for the pinned piece to choose its square. In general, however, d6 is a strong square for an advanced gold elephant, and this often holds true when that elephant is pinned:

• With the pinned gold elephant on d6, the frame requires a silver piece on c5 (except in the case of rabbit frames). If the silver elephant goes east, the c5 piece may be vulnerable to capture in c3.
• The pinned gold elephant on d6 stops Silver from moving the framed piece onto d6 or e6 for a fork.
• For the gold elephant, d6 is a better attacking square than c5. If the frame can be broken, Gold may then have a strong attack on the c6 trap.

If the framed piece is not at imminent risk of capture in f6, however, c5 is an acceptable square for the pinned gold elephant. In fact, this may make it easier for a gold piece to break the frame along the b-file.

Camel frames

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Gold combines a camel frame with a horse hostage. (Game)

When an elephant is pinned to a camel framed by the enemy camel and elephant, the four strongest pieces are all tied up. If the framer cannot rotate out his elephant or camel, the horses may decide the game. Due to elephant mobility, the framer's horses might be freer than their enemy counterparts, but the framed side might counter this by partially blockading the framing elephant and/or setting up a strong attack should it leave.

If the framing elephant or camel can be replaced by a phalanx of weaker pieces, the framer will have the strongest free piece while still rendering the two strongest enemy pieces completely immobile. The diagram shows another strong type of camel frame, in which a horse is held hostage by the framing camel. There is no single strongest free piece, but Gold has two free horses against Silver's one. Gold's progress may be slow, but Silver has little counterplay, having so much to lose if she abandons f3. A hybrid frame-hostage can be very strong, if balance is maintained.

Away frames

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An away horse frame.

In the course of a trap attack, it is sometimes possible to frame an enemy piece in its own home trap. On 13g of this game, Gold used a pull-and-replace to frame a silver horse in f6. If the pinned silver elephant were to move, the horse would be lost instantly, and more silver pieces could quickly follow.

The one potential threat to the frame is the silver camel. If the silver camel went east, however, the gold camel could dominate the west. Gold might get a strong attack on c6 before Silver could break the f6 frame and free his elephant.

Gold should not attempt to directly rotate anything out of this frame; a phalanx would not be viable, and replacing the gold elephant with the camel might allow Silver to get a horse-for-camel trade if the gold elephant didn't stand guard. However, Gold can advance more pieces in the east and perhaps eventually give up the frame but keep shared control of f6 even with his elephant elsewhere.

Non-elephant pins

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The silver camel is pinned to the c3 cat, and both pieces will be at risk if the gold elephant can step to d4.

A dog or cat frame which ties up the framer's elephant is usually not worthwhile. In this game, however, Gold's cat frame was strong, pinning down both the silver elephant and camel. With the silver camel pinned to the c3 cat, the silver elephant must stay on d4 to defend both the cat and camel. This leaves the gold camel as the strongest free piece; if this will remain so, the silver camel should abandon the cat.

However, Silver might hope to replace the elephant with a phalanx; this might also require a piece on c5 or b4 to prevent a flip. A d4 phalanx would divide up the board; the gold elephant might be forced to give up the frame and make its way east, but then the position would be unclear. If the silver camel were instead pinned on b3 while protected by a b4 phalanx and a piece on c5 or d4, Silver's shared trap control could be fairly solid. See, for instance, the blockade on 29s of this game.

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Gold to move can frame and then capture the e3 horse.

On 28g of this game, Gold played a pull-and-replace to create a frame which then forced a horse capture, as Silver could not keep the pinned dog in place or add a defender.

Elephant frame

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If the gold camel can dislodge the pinned silver horse while the silver elephant is still on f3, the elephant will be captured.

An elephant frame is occasionally possible, if an elephant has chosen to occupy a trap square. If the pinned piece can be dislodged, the framed elephant will be captured. On 12s of this game, Silver did not see the risk to his elephant. It is not always bad to place one's elephant on a trap square, but extreme caution is needed; an elephant should never be left in a trap that is not adequately defended.

Horse baskets

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The gold horse cannot escape, and might soon be framed.

In this position, the gold horse is in a basket: it is blocked on three sides, so that no escape is possible even if it is unfrozen from the fourth side. Silver to move could flip the gold horse into the trap, creating a frame which the silver elephant might soon rotate out of. Gold to move might possibly prevent a frame via congestion, if he can occupy both f4 and e5 while still defending the trap. Alternatively, Gold could delay the frame by flipping the e7 dog, although this might lose time if Silver plays correctly. With e7 empty, Silver should not flip the gold horse into the defended trap, as the horse could then push onto f7, where it would be well placed. Instead, Silver might pull the gold horse to f5 and move the h5 horse to g5, fencing the gold horse next to the trap. On Silver's next turn, the gold horse could be pushed into the trap in two steps, leaving another two steps to reestablish the phalanx.

Since rabbits can't retreat, a silver rabbit on the wrong square could end up blocking the intended frame. A silver rabbit on e7 could be flipped into the trap. A rabbit on f7 would make a fence less effective; with the gold horse on f5, the gold elephant could pull an f7 rabbit into the trap.

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Gold to move can prevent a frame.

To force a frame, a basket-holding elephant must usually be next to a trap. With f5 open, the gold elephant could take two steps and prevent a horse frame. The silver elephant might then have to move west to avoid a blockade.

Frame-breaking tactics

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A breakable frame may end badly for the framer. With Silver to move in the diagram at left, the silver horse can reach b3 via the pull-and-replace mb5sn Hb3n hc3w. Gold could restore the frame with a pull-and-replace of his own, but this would recreate a position which Gold has already created once. Silver could then repeat her previous move and force Gold to do something different. With the frame broken, Silver will have a good position: the formerly framed horse will be a strong attacker, and the camel might pull the gold horse to c6.

Gold to move could delay the frame-break with Ec4ns mb5e. If there is a silver piece on d5 or c6, however, the camel could return to b5 in a single step, thus undoing in one step what Gold did in three. Instead of wasting steps and letting Silver strengthen her position, Gold to move might flip the silver horse to b4; the horse might escape, but at least it wouldn't take b3. The advanced silver rabbits might then be vulnerable.

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The second diagram shows a similar position, but with the silver camel on b4 rather than b5. Now, the frame can be broken in three steps (mb4n Hb3n hc3w), but there is a complication: Gold could restore the frame with a pull-and-replace (Ec4sn hb3e Hb4s), and this time Gold would create a new position, since the silver camel would not be where it was after Gold's last turn. For this same reason, Silver would then need four steps for her own pull-and-replace, and thus would create the exact position she created the first time she broke the frame: the silver camel on b5, the gold horse on b4, the silver horse on b3, and nothing else different since she had no extra step. Gold could thus restore the frame and win the repetition fight, unless Silver found a different way to break this frame:

• mb4n Hb3n hc3w Cc2n pulls the gold cat into the trap to prevent Gold's pull-and-replace. This is the simplest, and thus most common, maneuver to break such a frame.
• mb4n Hb3n hc3w ed3w: The silver elephant occupies the c3 trap, and the silver horse cannot be dislodged from b3. An elephant occupying a trap must be very careful not to get captured.
• mb4n Hb3n ra3e ra4s: Silver rabbits block the gold horse out of b3.
• mb4n Hb3n mb5e Hb4n: By moving her camel to c5 and pulling the gold horse to b5, Silver establishes a phalanx which stops the gold elephant from stepping forward and unfreezing its horse. Gold could unfreeze the horse from below, but then the horse couldn't return to b3.

If a camel flip were possible, it would at least buy Gold some time. The d4 cat prevents a camel flip; a silver piece on c5 would do the same job.

In both diagrams, Silver's a4 rabbit keeps the camel unfrozen on b4. If instead a gold piece were on a4, the frame would be stronger.

Another way to break a frame is to take an additional key square while the framed piece is still in the trap. If a3 or b2 were empty, the silver camel could itself occupy b3, pushing the gold horse away. The camel might then be taken hostage, but the formerly pinned elephant might quickly rotate out of hostage defense.

Trap Control

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Silver's long-term threat to c3 is strong.

Trap control is related to ownership. A trap might be fully controlled by one side, or might be shared. At the outset, each player essentially has full control of his two home traps. Trap control depends on the key squares, especially the decentralized ones (e.g. b6 and c7 in the northwest, b3 and c2 in the southwest). Getting a non-elephant safely onto a decentralized key square of an away trap is usually an important step toward wresting control of that trap. Even if one doesn't take full control of an away trap, strong shared control can impact the rest of the board.

On 5s of this game, a horse procured a long-term trap control advantage for Silver. With a silver horse already behind the c3 trap, Silver would likely win an EMH attack race, so Gold needs to defend that trap. It is not clear whether Gold has any good way to do so, however. If the gold camel comes west to defend, Silver can still attack that trap and threaten the camel and other pieces with quick capture. If the gold elephant defends, Gold will have a poor alignment, as his elephant will be fighting a horse; furthermore, Silver could still advance more pieces in the west and perhaps rotate his own elephant out of that fight.

Deadlocked Traps

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There is an elephant deadlock at f6 and a camel deadlock at c3. (Game)

A trap is deadlocked when its strongest gold defender and strongest silver defender are equal. In the event of an elephant deadlock, no capture can happen in the deadlocked trap until an elephant chooses to leave. If both elephants stay beside the same trap, it is usually because both sides have a large stake there. Remember that a hostage position can tie down both sides, as a hostage might become an attacker if the hostage-holder simply leaves. Here, the silver elephant is not holding a hostage, but is defending against an attack which more gold pieces might soon join.

A camel deadlock will hold only so long as neither elephant can be bothered to break it. Despite Silver's material advantage, she has more to lose than does Gold, as a threat to the silver camel would by extension threaten the horse which it defends. Gold's attack on f6 is well ahead of any possible trap attack by Silver, who would need to get the gold camel off of b3 in order to make any capture in c3. Gold can now move his horse to f7, setting up a potential attack on c6 or swarm of f6, either of which could allow the gold elephant to go west and create a strong second threat. Even though there are currently multiple deadlocks, this game is likely to move quickly.

Since no capture is possible in a trap defended by both elephants, the player whose home trap is deadlocked is often at a space disadvantage. Enemy pieces can safely advance toward such a deadlock, whereas the home elephant would have to leave if it wanted to ensure safe advances of its own pieces. One unprepared to make a strong threat elsewhere on the board should avoid getting into a home elephant deadlock, as the opponent can work such a deadlock to his advantage if he has time. Here, Silver could have kept a horse in the east and defended f6 without her elephant.

Stronger vs. weaker pieces

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At each trap, the strongest local piece faces multiple weaker pieces which protect each other.

Shared trap control also occurs when one side has the strongest local piece, but the other has multiple weaker pieces which protect one another from capture. After 23s of this game, all four traps were contested in such a manner. A capture can happen only when one side gains full control of a trap. When a strong piece moves from one fight to another, the area it leaves could be affected; here, Gold would face at least a horse loss in f6 if he moved his elephant away from that trap. A position with multiple trap control fights may become a race if each side prioritizes offense.

Losing control

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As long as Gold owns no trap, Silver has nothing to fear. (Game)

Silver currently defends all four traps, and will face no capture threat until Gold can change that. The gold elephant can't take a strong hostage, and can't afford to leave c3. Even if one can take a seemingly strong hostage, it won't ultimately be effective without a second threat. To have any chance here, Gold must advance his camel and reassert full control of f3; if that draws the silver elephant east, Gold can then own c3 instead of f3. Once Gold owns a home trap, he might then attack the away trap on that wing. It is crucial to own at least one trap, so that the opponent is somewhat limited by capture threats.

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To gain ownership of a trap, Silver must attack one of Gold's home traps.

After 15g of this game, Gold had strong shared control of f6 even without his elephant directly beside it. Consequently, Silver owned no trap and was close to being overloaded. Silver's only chance is to attack c3 or f3, perhaps advancing her eastern horse, which is of no use around f6. The silver elephant should defend f6 for now, but might eventually join an attack. Even if the gold elephant leaves c6, Silver may not have time to pull pieces toward it.

Distribution of Force

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Right next to the silver camel and far away from both silver dogs, the gold horses are poorly positioned. (Game)

To create effective threats, one must use pieces efficiently; strength should not be wasted. A related concern is activity: strong pieces should be kept flexible and available for duty. The b2 gold horse is passive due to being blocked in. The a3 gold horse is less blocked, but still poorly placed; Gold's position would be stronger if he had a horse in the east to fight the silver dogs. Conversely, Silver is being highly efficient by placing a dog on g3, where it is currently as safe as a silver horse would be.

Pieces are often passive because they are blocked in at home, but even a functional advanced piece is passive if it is not doing anything useful. In a race, a piece is passive if it doesn't have time to do something.

Having the strongest local piece can be an asset. If the silver camel is next to a trap, no silver piece can be captured therein unless the gold elephant joins the fight. The strongest local piece can also help with goal attack, goal defense, mobility fights, etc.

Alignment

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With Gold's forces restricted, the silver dogs are strong attackers. (Game)

Alignment refers to the overall positioning of one army relative to the other, especially in regards to which piece faces which. A strong alignment will not, for example, waste an elephant on an enemy horse while the enemy camel is active elsewhere. Here, Silver's alignment is near-perfect: the silver elephant fights the gold camel, the silver camel fights both gold horses, and other silver pieces take advantage of the freedom this provides. The silver camel and c2 horse are both strongest local pieces, whereas Gold does not have a uniquely strong piece in any area.

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The silver elephant and camel ignored the gold horse.

Alignment may seem unimportant when a forced goal is in sight. However, a poor alignment could allow the opponent to get a quick goal attack of his own. In this endgame, Silver's apparently strong goal attack left the one remaining gold horse unopposed in the east. After 38g, Silver suddenly faced a goal threat which could only be stopped via an elephant sacrifice.

Balance

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Silver needs a dog in the west.

If too much strength is concentrated on one wing, the other may become vulnerable. A dog can be a strong attacker if there is no active enemy horse nearby, and stronger still if there is not even an enemy dog to counter it. Note that Gold currently has the uniquely strongest non-elephant piece in both the west and the east. The e7 dog can move west, however, perhaps delaying a Gold takeover of c6 long enough for Silver to counterattack in the east. The silver elephant needed to face the gold horse, not the gold dog as it did in the actual game. There was not much point in having both silver dogs on the same wing as the gold horse; a second dog would not substantially strengthen an attack on f3, whereas a silver dog could have made a difference in the west.

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The silver elephant is stuck defending a horse and dog, but the gold elephant is stuck defending goal. (Game)

Weak pieces should usually be balanced also, as a goal threat might negate an advantage elsewhere. Gold's hybrid frame–hostage–partial elephant blockade may appear strong, but it leaves Gold very weak in the west. The gold elephant is currently stuck defending goal, so the silver camel is free to disrupt the blockade. Using one's elephant to defend against rabbits is extremely inefficient.

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With a horse flip, Gold can unbalance Silver's forces.

Even on a full board, one wing might become quite weak. On 12g of this game, a horse flip unbalanced Silver's forces, allowing the gold dogs to become strong eastern attackers. A trap defender should watch out for such a flip, and watch out for a pull-and-replace which might set the stage for such a flip.

Centralisation

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The gold camel cannot safely advance without the support of the gold elephant. (Game)

A centralized elephant affects all four traps. Here, the gold camel cannot defend f3 until the gold elephant comes east. If Gold played Me2n De1n Me3e De2n, Silver could push the gold camel to f4 (De3s ee4s Mf3n ee3e), where it would be doomed to capture in f6. This would not work for Silver if the gold elephant were in the center.

While attacking or defending a trap, an elephant should usually be on one of the more centralized key squares, e.g. c4 or d3 when next to c3. An exception might occur when there is a chance to threaten the enemy camel. However, an elephant should not automatically go after an enemy camel which is still in its own home territory.

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Gold pieces can move through the center. (Game)

Control of the center itself is also important, as pieces would often like to move through the center. The side with greater elephant mobility will tend to have better central control. In the diagram at left, Silver is limited by potential capture threats in c3 and f3. By contrast, Gold currently defends all four traps; the silver elephant's isolation allows the gold camel to defend c6, making the center safe for more Gold advances.

Even when neither elephant is marginalized, shared control of an away trap may improve one's central control; if the opponent owns only one trap, pieces in the center are safer. It is sometimes even possible to blockade the center.

Rabbit Advancement

An elephant, camel, horse, dog, and cat differ only in their power over and vulnerability to enemy pieces. Rabbits, however, are unique in two ways: a rabbit can score a goal, and it can't step backward. A defensive player may be loathe to advance any rabbit unless it can quickly reach goal, but keeping half of one's army in the back rows may be untenable.

Disadvantages

Exposed to capture

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Silver's advanced rabbits are no threat to goal, and the silver elephant can't defend them all. (Game)

Unable to retreat homeward, advanced rabbits are often vulnerable to capture in away traps. Going fishing for rabbits would be slow, but when rabbits advance on their own, they have done part of the job for the opponent.

Silver's three advanced rabbits are doing nothing useful, and can't all be saved. As long as the silver elephant defends in the west, Gold can create new threats in the east. Whatever Silver now does, Gold may soon gain a large material advantage.

Rabbit advances should be part of a larger plan. Rabbits might participate in a swarm, or might advance on the a-file to give friendly pieces greater mobility on the b-file. The problem here is that the silver elephant is only protecting rabbits, and there is little prospect for an attack on c3.

Weaken goal defense

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With no rabbits on her back row, Silver can't block Gold's western goal.

Rabbit advances also affect the area they leave behind. If one's home rank is left sparse, an enemy rabbit may have an easy path to goal. In this game, Silver had no way to block the western goal line, because there was nothing to unfreeze the c8 dog. No matter what Silver does here, Gold can play Hc7wn ra7e Ra6n, forcing goal on the next turn.

By contrast, Gold has four rabbits still on his home rank. The three advanced gold rabbits threaten goal right, left, and center, yet the four gold rabbits at home ensure that Silver would have to fight through more than one line of defense to score a goal.

Impede friendly pieces

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Unable to step south, the e5 gold rabbit blocks the gold elephant from moving west.

An enemy rabbit can be pushed in any cardinal direction that there is an empty square, but there is no way to move one's own rabbit backward. Advanced rabbits may thus end up blocking their own friendly pieces.

After 18s of this game, the gold elephant was cut off from the west, where the silver camel was thus a strong threat. If Silver keeps her own elephant and g6 horse in place, and also keeps the e5 gold rabbit blocked from the north and west, the gold elephant will have to maneuver through the southeast in order to go west. This will give Silver time to drag a gold piece to c6. Furthermore, the e5 rabbit will itself be at risk when the gold elephant leaves, although capturing it should not be Silver's first priority.

Multiple misplaced rabbits could prove even more disastrous, perhaps allowing for a complete blockade of the friendly elephant. Misplaced rabbits may also block a friendly attack or capture.

Advantages

Measured rabbit advances, however, can be quite effective even when there is no forced goal in sight. Since rabbits constitute half of one's army, various jobs could fall to them. Rabbits might advance to block enemy pieces, unfreeze friendly pieces, help control a trap, or threaten goal. A strong rabbit advance may end up doing all four.

Tactical goal threat

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Silver's superior army is limited by Gold's goal threats.

Once substantial material has been traded or become tied up in local fights, holes start to appear in each side's defenses. A formidable goal threat may occur at any stage of the game, but goal threats eventually become the central focus. In this endgame, Gold was way behind in material, but the a7 and h7 gold rabbits generated significant winning chances. Gold to move could threaten goal on either wing: Ed7e rf7n Ee7e would force Silver to use her entire turn on goal defense, leaving the silver camel or g7 rabbit to be captured in f6. If Gold wants to first threaten goal in the west, cc7s Ed7w hb7s Ec7w would likewise force Silver to use all four steps to ensure that the a8 rabbit could not be pulled away in time for the a7 rabbit to reach goal. Either way, the situation would remain precarious for Silver; with the latter move, Gold can force a goal in five turns.

If Gold presses the goal threats, the silver elephant won't have much time to move. Other silver pieces have also lost power; Gold's western goal threat effectively ties up both silver horses, and the silver camel could be captured or forced to the goal line if Gold pursues the eastern goal. Goal threats often outweigh a raw material lead, and may result in tangible gain even if the goal is stopped.

Strategic goal threat

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The a7 gold rabbit will force Silver to keep the northwest fortified.

An advanced rabbit can restrict the opponent's development, especially if the rabbit presents a strong potential goal threat. In this game, Silver had to carefully guard the western goal line against a gold rabbit on a7. Gold eventually lost shared control of the c6 trap, as the gold horse and dog were captured in a material exchange, but Silver never had time to capture the rabbit. With material depleted, blocking this western goal was costly for Silver, especially when Gold made another goal threat in the east.

Trap control

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Besides threatening goal, the silver rabbit on b3 currently gives Silver control of c3. (Game)

As forces thin, rabbits become more consequential. Despite Silver's material and alignment weaknesses, her dog-rabbit attack on c3 threatens a two-turn goal. Had a gold rabbit been on b3, any silver attack on c3 would have been slower and riskier.

Elephant Blockade

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Guarded by a horse and camel, this elephant blockade allows the gold elephant to dominate the board.

An elephant mobility advantage is most often procured by threats which keep the enemy elephant on defense. Sometimes, however, an elephant can be physically blocked. If an elephant is surrounded and can't simply push its way out, that elephant is blockaded.

The corners can be dangerous places for elephants. Gold might willingly expose a small piece to capture in c3 if such a capture would require the silver elephant to end the turn on c2. Early on, players discovered that some bots could be lured into a blockade this way. Once the elephant found itself surrounded, it would look for a quick escape, and thus could be tempted further by an empty c1; the blockade could then become stronger, as it is easier to smother a piece against the edge.

In this game, Silver took the bait and was strategically lost by the ninth turn. Due to the b1, d1, and c2 phalanxes, the silver elephant has no move at all. With the only functional elephant, Gold is in firm control. Silver could try to free her elephant, but Gold could ward off or capture any silver piece which approached the blockade. To keep it intact, Gold must continue to occupy c3, and thus should restrict most home captures to f3.

Rotation

Most elephant blockades are not as lopsided as the one above, which was only possible because the bot thought nothing of where it placed its elephant. An elephant even one square away from the edge will at least have a potentially quicker escape path.

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The gold elephant is blockaded, but at the cost of much silver material.

Having his elephant stuck on g7 would be no problem for Gold if Silver kept this exact blockade in place. Until Silver moves a blockading piece, the strongest free piece is the gold camel.

Silver can, however, rotate pieces out of the blockade. If Silver now slides his camel and three rabbits with mh6s rh7s rh8s rg8e, those rabbits will block the gold elephant from h7, and the camel can move west. Although g8 is left empty, it is not an escape path; the gold elephant must stay on g7 to avoid being completely smothered against the edge.

Silver should try to form a phalanx to replace her elephant, which could then dominate the board. Gold must race to free his elephant; a gold piece, maybe the camel, must reach some place where it can pull away a blockading piece, thus allowing the gold elephant to push its way to freedom. Silver could make such a rescue harder by playing a move such as ce7s ce8s rd8s. If a path does open for the gold elephant to move west or south, it must do so immediately. Even if the gold elephant escapes, the rescuing piece may be lost, but that is better than having one's own elephant stuck and the enemy elephant free. Gold must throw caution in the wind to break this blockade.

For the blockade to remain intact without the silver elephant, a silver phalanx must extend to g5, so the blockade would use more pieces and be more breakable than one which stuck the elephant against the edge. Still, a free silver elephant could easily neutralize the gold camel, and the silver camel could stop any other gold piece. In the actual game, the silver camel went to g5, rounding out this phalanx while continuing to protect the h-file.

Were the gold elephant on g6 and the silver elephant on g5, it would be a different story; a silver phalanx extending to g4 and f5 could be quite vulnerable, so elephant rotation might not be feasible for Silver. If rotation is not an option, the strength of a blockade depends on the free pieces. The opponent might attack on the other wing, or might try to break the blockade from the center; the blockader might then give up the blockade but capture a piece.

In any blockade position, a blunder by either side could be huge. Both sides must keep track of possible escape paths and even possible captures.

Cost

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This blockade is still highly dependent on the gold elephant, and Gold is vulnerable in the west.

As with a frame, an elephant blockade may require too much material when one's forces are already depleted. The silver elephant appeared hopelessly stuck in this game, but Gold had to move pieces west to defend goal.

Elephants in middle

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Silver to move can block the gold elephant in three directions, and limit its eastern movement. (Game)

With ee4nn rc6e, Silver to move can block the gold elephant from the south and west; d7 would be blocked by a phalanx, and e6 would be blocked by the silver elephant, which would also defend f6 so that Gold couldn't capture anything there. Surrounded on three sides, the gold elephant couldn't flip any piece. The gold elephant might hope to escape via the east, but Silver could stop that with solid tactics, beginning with a fourth step of rh8s, which would allow Silver to block the gold elephant on both the g- and h-files.

With no clear escape path, a surrounded elephant should probably stay as close to the center as possible; this blockade would not be strong unless the silver elephant could rotate out, which would be much more likely if the gold elephant went east and thus marginalized itself further. Gold might instead create a western threat to force the silver elephant to abandon the blockade.

Friendly rabbit blockade

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All seven gold rabbits are stuck in place, neutralizing the entire gold army.

Unable to step backward, a rabbit blocked in the other three directions cannot be moved by its owner. When advanced rabbits of the same color are side-by-side, they might all get stuck in place, forming a wall which could severely limit the movement of other friendly pieces.

After move 48s of this game, well-placed silver pieces combined with five advanced gold rabbits to blockade the gold elephant, camel, and dog. In the east, four more gold pieces couldn't move at all. The gold horses were stuck in the south. For the next eight turns, Silver's elephant and eastern horse did all the work, pushing Gold toward complete immobilization. To avoid this, Gold sacrificed his elephant.

Such a blockade could be risky on a depleted board. In this game, the stuck silver rabbits threatened goal, and Gold walked a tight rope to keep them blocked while also defending in the east.

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The g4 and h4 gold rabbits block the gold camel and horse, which in turn block the gold elephant.

Blockading the gold elephant on g6 would often require the silver elephant to remain on g5, since a silver phalanx extending to g4 and f5 could be highly vulnerable. In this game, however, such a phalanx was formed mostly by stuck gold pieces. Gold might have hoped to get a piece onto e6 or f7 and then move his elephant through the trap, but Silver can now easily prevent that. Two advanced gold rabbits have allowed Silver to completely immobilize three strong gold pieces.

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An advanced gold rabbit blocks its elephant and dog.

With a gold rabbit on a5 and the silver elephant on b5 in this game, the gold elephant was stuck in the northwest. If Silver can get an additional gold rabbit onto b5, the silver elephant could rotate out and dominate the board.

Partial blockades

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The gold camel can capture a piece in f3 before the silver elephant can get free. (Game)

Even if an elephant can't be fully smothered, it might be marginalized for several turns. With Silver's elephant boxed in, his horse-by-camel hostage is useless; the strongest free piece is the gold camel. The silver elephant could eventually escape, perhaps through the c6 trap, but the gold camel could make a capture in the meantime.

The Center

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The gold elephant is cut off from the center. (Game)

A semi-centralized elephant can sometimes be blockaded by a phalanx on a central square. Such a phalanx will occupy three of the four central squares; a strong piece on the fourth central square might protect and reinforce the phalanx. Silver's central blockade is strong, not only because of his camel but also because of his advanced elephant and horse. Even if Gold got his elephant onto d5 via Hc4w rd4w cd5s Ec5e, Silver could then capture the c3 rabbit by dislodging the c2 cat; Silver would then have a strong trap attack and goal threat.

This strategy requires great caution; if a central dividing wall does not hold, the pieces likely can't all retreat. This blockade worked because of the attack on c3, which the silver elephant soon rotated out of.

Swarm

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The gold elephant has been blockaded in its own home territory.

Even in its own home territory, an elephant is not always safe from a blockade; a swarm can sometimes blockade an elephant next to its home trap. In this 2005 Arimaa Challenge game, Silver exploited the bot's susceptibility to elephant blockades.

The frozen gold cat has become part of the blockade holding in the gold elephant. Gold might try to change that with ha3s Eb3w rb4s Ca4e, but an elephant usually can't escape a blockade via the edge of the board; in this case, the c4 horse could then push the gold cat back to a4, immobilizing both the cat and elephant, as b3 would now be blocked by a silver phalanx.

As things stand, the gold elephant might eventually escape to the center via the second rank, but then Silver could make captures in c3, and the advanced silver rabbits would become strong goal threats. Silver's swarm has put the gold elephant in an impossible situation; a home hostage-holder must be wary of such a swarm.

Relative Value of Pieces

A piece's value depends not just on its raw strength, but on its practical impact. The "weakest" pieces, rabbits, are the only ones which can score a goal; rabbits thus gain influence as goal paths open up. Other pieces gain influence when stronger enemy pieces are captured or marginalized.

Functional Strength

As the one piece that cannot be pushed or pulled, the elephant can roam the board freely, at least until it gets blockaded or needs to defend against a threat. An elephant mobility advantage can amount to a lot.

If the silver camel is captured, any remaining gold horse becomes stronger, as the silver elephant is now the only threat it faces. There is a similar effect on down the line; as threats are eliminated, weaker pieces can do more.

A strong goal threat is a valuable commodity; when one side has a path to goal, the opponent must stop that goal at any cost. One forced to prioritize goal defense could lose material simply because there isn't time to save it. Strong pieces might get tied up defending goal, or might not have time to move as other pieces defend goal.

"Even" Exchanges

In an even exchange, each side captures identical material within a few turns. This is not always a wash; such an exchange might actually undermine a strong position. Suppose Gold has lost a dog while Silver has lost her camel, with all other pieces remaining. Each side retains two horses, but Gold's are now functionally stronger, as there is no silver camel to threaten them. An "even" horse trade would leave Gold fewer pieces with which to threaten the two silver dogs and to support the gold camel.

If a friendly piece cannot be saved, getting compensation for it is the best that one can do. When one can save a piece or give it up for equal material, here are some considerations:

• A blockader or framer should normally try to avoid even exchanges, which could leave his forces thin elsewhere.
• A hostage-holder's advantage might also be undermined by an "even" trade; with fewer pieces, it might become more costly to have one's elephant in a home corner.
• By contrast, even exchanges may strengthen a goal threat, by clearing space and reducing threats to advanced rabbits.
• One who is well ahead in quantity of pieces will usually benefit from even trades, as a material loss tends to be harder on an already depleted army.
• An even piece-for-piece trade will strengthen weaker pieces, but may indirectly weaken stronger pieces.
  • A player up by a dog will usually benefit from an exchange of camels or horses, as this will reduce the threats to dogs. Cat-for-cat or rabbit-for-rabbit trades, by contrast, might undermine a dog advantage, which makes one's own cats and rabbits stronger than the opponent's.
  • A player with the only remaining camel shouldn't readily trade a horse, as a horse can be quite powerful against a camel-less opponent.
  • A player with the only remaining camel should be wary of "even" trades in general, unless he is well up in quantity of pieces.
• An even trade of strong pieces may favor one whose remaining forces are more balanced than the opponent's, as the opponent will then have a weak wing until he can move a strong piece across.

If none of the above clearly apply, one contemplating an exchange should consider simplicity versus complexity. Removing pieces from the board will leave fewer possible moves, perhaps making it harder to surprise or confuse the opponent. One who is behind can sometimes benefit by complicating the position, and might thus want to retain as many pieces as possible, if there is no clear upside to an exchange.

On 29g of this game, Gold defended c3 rather than exchanging camels, as Silver would have had a strong goal attack once the gold camel was gone.

Uneven Trades

When material is traded for non-identical material, the implications likewise depend on what has happened beforehand. Capturing a camel for a horse may not help a player who is well behind in quantity of pieces, as his dwindling army might be overloaded even by a camel-less opponent. Sometimes, one stronger piece is traded for two weaker pieces; such a two-for-one trade could favor either side, depending on the pieces and the position.

Since an elephant can't be pushed or pulled into a trap, an elephant is never traded for material. It is thus moot to consider an exchange value of an elephant relative to other pieces. On a full board, a cat is normally quite limited, so is worth only slightly more than a rabbit. The difference accelerates somewhat with each respective stronger piece. For a while, two-to-one balances might be figured thus:

• A Dog is worth approximately two Rabbits.
• A Horse is worth approximately a Dog and a Rabbit.
• A Camel is worth approximately a Horse and a Cat.

Such balances are never hard-and-fast, as every position is different. A piece may greatly rise in value when a just-stronger enemy piece is captured or marginalized; after a horse exchange, for example, each dog may be worth more than two rabbits, even though rabbits themselves have been slightly strengthened also. If an exchange would open the door for a strong goal threat, the material involved might not matter.

When forces become uneven, subsequent gameplay must account for the asymmetry. If one side has the only remaining camel but the other has more total pieces, any exchange which deprives the camel of a friendly horse might render the camel useless, as the enemy elephant might then neutralize the camel at little cost elsewhere. The implications of a trade depend on what pieces it strengthens. If one side has lost a horse and the other has lost multiple weaker pieces, a camel exchange may allow the side with two horses to overload the side that has more pieces.

Material vs. Position

Taking a hostage might sometimes require one to forgo a capture or leave a friendly piece hanging. A hostage is usually worth less than a dog, so it would usually be better to save or capture a dog than to take a hostage. Even a hostage taken at no material cost will not always improve the hostage-holder's position; there is a cost to keeping one's elephant in a home corner.

The value of a frame likewise depends on the free pieces. A strong horse frame is sometimes nearly as good as an outright horse capture; if the opponent refuses to cut his losses and abandon the framed horse, the advantage could become greater still. In this game, Silver gave up a cat and a rabbit to secure a horse frame which the silver elephant then rotated out of; this paid off for Silver. Any position that gives one the only free elephant is highly valuable.

Strong pieces are often sacrificed in the endgame, when the focus is on goal threats. In this game, Silver gave up his camel at home but soon got a rabbit to goal. In this game, Gold gave up his camel in the northeast but soon forced a goal in the northwest. One must assess the strength of a goal threat before making such a sacrifice. If defending goal would require a material sacrifice, there is no choice, unless one can reach goal first.

Overall Position

In a given Arimaa position, it is not always clear which side has the ultimate advantage. For estimates regarding specific material balances, see these material evaluators, of which HarLog is considered the most accurate. Raw material is not the whole story, however. Furthermore, any advantage depends on the player knowing how to capitalize; often, the real advantage is with the one who best understands the position at hand.

Advanced Tactics

Short- and long-term planning are both essential to Arimaa. A position might be greatly improved in one or two turns, if one can spot the correct move.

Double threat

A turn might create multiple immediate threats that can't all be stopped. Such moves can be hard to anticipate, but solid home defense will leave one less vulnerable to a surprise double-threat.

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Use this link to make moves on the board.

Problem: Silver to move and win material

Solution: Dd3w ee3w Hd4n ed3n (or ee3n Dd3e Hd4n ee4w, threatening the gold cat instead of the dog). Silver makes threats in both c3 and c6; Gold would need four steps just to save the now d5 horse, leaving the gold dog or cat to be captured in c3. With only two defenders, the c3 trap was vulnerable. This tactic would not have forced a capture had a gold rabbit been on b3.

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plan window

Problem: Silver to move and win material

Solution: Hb4n ec4w re7ss. Gold could prevent a capture only by moving his elephant to c5, but that would allow the now e5 rabbit to reach goal. A gold rabbit on e1 or e2 would have made a difference.

Counter-threat

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Gold faces a strong double-threat, and must create a counter-threat in order to avoid a large material deficit.

After 18s of this game, Gold faced two strong capture threats. Currently, the gold horse on g5 faces capture in f6. The gold elephant is blocked from e5, so the silver camel is currently safe. The g3 dog could unfreeze the horse, but then the horse could only travel north, at best reaching h6 where it could be immediately threatened again.

The gold elephant could, in two steps, occupy e6 and thus protect f6, but then the gold camel could be captured in c6. The gold camel is frozen, and would thus need three steps to retreat. Rb4n rc4sx Mc5s or rc4sx Cd4w Mc5w would work, but neither would leave the requisite two steps for the gold elephant to protect f6.

Since the horse capture would currently require four steps, de6e Ed6ew would delay a capture. This is a three-for-one, as Gold would use three steps which Silver could undo in a single step. For Gold, the question is whether any fourth step could offset the lost time. Gold might advance the g3 dog in hopes of burrowing his horse on the next turn, but the silver horse could push the dog back and block any further attempt to unfreeze the gold horse; a step would remain for the silver dog to return to e6, clearing f6 and reestablishing a one-turn threat which Gold would need two steps to defend against. Unless Gold can substantially change the position, Silver could force a capture by pushing the gold camel onto c6; the camel could push its way off, but could still be captured if Gold used the other two steps to defend f6. Gold appears to have no fourth step which would prevent a camel or horse capture within a few turns. A three-for-one will be effective only if the opponent cannot spare even the one step to undo the three steps.

Facing the forced capture of a strong piece, Gold must create a counter-threat. If Gold could threaten the b6 horse with one-turn capture, he might either get a horse exchange or buy time to defend on both wings. Rb4n Mc5n cc7w Mc6n may look promising for Gold, but would in fact open a goal path for Silver, who could then advance the c4 rabbit to b2. With the western goal line thinly defended, this would at least delay Gold long enough for Silver to come out ahead.

Gold spotted a different way to threaten the b6 horse: rc4sx Cd4w Mc5w Ed6n. The silver rabbit was captured, and the gold camel was out of immediate danger, allowing the gold elephant to step north. Gold's resulting false protection threat offered Silver a horse exchange that would leave Gold up by a rabbit. Silver could decline this exchange and reestablish a double-threat, advancing his dog from a7 to a5 so that the gold camel would need two steps to move again. With the silver elephant having stepped west, however, the gold elephant might soon reach e5, threatening the silver camel if it remained on f5. Whatever the ultimate outcome, this horse capture threat appears to be by far Gold's best option for 19g, as any other move would cost him a horse or camel for little in return.

Congestion defences

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Sometimes, occupying a particular square can stop the opponent from playing a particular move. A simple example is at right: Silver threatens to frame the gold horse with ef6s Hf7s cf8s re8e, but Gold to move can place his dog on f5 to block the pull. Since a pull can be blocked by any piece, this type of frame threat can usually be thwarted.

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After 23s of this game

Congestion is commonly used to block an undesirable flip. A flip is only possible if the flipping piece is adjacent to two empty squares, one for it to pass through and one for the piece to be flipped onto. Here, Gold cannot flip the silver dog, and thus Silver's defense of c3 is intact for now, provided the gold camel is not in a position to dislodge the silver horse.

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On 24s of this game, Silver established a one-turn goal threat which could not be blocked on the goal line. By stepping his horse east, however, Gold surrounded the silver horse, which could not then pull the g2 rabbit. Silver then moved his elephant to f1, leaving an "air bubble" on g1 which ensured a Silver goal. Had the elephant moved all the way to g1 on 25s, a gold dog could have occupied f1, once again blocking the pull needed for a goal.

Pinch

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In the first diagram (31s from this game), the silver camel is threatened. No other silver piece can defend the c3 trap, and other advanced silver pieces prevent a one-turn escape. However, Silver to move can defend with rb5e cb4n mb3n Ra3e, which sets up a formation known as a pinch. In the second diagram, note that all four key squares are occupied by gold pieces, and the gold elephant is surrounded on three sides, leaving no room for any capture. Gold can renew the threat by vacating a key square, but the silver camel and dog now have time to scatter.

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A pinch may give a trap attacker time to secure key squares. At right, Gold would like to attack c6, but would need four steps just to get his elephant to d6; the silver horse could then retreat to b6, blocking the gold horse. Gold would prefer to advance his horse immediately, but could then lose it in c6, unless the silver elephant could be pinched. Ed3nn Dc3n Hb4n would do the job, and would also give the gold camel a chance to threaten the silver horse in c3.

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A pinch defends against capture by blocking capture moves. Not all capture moves are equal; one can sometimes afford to lose a piece if the capturing piece would land on an inferior square. Silver would gladly trade her hostaged horse for a gold horse; ee3n De2n ee4nw can bring about an even horse trade. The dog pull is crucial, as it will force the gold camel to end its capture on g3 or f4. If the gold camel could instead finish on e3, Gold would have a follow-up threat to the d3 horse.

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Capture congestion can strengthen a goal threat. At right, Silver cannot do a flip capture, and cannot afford to move her camel east; any pull or push capture would allow for a one- or two-turn goal by Gold.

Split capture

One sometimes has the choice of a split capture or a capture done entirely by one piece. On 13s of this game, the silver camel could have simply pushed the gold horse into the trap. By using his elephant for the second push, however, Silver created an immediate follow-up threat to the gold camel.

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Gold has multiple ways to capture the g4 rabbit.

A split capture might not be the best option even if it appears to create a follow-up threat. In this game, the gold elephant got pinched after making a rabbit capture which could have been made entirely by the gold cat. Gold then lost crucial time moving his elephant and cat back to their previous squares.

Blocking the defender

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Forcing a capture often depends on keeping a defender away from the trap. Even an elephant right next to a key square might be blocked by a phalanx. In the first diagram, Silver to move cannot save the g3 horse; Gold will capture it with Cf3s Ef4sn hg3wx. Since such a phalanx must include a piece in the trap, most instances of this tactic have the threatened piece next to the trap. The second diagram shows an exception, where Gold can play a split capture of the silver dog.

Opposite-trap blocking

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24s from this game

An elephant might make a capture in c3 and then wish to defend f6, but this is four steps' distance even with a clear path. If there is not a clear path between diagonally opposite traps, an elephant may not be able to stop a multi-turn capture after making a capture.

Gold has just threatened a silver horse in c3, perhaps thinking that due to the silver dog on f6, Silver would not have time to capture the gold camel in return. This was incorrect; if Silver now plays ee4ew Mg4w mh4w and Gold captures the horse, Silver can then play Mf4n ee4e df6e dd6e, occupying e6 and pushing the gold camel to f5, where it cannot be unfrozen in time to move, as g5 is occupied by a silver cat. Since the camel capture will only take two more steps, Silver can use the other two steps to counter any follow-up threat by Gold.

After Silver plays ee4ew Mg4w mh4w, Gold can still save his camel if he abandons the threat to the silver horse. The horse might then threaten a gold rabbit in c6, however.

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plan window

In this diagram, Silver has a single move which forces the capture of the gold horse: Hg4n ef4e cf7ss. Silver pieces on e6 and now f5 prevent Gold from defending the f6 trap in one turn. The subsequent horse capture would take a full four steps and leave the silver elephant decentralized, so Gold will have time to force a capture of his own if indeed Silver follows through with the horse capture. The now advanced silver cat is vulnerable, as is the silver dog, but Gold can do better, threatening the silver horse with Ec4nwe hb6s. Silver could then undo the horse pull in one step, but that one step would preclude the capture of the gold horse currently on g5, and the now c5 gold elephant could then defend f6. If Silver goes ahead with the horse capture, her own horse will remain on b5, from where it could be pushed to b4 and thus doomed to capture in c3; from g6, the silver elephant could not defend it in time. This tactic is rather delicate: if Silver had a rabbit on d8, she could instead reply with hb5n rd8sss, rescuing her horse while also placing two pushes, and thus five steps, between the c5 gold elephant and f5 or e6. The c7 cat couldn't be used for this, since the silver horse could then be captured in c6.

If from the diagrammed position Silver declines the forced horse capture, she will still be down two horses to one. With the camels gone, this may be worse than being down one horse to none, as two horses might easily overload a camel-less opponent. Silver should thus capture the horse, and try to get a further threat in the east if indeed Gold goes for the western horse capture.

False protection patterns

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plan window

Capture threats in which a piece is held right next to a trap are not overly common, as one's own piece might have to occupy the square to keep control of the trap. Such a threat might be effective, however, if no defender could reach and hold a second key square. Sometimes, a false protection capture will be possible if the opponent attempts to defend against such a threat.

In the diagram, the gold cat must leave f3 before the silver camel can be captured, so Silver might have time to save the camel. If the gold elephant went to f4, or pulled the camel onto f4, Silver could unfreeze and retreat the camel. Gold to move could keep his elephant in place and block both f4 and e3 with Hd4ee Cf3w, but this would leave Silver well-positioned to get compensation for the doomed camel, especially since Gold would need another full turn to capture it. Gold could instead push the camel to g3, but would not then have time to adequately block both f4 and e3, and thus Silver could add a second defender to the trap (if the gold elephant pushed the camel south and then moved to f4, the camel could escape up the h-file). However, Gold can indeed push the camel to g3 and use his other two steps to doom the camel on the next turn. If Gold plays mg4s Eg5s Cf3w Hd4e, any possible Silver defense of f3 would not hold, due to false protection; if a silver rabbit or dog moved to f4, Gold could capture the camel and threaten the piece which came to defend it. If Silver foresaw this and didn't try to defend f3, Gold would then capture the camel in two steps, leaving more time to respond to any Silver counter-threat. Moving the gold horse to e4 also makes the horse safer than it would be on d4 or f4; this move should preserve the gold horse, although the b8 dog can be captured.

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plan window

Problem: Gold to move and win the silver camel

Solution: Mg3n rf3e Ee5s Dd2n. This wins the silver camel on the next turn, by forcing a false protection capture. By contrast, capturing the rabbit by dislodging the camel right away would allow the camel to retreat or be defended by the silver elephant. This camel-capture tactic would not work if Silver had a piece on f6, as Silver could then unfreeze her camel and move it through the trap to f2, since the silver rabbit would be on g3.

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One facing a false protection capture might create a phalanx to block a push. A pull might still be possible, however. After being pinched on 17s of this game, Gold moved his horse onto f3 and pushed the silver camel onto g3. Silver moved a dog to f4 and blockaded that square, but the dog was then pulled into the trap after the silver camel was pulled away; the dog capture was accomplished via two pulls.

Repetition fights

Arimaa rules prohibit any move which results in a position identical to one which the same side has created twice before, at any point in the game. A repetition fight occurs when each side aims to restore a previous position or something close to it. When the three-repeat rule forces one side to deviate, the other has won the fight, for whatever that ends up being worth.

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Pull and replace moves are a common source of repetition fights. In this diagram, Silver to move can break the horse frame with mb5sn Hb3n hc3w. Gold could reverse this move by pulling the silver horse back onto c3 and moving the gold horse back to b3. With this pull-and-replace, however, Gold would restore a position he created previously, and thus could never again end on that exact position. Silver, by contrast, created a new position the first time she broke the frame, and thus can repeat that move and force Gold to do something different. After a change elsewhere on the board, this repetition fight could potentially reoccur, since the overall position would be different.

Some repetition fights include several different positions; the outcome depends on who runs out of positions first. If a move can be undone and redone in three steps each, the fourth steps will be critical. With a nearly unlimited selection of fourth steps, such a repetition fight could go on and on if neither side chooses something different. A prolonged repetition fight might be a way to build reserve time, but one should look for a way out before the opponent finds one.

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Pull-and-replaces would use four steps each. (Game)

If a move creates a new position, and four steps are needed to restore the previous position, reversing the move would only be a way to stall. With Silver to move in this position, a sequence of four pull-and-replace moves is possible. Silver plays mh4we Hg3n hh3w (gold horse to g4, silver horse to g3). Gold then establishes a frame with Ef4sn hg3w Hg4s (silver horse to f3, gold horse to g3). Silver breaks the frame with mh4sn Hg3e hf3e (gold horse to h3, silver horse to g3). Gold can then retake g3 with Ef4ew hg3n Hh3w (silver horse to g4, gold horse to g3). Any of the last three moves was reversible, but could have then been repeated, while the reversal could not have been. In any event, Silver is the one forced to play a move other than a pull-and-replace.

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A two-turn cycle occurs when each player essentially repeats his previous move, but with two pieces transposed. If Gold flips the silver cat to c6, Silver's only goal defense is to move her dog to c8 (dd6n cc6e dd7nw). If Gold then flips the dog to c6, Silver's only goal defense (cd6n dc6e cd7nw) will restore the initial position. After four such flips by Gold, Silver must deviate, allowing goal.

If the d6 piece were a cat, this would only be a one-turn cycle, since swapping the two cats would not change the position.

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Here Gold wants to pull the silver horse to c4 to threaten it in c3, while Silver wants to free the horse and retain the threat to the gold camel. After pulling the horse with three steps, Gold must step his western dog or cat north, to stop the silver horse from escaping via eb5s hc4ee eb4n. In getting the horse back to d4, Silver will push the dog or the cat; the dog could be pushed to b3 or a4, while the cat could be pushed to d3, e4 or d5. Gold always moves the cat to d4 or the dog to b4, and thus Gold will run out of positions sooner despite having started this repetition fight. The silver horse can thus escape.

This position is based on the one after 8s of this game, but there d6 was vacant, and the silver dogs were both on the a-file. Gold could have captured the c7 rabbit, but preferred to threaten the silver horse instead, as Silver otherwise appeared poised for a strong camel hostage. Not wanting an additional gold attacker at c6, Silver opted not to push the gold cat to d5 until the repetitions precluded a push to d3 or e4. Once the gold cat was pushed to d5, it went to c7, capturing the rabbit and also threatening to free the gold camel. Silver could have avoided this by moving the a5 dog to b4 on 16s or even on 12s, as this would have changed the position, and the silver horse could not have then been frozen on c4.

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In this game, Silver flipped the g4 gold horse to f5, hoping to capture it in return for the doomed silver camel. Gold undid the flip with Ee4n Hf5es Ee5s, but Silver repeated the flip and thus seemingly won the repetition fight. However, Gold then played the ko threat Mb5es hc6s Ha5e, threatening a silver horse in c3. After that horse retreated, the eastern gold horse moved back to g4. Since Gold's ko threat and Silver's response changed the position, Gold was now winning the eastern repetition fight.

"Ko threat" is a term borrowed from Go, which applies much less commonly to Arimaa. A ko threat need not be a good move locally; Gold's western position is of secondary importance here. The purpose is to restart the eastern repetition fight.

Setup

There are 64,864,800 possible setups for each side, although Gold in effect only has half that many, since an east-west reflection amounts to the same setup for the one going first. Players frequently experiment with different setups, but certain guiding principles are usually followed:

• Elephant centralisation: The elephant usually starts on the d- or e-file; less commonly, on the c- or f-file.
• Activity: A piece typically does not start directly behind a weaker piece. A strong piece usually does not start directly behind a trap, unless one has a plan to quickly advance and replace it.
• Balance: There should be some strength on each wing, so that each home trap has some protection and there is at least a potential threat to each away trap.
• Rabbit protection: Since rabbits can't retreat, they should not be exposed to easy pulls.

A small minority of the possible setups meet these criteria. However, there is still plenty of scope for variation. A setup which buries strong pieces may be a form of handicap.

Elephants tend to stay near the centre until strong enemy pieces draw them to the outskirts. Unless both sides play a lone elephant opening, an early camel or horse advance could set the tone. The placement of the camel and horses is thus the essential characteristic of a setup. A symmetric setup, with the camel in the middle and a horse on each wing, is the most flexible. However, one planning a quick trap attack might begin with the camel decentralized, as non-elephant pieces don't often advance through the center during an initial attack, due to the risk of a fork. The calculus is different for Gold than for Silver; if the gold camel began decentralized, the silver horses could both start far away from it, giving Silver an early alignment advantage. Any first-move advantage Gold might have is balanced by Silver's ability to respond to Gold's setup.

Symmetric setups

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Each setup is a mirror reflection of itself, except where the elephant and camel are concerned.

The diagram shows two standard symmetric setups. Gold uses the classic 99of9, named for a player who popularized it early on. A 99of9 setup prioritizes flexibility and to some extent defense. The camel can quickly defend either home trap. Rabbits are arranged so that they won't get in the way of friendly pieces; a rabbit advanced in the middle could be a problem, whereas the opponent has less to gain by pulling an a- or h-file rabbit. Eventually, the c- and f-file rabbits might step into the middle to block the goal line.

The horses will step forward, to defend the traps from the sides. One horse or the other might soon advance to create a threat. The d1 or e1 piece might soon advance two squares, to help defend a trap or to act as a linchpin so that the camel can remain in the middle without getting pulled forward. Such a linchpin piece might itself get pulled forward; a cat would be even more vulnerable than a dog, but on the other hand a dog loss would be costlier. A similar dilemma concerns the pieces which begin directly behind the traps. A dog can't be pushed aside by an enemy dog, but if the opponent does get a strong attack, the piece behind the trap might be the first to go, which would be costlier if that piece were a dog. It is more common to place cats behind the traps, perhaps because both cats might stay there for most of the game, whereas it is unlikely that both dogs would. One with a different plan for each wing might place a dog behind one trap and a cat behind the other.

Silver uses the Fritzlein setup, in which rabbits are placed behind the traps, and cats may advance on the b- and g-files. A silver cat might quickly advance behind its horse, to defend its home trap from the side or to support an attack. If the c7 or f7 rabbit is pushed or pulled forward, this may complicate a home trap control fight for Silver, since a rabbit can never step backward. With that said, winning a fight at home may not be a priority for one inclined toward aggressive play. Silver's setup may thus be good for a player who intends to attack somewhat quickly and not worry too much about his home traps. Again, the dogs and cats might be switched.

Note that the silver elephant does not directly face its gold counterpart. Had Silver placed her elephant on e7, the gold elephant could immediately go to e6 and delay the silver elephant's advance. That would be bad for Silver, unless she had a quick way to attack and force the gold elephant to return home.

MH setups

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

Silver might quickly attack in the west.

At left, Silver uses an MH (camel-horse) setup. Silver plans to advance her horse and camel in the west, to attack c3 and/or drag the gold horse toward c6.

Silver's attacking threat justifies having her elephant directly face the gold elephant. Gold might play 2g Ed2nnnn, but then Silver could play 2s ha7s mb7s cc7w hg7s and, if the gold elephant stays on d6, 3s ed7wsse. Silver loses some time with sideways steps, but Gold will lose even more time moving his elephant, which must step around its silver counterpart and go back home to defend c3. One facing an MH setup must keep his elephant near the home trap which faces the MH attack threat, at least until he can get a stronger attack of his own.

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

The setup from this game.

At right, Gold has set up for a quick EMH attack in the west. To slow this down, the silver camel directly faces the gold camel. Silver could place both horses in the east, far away from the gold camel, but prefers to place one horse in the middle so that it can quickly go to either wing. Gold might move his camel east and still get a strong western attack; to avoid being pulled toward c3, the silver camel may need a supporting horse.

Another idea for Silver (illustrated here) would be to put the elephant in the west and camel and horse in the east, reasoning that Silver will be faster in an attacking race since Silver's attack is further from the elephants. Yet another idea, from this game, is to play an approximate mirror image of Gold's setup, leading to a slow maneuvering opening.

Even having placed the camel in the west, one might quickly move it east. A setup is not a hard commitment to a particular strategy; the game must be played move-by-move. If Silver places her camel directly opposite Gold's camel, Gold might immediately move his camel to the other wing. Although this would use up a turn, some players might find a camel gridlock too tedious to play through.

HH setups

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

The setup from this game.

Placing his horses and elephant together in the west, Silver intends to create a fairly quick threat on that wing. A full-on EHH trap attack can sometimes work, but it might be tricky to get a silver horse safely onto b3 when the silver elephant is the only piece which can displace a gold horse from that square. Silver might initially aim to pull the western gold horse homeward and surround it. This could lead to a frame in c6 which the silver elephant might rotate out of.

Gold might move his camel west to face the silver horses. An EMH attack against c6 might seem tempting, but could leave Gold vulnerable in the east, where the silver camel would then be the strongest piece. Gold might first attack in the east; the silver camel might have trouble holding g6 with no silver horse nearby. A silver dog is placed on f7 to keep that square as secure as possible; if the silver elephant had to come east to defend, that would be the end of any EHH threat in the west, where Gold might then get a strong MH attack.

An HH setup by Gold would be extremely risky, as the silver camel could directly face both gold horses, and weak silver pieces might face the gold camel, causing it to waste its strength. In this game, a silver dog and cat were strong attackers in the east, and neither gold horse could do much in the west.

Statistics

Percentage popularity of camel and horse distributions for Gold

Silver responses to a symmetric gold setup

Average number of forward rabbits

These statistics are based on games between two humans each rated over 1800. Setups where one wing has no horse or camel are rare and excluded here. Note that in this classification, 'old-style' EHH setups (e.g. with b- and d-file horses) are counted as central horse setups.

Race Positions

Arimaa/Race Positions

Trap Attacks

Overview

Arimaa/Attacking/Overview

Positioning

Arimaa/Attacking/Positioning

Techniques

Arimaa/Attacking/Techniques

Camel attacks

Arimaa/Attacking/Camel Attacks

Attacks Against a Camel Trap

Arimaa/Attacking/Attacks Against a Camel Trap

Elephant-Dog Attack

Arimaa/Attacking/Example: Elephant–Dog Attack Template:Clear

Lone Elephant Attacks

Arimaa/Lone Elephant Attacks Template:Clear

Sample Games

Arimaa/Sample Games Template:Clear

Arimaa Challenge History

Arimaa/Arimaa Challenge History Template:Clear

Glossary

Arimaa/Glossary Template:Clear

Resources

Arimaa/Resources Template:Clear

GNU Free Documentation License

GNU Free Documentation License