Arimaa/Introduction to Strategy/Elephant Blockade
Elephant mobility can be limited in three different ways. An elephant may be stuck defending a particular area, it may not have time to get where it wants to go, or it may actually be blocked. If an elephant's movement is severely limited by pieces which it can't simply step around or move, 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 (and probably 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.
Most elephant blockades, however, are not as lopsided as that one, 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.
Here the gold elephant can't move, but Gold is fine with that as long as Silver can do nothing else while holding the blockade. Indeed, if all the blockading pieces stayed put, the strongest free piece would actually be 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.
If Gold plays passively, Silver can continue to rotate pieces, freeing her elephant as well in two or three more turns. Thus Gold must quickly try to erode the blockade from the side, or even from the front if the silver elephant tries to leave. This will expose gold pieces to danger, but at least it puts some play into the position. For Gold to hang back is to await execution.
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, any gold piece which tried anything would be at the mercy of the silver elephant. Gold's best hope is to disrupt the blockade while the silver elephant is still a direct part of it.
Were the gold elephant on g6 and the silver elephant on g5, it would be a different story; a silver phalanx extending to g4 would be highly vulnerable. Thus the silver elephant would have to be a permanent part of such a blockade, if indeed Silver wanted to keep it intact. With this in mind, Gold might attack the blockade from the side, although the silver elephant might then abandon the blockade but fork an attacking gold piece. In any blockade position, a blunder by either side could be huge.
Friendly rabbit blockade
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.
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 has a horse-by-camel hostage, which ideally would make the silver elephant the strongest free piece. With the silver elephant boxed in, however, the strongest free piece is in fact 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.
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.
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.
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.