Arimaa/Trap Control

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At the outset, each player essentially has full control of his two home traps. Each elephant can quickly share control of one away trap, but as long as a home player can occupy two key squares of each home trap, having the enemy elephant next to one is not a problem. However, if one can get a non-elephant safely onto a decentralized key square of an away trap (e.g. b6 or c7 when attacking the c6 trap), there is at least the potential to take full control of that trap.

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The b2 horse effectively gives Silver shared control of the c3 trap. (Game)

Sharing control of an away trap will limit the opponent's capture threats, allowing one to play more aggressively. As long as one adequately defends an away trap, no friendly piece can be captured therein. This allows more pieces to advance toward it, and perhaps soon take full control of the trap if the opponent doesn't prioritize its defense. If one does get full control of an away trap, several quick captures may be possible, since an enemy trap usually has plenty of enemy pieces nearby. Once space has been cleared, by captures or by enemy pieces scattering, a strong goal threat may be possible. If the enemy elephant defends its own home trap in order to prevent this, that elephant will be less of a problem elsewhere.

On the other hand, one attacking for trap control might soon find the tables turned on him. If too many pieces advance too quickly, the home traps may be vulnerable to a counterattack. Moreover, advanced pieces may end up hostaged, framed, or blockaded. Even if the trap defense appears too weak for that, stronger defenders may arrive later, if the whole-board fight allows. Attackers may even end up blocking each other. Rabbits often advance to support an attack, but since they can't retreat, the defender might use them against other attackers. The attacking side might then be weak on the entire wing, with any attack blocked and fewer pieces defending home territory.

In the position shown, a silver horse has penetrated enemy lines in the opening, giving Silver a long-term trap control advantage. Although Silver has no immediate way to take complete control of the c3 trap, Gold has no direct way to deal with the intruding horse: the silver elephant would stop the gold camel, and Gold cannot afford to decentralize his elephant just to deal with a horse. Silver might soon advance more pieces in the west.

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. 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.

When both sides commit an elephant to the same trap, neither can capture anything in that trap. This can create a space disadvantage for the player whose home trap is deadlocked, especially if the home 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 force the opponent to do something other than work that deadlock to his advantage. 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 for an attack on the other wing.

Contested Traps[edit]

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All four traps are contested, since each strongest local piece faces multiple weaker pieces which protect each other. (Game)

A trap is contested 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. Until one side can establish full control of some trap, no captures will be possible. With a fight at each trap, however, things may progress quickly.

While not yet a capture race, this could be characterized as a positional race. One poised to lose control of a home trap must either defend that trap or counterattack somehow. Here, Gold can soon take over f6 or perhaps c6, unless the silver elephant goes north. If the silver elephant moved, however, the gold camel could go west, and the silver horses and camel could fall like dominoes. Silver has no good way to confront either gold horse; slow maneuvering would not work, as Gold can do damage quickly. Unable to defend c6 or f6, Silver must attack c3 or f3. The western gold horse would stop any Silver swarm of c3, so that leaves an attack on f3 as Silver's best immediate option. Even this, however, would further weaken Silver's already thin home defense.

Each local fight must be considered in the global context. When a piece crosses quadrants to attack or defend a trap, the area that piece left might be affected.

Losing control[edit]

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The gold camel must take control of the f3 trap. (Game)

One who defends all four traps can likely make quick progress, unless a defender is displaced. In the position at left, Silver retains full control of both home traps, and shares control of both away traps. With both gold horses blocked in, Silver's position is strong.

To have any chance, Gold must advance his camel and threaten the g3 horse; 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.

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Gold shares control of f6, but Silver has taken full control of f3. (Game)

In the position at right, Gold attacked f6, but Silver counterattacked f3 and now has full control of it, whereas Gold only shares control of f6. Silver's eastern strength is likely too much for Gold to overcome; Gold might attack in the west, but Silver is well ahead in any race, and could likely even afford to move his elephant west.

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Silver owns no traps, and can't even move pieces through her home traps. (Game)

In the position at left, 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.