Arimaa/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. Although Silver had no immediate way to force a capture, Gold had no good way to deal with the intruding silver horse: the silver elephant would stop the gold camel, and Gold would rather not decentralize his elephant on account of a horse. With a silver horse already behind the c3 trap, Silver would likely win an EMH attack race. While not ideal, a horse-by-elephant hostage might actually be Gold's best option here, as it would create an immediate threat while also protecting c2 and b3.
Deadlocked Traps Edit
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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 will be possible 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 while Silver faces multiple threats.
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Gold will lose a horse for abandoning c6; Silver will lose a dog and some rabbits for abandoning c6. |
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, especially if his elephant is decentralized. 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. If the deadlock is the result of a hostage position, the defender's space advantage might allow him to rotate his elephant out of hostage defense.
Before and after diagrams illustrate the effect of gold rabbit advances on a northwestern elephant deadlock. In the before diagram, Gold would stand to lose his horse if his elephant were to abandon c6. If the silver elephant were to abandon c6, the gold horse and elephant together could force the capture of any silver piece near the trap. This is typical of an elephant deadlock: it would be costly for either elephant to leave.
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Gold will lose a horse and some rabbits for abandoning c6; Silver will lose a dog, some rabbits, and the game for abandoning c6. |
In the after diagram, gold rabbit advances have further raised the stakes for both sides. If the gold elephant were to abandon c6, Silver would then clean house. If the silver elephant were to abandon c6, a gold rabbit would soon reach goal. With so much now at stake in the northwest, the deadlock has tightened considerably.
Having effectively committed to the c6 trap, Gold should now advance his western dog and then his camel, so that his elephant can rotate out before the silver camel does much damage in the east. Had Gold kept his western rabbits at home, his goal line would be well-defended and he would have less to lose in c6, affording him much greater flexibility.
One whose elephant is stuck in a home deadlock must ensure that the enemy elephant has no good way to leave. One unprepared to make a strong second threat should avoid getting into a home elephant deadlock; for example, taking a hostage could backfire if one is not already poised to attack on the other wing.
Stronger vs. weaker pieces Edit
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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 will be possible only when one side can establish full control of some trap. When a strong piece moves from one fight to another, the area it leaves could become vulnerable; 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 Edit
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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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Silver owns no traps, and can't even move pieces through her home traps. |
In this game, Gold's advances gave him strong shared control of both c6 and f6. As long as the silver elephant defends f6, the gold elephant can dominate the west. Gold's home defense is now thin, though it would not be easy for Silver to get anything started.