Arimaa/Elephant Blockade

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The silver elephant is completely stuck, while the gold elephant is free.

Elephant mobility can be limited in three different ways. An elephant may be compelled to defend a particular area, it may not have time to get where it wants to go, or it may actually be blocked. If an elephant is physically stuck in a particular area, that elephant is blockaded.

A weak piece is typically left behind each home trap; sometimes the home defender will let the enemy elephant capture that piece and thus decentralize itself. An elephant which carelessly wanders toward a corner might then get boxed in. Early on, players discovered that some bots could be lured into this by an early capture opportunity; the elephant would then look for an escape, and could be tempted further by an empty square on the edge of the board, where the blockade could become stronger.

In this game, diagrammed at right, Silver took the bait and is now strategically lost. Due to the b1, d1, and c2 phalanxes, the silver elephant has no move at all. With the only functional elephant, Gold has the most decisive advantage possible. Silver could try to free her elephant, but the gold elephant and camel could ward off or capture any silver piece which approached the blockade. To keep it intact, Gold must continue to occupy c3, and thus only capture something there if the dog can return to c3 in the same turn.

Rotation[edit]

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. If an elephant stays even one square away from the edge, an effective blockade becomes trickier.

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

Here the gold elephant can't move, but that 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. A rabbit on h6 would work just as well as a camel. Silver to move can play mh6s rh7s rh8s rg8e, sliding the camel and three rabbits; those rabbits now block the gold elephant from h7, and the camel is free. Although g8 is now 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, probably 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 to move could place pieces on e6 and d7, making such a rescue harder. 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 in order 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 stop the gold camel from doing anything, and the silver camel could stop any other gold piece. In the actual game, the silver camel went to g5, rounding out this phalanx and ensuring that a gold horse had no chance to break it.

Were the gold elephant on g6 and the silver elephant on g5, it would be a different story; a gold rescue mission could be quicker, and a silver phalanx extending to g4 could be vulnerable. Such a blockade should perhaps be regarded as temporary. If it were attacked from the side, the blockading elephant might abandon the blockade but fork an attacking piece. With a relatively weak elephant blockade, the blockaded player can and should be cautious, but must still stop it from becoming strong; breaking it may or may not be worth a material sacrifice. In any blockade position, a blunder by either side could be huge.

Friendly rabbit blockade[edit]

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Unable to step backward and blocked in all other directions, all seven gold rabbits are stuck in place, neutralizing the entire gold army.

The ideal pieces for blockading an elephant are rabbits of the same color. 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. Even a centralised elephant can sometimes be blockaded by its own rabbits.

At right, observe the position after move 48s of this game. Well-placed silver pieces combine with five advanced gold rabbits to blockade the gold elephant, camel, and dog. In the east, four more gold pieces can't move at all. The gold horses are stuck in their home half of the board. Silver must be careful not to loosen the blockade, but the g4 dog can be safely captured or moved, as long as no viable path is opened for it or a gold horse to dislodge the silver cat on f5. Short of a miscue by Silver, Gold has no way to free his elephant, although he could get limited freedom for other pieces by sacrificing the elephant, which he did on 57g.

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

Blockading the gold elephant on g6 would often require the silver elephant to remain on g5, since a silver phalanx extending to g4 could be highly vulnerable. Here, however, that phalanx is 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 the silver elephant can now easily prevent that. Two advanced gold rabbits have allowed Silver to completely immobilize three strong gold pieces.

Partial blockades[edit]

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The gold camel can capture a piece before the silver elephant can get free.

A full blockade is hard to achieve, but sometimes an elephant can be marginalized enough that it won't be a factor for several turns. In this position (see game), Silver's horse-by-camel hostage is useless; with the silver elephant boxed in, the strongest free piece is the gold camel. The blockade is not total: the silver elephant could eventually escape through the c6 trap, though such maneuvering would mess up Silver's position and also give the gold camel time to make a capture.

The Center[edit]

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The gold elephant is cut off from the center.

When an elephant is next to a trap, it is somewhat decentralized, and thus can potentially be cut off from a substantial part of the board. If the enemy elephant is not on one of the four central squares, it is occasionally possible to station a clump of friendly pieces on those squares, creating a substantial barrier between that elephant and at least one trap. In the diagram at right, from this game, the six central silver pieces keep Gold's elephant away from his own eastern home trap.

This strategy must be used with great caution, however; if the dividing wall does not hold, the pieces likely can't all retreat. This blockade worked because Silver had a strong position overall. Silver subsequently slid his elephant to e4, from where it then captured the gold camel.

Swarm[edit]

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Silver's many advanced pieces have hopelessly blockaded the gold elephant.

When an elephant is decentralized in its own home territory, perhaps holding a hostage, there may be an opportunity to blockade that elephant with a swarm of advanced pieces. In this 2005 Arimaa Challenge game at left, Silver has exploited the bot's susceptibility to elephant blockades.

Notice that the immobilized gold cat has become part of the blockade holding in the gold elephant. While the gold elephant might try to escape by pushing the a3 horse south and then using its newly mobilized cat to push the b4 rabbit south, that would play further into Silver's hands. The c4 horse could push the cat back to a4, totally blocking in both the cat and the elephant, which couldn't get back to b3 due to the phalanx.

Often in such situations the gold elephant is not absolutely blockaded, because it may still escape to the center of the board via the first two ranks. Even if the gold elephant could so escape, however, the blockading silver pieces would surge forward in its wake, ensuring long-term trap control of c3 for Silver, and consequent indirect goal threats.