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 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. If the silver elephant captures a gold piece in c3 and ends the turn on c2, it might then get boxed in. Early on, players discovered that some bots could be enticed 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, where the blockade could become stronger.

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[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, a blockade will at least require more material.

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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. 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, 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 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 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 making it nearly impossible for Gold to break.

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 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.

Elephants in middle[edit]

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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[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, whose owner cannot move them backward. Even a centralised elephant can sometimes be blockaded by its own rabbits.

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.

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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 and f5 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.


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With an advanced gold rabbit blocking its only escape path, the gold elephant is blockaded. (Game)

In this position, Gold must be very careful about any further rabbit advance. The gold elephant is blockaded, but the silver elephant is currently an essential part of the blockade. A second advanced gold rabbit could allow the silver elephant to rotate out and dominate the board.

Partial blockades[edit]

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

A full elephant 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 silver elephant could eventually escape through the c6 trap, but the gold camel could make a capture in the meantime.

The Center[edit]

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The gold elephant is cut off from the center.

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, dividing up the board. In the diagram at right, from this game, the six central silver pieces severely limit the gold elephant's movement.

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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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 a hostage-holding elephant. 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 that would let Silver strengthen the blockade; the c4 horse could push the gold cat back to a4, totally blocking in both the cat and the elephant, which couldn't get back to b3 due to the phalanx formed by three rabbits and a horse.

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.