Arimaa/Introduction to Strategy/Elephant Blockade

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The silver elephant has no legal move, so the gold elephant is the strongest free piece.

Not long after discovering the camel hostage strategy, human players discovered that some bots could be lured into an elephant blockade by the offer of a free piece for capture. From there, the elephant would look for an escape, and thus could be tempted by an empty square on the edge of the board, where the blockade could become stronger.

In this game, diagrammed at right, Gold has lost a cat while Silver has a full army, but Silver is nonetheless completely 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 (and probably capture) any silver piece which approached the blockade.

Rotation[edit]

Most elephant blockades, however, are not as hugely advantageous as that one. It is a rare opponent who will voluntarily move his elephant to the edge of the board when a blockade is looming. The diagram below left, from this game, shows a slightly less advantageous situation with the blockaded elephant one square away from the edge of the board.


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The gold elephant is blockaded, but the game is not over.

Here the gold elephant can't move, true, but nine silver pieces are required to maintain the blockade, including both the silver elephant and camel. Indeed, if all the pieces involved in the blockade stayed put, the strongest free piece would actually be the gold camel.

As it happens, however, Silver can undertake a rotation (or replacement) of the pieces participating in the blockade. When it comes to being in the way, a weak piece serves just as well as a strong one. Silver to move can free his camel for duty in only four steps, while maintaining the blockade: camel h6 south, rabbit h7 south, rabbit h8 south, and rabbit g8 east. The gold elephant can't make use of g8 to dig its way to freedom without getting smothered against the edge, so Silver can fill in that hole next move. Thus Silver needs only one turn to equal Gold for having the strongest free piece.

Furthermore, if Gold plays passively, Silver can continue to rotate pieces, freeing his elephant as well in two or three more turns. Because of this threat, it is very important that Gold not remain passive. Gold must immediately begin preparing a rescue mission to erode the blockade from the side, or even from the front if the silver elephant tries to leave. This will necessarily expose gold pieces to danger, but at least it puts some play into the position. For Gold to hang back is to await execution.

Note that even if Silver manages to rotate the elephant out of the blockade, it will require a few more pieces to maintain than a blockade on the edge. Furthermore those pieces will protrude one square further, making them slightly easier targets for would-be blockade busters. Still, the blockade is quite advantageous to Silver.

When rotation is impossible[edit]

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Silver has blockaded the gold elephant, but would gladly give up the blockade to take the Gold camel hostage.


The diagram at right, from this game in the 2006 Arimaa World Championship, features an elephant blockaded one step further from the edge of the board, which is correspondingly less advantageous. Indeed, it is no longer realistic for Silver to expect to be able to free his elephant by rotating blockaders appropriately. True, the f6 trap is participating in the blockade at the moment, but Gold might bring a piece to f5 or e6, allowing the gold elephant to step to freedom, so Silver must soon occupy at least the latter squares.

An elephantless blockade would require silver pieces on g8, f7, g7, h7, e6, h6, f5, g5, h5, and g4. Not only are ten pieces necessary, but the bubble of blockaders also presents a large surface area for Gold to assail, extending within two steps of Gold's home trap at f3. Silver would be too busy warding off threats to the blockade to ever start capturing pieces with his freed elephant.

Since Silver can't rotate his elephant out of this blockade in practice, it does not give him the strongest free piece like an ideal blockade does. Yet the blockade is not worthless. Its value is that, although both Gold and Silver have a free camel, the silver camel is more free.

Suppose that Silver, while maintaining the blockade, were to use his camel to attack the c3 trap. Gold could defend c3 with his own camel, but couldn't endanger the attacking silver camel. In contrast, if Gold were to attack c6 with his camel, Silver would have the option of giving up the blockade to cross wings and take the gold camel hostage. (This principle recurs again and again in the study of elephant mobility.)

This difference of freedom pegs the value of the blockade to Silver at somewhat less than a camel hostage. Silver certainly can't expect to get more out of the position, because if Gold is willing to give up his camel as a hostage, he can frustrate anything else Silver might undertake. Indeed, the gold camel can probably break the blockade at any time if it is willing to expose itself. On the other hand, Silver can't necessarily force Gold to expose his camel. Gold can play in the west as well as hovering in the east making threats to break the blockade. If Silver has trouble generating a threat in the west while maintaining the blockade in the east, he may be forced to give up the blockade for an advantage smaller than a camel hostage.

Partial blockades[edit]

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A partial elephant blockade makes the gold camel the strongest free piece.


Because of the difficulty of blockading an elephant in the centre of the board, complete elephant blockades are uncommon in games between strong players. Partial blockades, keeping the elephant from accessing an important area of the board, are more frequent. In this position (see game), Silver has a horse hostage, which ideally would make the silver elephant the strongest free piece. In this case, however, the elephant is blockaded away from the centre of the board; the strongest free piece is in fact the gold camel. Note that the blockade is not complete: the elephant can escape through the c6 trap. This maneuver would take several turns, allowing the gold camel to capture a piece in the meantime. Furthermore, it would disrupt Silver's defense of c6, probably allowing Gold to share control of the trap.

Swarm[edit]

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


If a defending elephant becomes decentralized while holding a hostage near a home trap, there may be an opportunity for the attacking side to blockade it with a swarm of weak pieces, i.e. rabbits, cats, and dogs. 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.

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 one has several pieces near the center, and 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. Silver could threaten goal in the west while also making a threat in the east.

This strategy must be used with great caution, however; if the dividing wall does not hold, at least one of the pieces will likely be lost. At right, if Gold could break through the wall, some silver piece would likely perish in f3. If an elephant is even mildly mobile, enemy pieces other than its counterpart should be cautious about occupying any central square, let alone all four.

Rabbit Advancement · Race Positions