Arimaa/Introduction to Strategy/Camel Hostage

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[edit] Strongest Free Piece

In the position at right, from this game, the gold elephant is holding the silver camel hostage. The camel is frozen, so it can't run away, and on any turn Gold could flip it into the c3 trap. In order to prevent the camel from dying, Silver must station his elephant next to the c3 trap. Silver can't defend with less than the elephant, because any weaker silver piece could be captured by the gold elephant.

Herein lies the answer to the defensive conundrum of equal forces stalemating each other. Gold's elephant is tying up Silver's elephant and camel both, leaving Gold's camel unopposed as the strongest free piece. The gold camel can dominate the f3 trap: anything that the gold horses drag to f3 will be captured. The silver camel can't defend because it is hostage, and the silver elephant can't defend without allowing the silver camel to be captured. If the silver horses try to defend f3, they will be captured as well.

[edit] Horses Advance

It might seem counterintuitive at first that Gold takes advantage of having a free camel by advancing horses rather than by attacking with the free camel, but it turns out to be the safest way to play for advantage. Imagine in the diagram above that the gold camel on f2 switched places with the gold horse on a6. In that case Silver to move could send his elephant to b6, abandoning the silver camel to its fate, but taking the gold camel hostage at the same time. Gold's advantage would evaporate with that move, and an even camel trade would be the likely outcome. With a positional hammerlock, there is no need for Gold to take any chances.

Indeed, the gold horse on the west wing is actually not attacking so much as it is defending the c6 trap. Silver's elephant is tied to the defense of the hostage camel, but it can dart next to or even behind the c3 trap as long as it is careful. This mobility is often enough that the silver elephant can dislodge a small gold piece and gradually bring it towards c6. If the silver elephant could stand on c4 holding a gold piece hostage on c5, Silver would threaten to capture the gold hostage in two steps and return to c4 in time to keep the silver camel safe. The gold horse on a6 pre-emptively guards against any such shenanigans by the silver elephant.

For gold to use one horse on the east wing to drag one little piece at a time for capture in f3 may seem tedious, but Silver is helpless in face of this strategy. We will see later that the best response to an invading horse is to attack it with one's camel, but the silver camel is stuck. The long-term outlook is so bad for Silver, he should probably immediately move his elephant to b6 to take a horse hostage. This loses a camel for a horse, and leaves Gold with the upper hand to force a capture in the future, but it is better for Silver than shuffling aimlessly while little silver pieces are picked off one by one. Alternatively, Silver could unfreeze his camel with the horse and push the Gold dog away, burrowing the camel so that it is not threatened with capture in 1 move.

[edit] Active Defense

If Gold does not present a horse in a way that allows Silver to capture it in exchange for the hostage camel, then the only active defense lies in bringing a wave of pieces up to the hostage trap in hopes of freeing the elephant from its defensive duties. In this game, diagrammed at right, Gold is strategically lost because the arrival of the silver dogs has freed the silver elephant to roam, whereas the gold elephant must stay put to prevent an immediate goal. Suddenly the tables have been turned and Silver has the strongest free piece, i.e. the silver elephant.

This is the last and most subtle reason for the gold camel to stay home on defense when Gold has the silver camel hostage. If the gold camel were at home in the diagram at right, lurking on d2 for example, it could threaten whatever pieces Silver brought up to defend f3. The silver elephant would have a tough fight to try to prevent the loss of a piece in c3 without losing control of f3. The tactics can get complicated, but with the camel helping out, Gold should be able to make captures somewhere, or at a minimum keep the silver elephant from straying far.

The most active defense against a camel hostage is to bring up pieces either numerous enough or strong enough to contest both enemy traps. In this game, diagrammed at left, Gold can't make a capture in either c3 or f3, despite holding the silver camel hostage. The gold camel would like to help regain control of c3, but the silver elephant is well-positioned in the way.

Who has the strongest free piece now? The silver elephant is more free than the gold elephant, but it isn't totally free, because if it crosses back to the silver side of the board, the gold camel will smash across into the silver horses around c3. Similarly the gold camel isn't really a free piece, because it needs to lurk around committing the the silver elephant to defense of c3.

As it turns out the gold horses are suddenly the strongest free pieces. Gold can't force a capture at home, but has an excellent chance of forcing captures abroad, in Silver's half of the board. This type of position, where both players are trying to take over each other's home traps at the same time, tends to be very difficult, both strategically and tactically. Gold still has the whip hand, though, and it all traces back to holding a camel hostage. When the bloodletting begins, Gold is likely to be able to capture bigger pieces sooner.

These few positions are only scratching the surface of possible play when a camel is held hostage, but they should give an inkling both of how a camel hostage gives one an advantage, and of how it is the foundation of much deeper strategies.

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