< Arimaa
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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 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.

In this opening, a horse procured a long-term trap control advantage for Silver. Although Silver had no immediate way to force a capture, Gold had no direct way to deal with the intruding silver horse: the silver elephant would stop the gold camel, and Gold could not afford to decentralize his elephant just to deal with a horse. From here, Silver swarmed the c3 trap and overloaded Gold, whose elephant stayed beside c3 and thus could not defend in the east.

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 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 could become an attacker if the hostage-holder simply left. 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. Here, Silver is well up in material, but has more to lose than does Gold; the silver camel and hostaged horse would both be at risk if the gold elephant went west. What happens in the northeast will help decide what happens in the southwest.

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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, the gold elephant does not want to abandon c6, because Silver would capture the b7 horse. Likewise the silver elephant does not want to abandon c6, because the gold horse and elephant together could force the capture of any silver piece near the trap. This is the essence of an elephant deadlock: either side would suffer for leaving.

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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, the advanced gold rabbits have further raised the stakes for both sides. If the gold elephant abandoned c6, Silver would then clean house. If the silver elephant abandoned c6, a gold rabbit would soon reach goal. With so much now at stake in the northwest, the deadlock has tightened considerably.

In advancing three rabbits in the west, Gold may have figured that the threat of an eventual goal outweighed the risk of eventually losing a few rabbits. That is often correct, but the whole board must be considered. If the silver camel advances in the east, it can soon cause trouble unless the gold elephant leaves the deadlock. The result could be a three-for-one trade, which would strongly favor Silver on this already depleted board. Gold should have kept his western rabbits at home, and taken advantage of the effect the original deadlock had on the respective camels.

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

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

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. At right, all four traps are contested in such a manner. Until one side can establish full control of some trap, no captures will be possible.

Each local fight must be considered in the global context. When a piece moves, the area it leaves may be affected. If the gold elephant went south, the hostaged gold horse would likely be lost, and Silver might have further threats in f6.

Losing control

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

Here, Silver is close to dominating the whole board. To have any chance, Gold must advance his camel and reassert full control of the f3 trap; 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. (Game)

In the position at right, most of Gold's army has advanced into Silver territory; Silver is severely cramped, with silver pieces unable to move through their own home traps. The silver elephant can't afford to leave f6, and thus the gold elephant can dominate the west. Gold defends all four traps, and Silver has nothing close to a capture threat anywhere. Gold pieces block nearly anything Silver might try.

Gold's one potential weakness is his thin home defense. Gold should keep an eye on Silver's h-file horse and dog, which might come down and try to start something in the southeast.

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