Arimaa/Introduction to Strategy/Camel Hostage
Strongest Free Piece
In the position at right, the gold elephant is holding the silver camel hostage. The camel is frozen, so it can't escape, and on any turn Gold could flip or pull it into the c3 trap. To preserve the camel, Silver must station his elephant next to the c3 trap. Silver can't defend with less than the elephant, because any other silver defender could itself be captured in c3, unless there were two silver defenders securely in place, which would be hard to maintain if the silver elephant were elsewhere.
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. As long as the camel hostage remains in place, Gold can dominate the other side of the board. The silver camel obviously can't defend f3, and at present the silver elephant can't defend f3 without losing the silver camel.
In order to gain advantage from the camel hostage, Gold must actively use his camel. However, the camel advancing alone is vulnerable. Imagine in this diagram that instead of the horse, the gold camel were on a6. Silver to move could send his elephant to b6, setting the stage for an even camel trade, which would be a disappointing outcome for Gold. Since the camel captures would each use all four steps of a turn, neither elephant could come back and save its own camel. Therefore, the camel should only advance with the support of weaker pieces.
The gold horse on the west wing is actually not attacking so much as it is defending the c6 trap. The hostage camel keeps Silver's elephant next to the c3 trap, but it can still dart around as long as it is on c4, d3, or even c2 at the end of a turn. This mobility could allow the silver elephant to dislodge a small gold piece and gradually move it up. If the silver elephant could get a weak gold piece into silver territory, and Gold had nothing there to protect it, that gold piece would soon be lost while the silver camel would remain safe. The gold horses are prepared to defend the c6 and f6 traps, short-circuiting any such shenanigans by Silver. The gold horse in the west must keep some distance from the silver elephant, to avoid being frozen on c5 and then captured in two steps.
While holding a camel hostage, Gold will ideally make a second threat using his camel as strongest free piece. Gold could use his eastern horse to drag little pieces down for capture in f3. With the silver camel stuck in the west and the silver elephant committed to defending it, any silver piece which tries to protect the f3 trap will itself be captured by the gold camel. Alternatively, Gold could take control of f6 using his horse and camel, and then advance rabbits in order to threaten goal.
Realizing that Gold is poised to take control, what should Silver do? Silver needs to free his elephant. Silver could give up his camel in exchange for a horse: if the silver elephant moves to b6, and the silver camel is then captured, Silver can pull the gold horse from a6 into c6, capturing it in return. Alternatively, Silver could unfreeze the camel with his horse and push the gold dog away, burrowing the camel so that it could not be captured in one turn—this is an option only because Gold has neglected to put a piece on b2, which would have fenced in any a3 hostage. Burrowing the camel would only be a delaying tactic by Silver, since the camel would hardly be free, but it would allow the silver elephant to leave c3 temporarily.
Whether or not one can get immediate compensation for a camel loss, it is crucial that one's elephant be freed from a hostage which gives the enemy the strongest free piece. The best answer to a camel hostage is to rotate out one's elephant. Two other pieces can defend the trap if they have support behind them. 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 turned and Silver's elephant is the strongest free piece.
Because of this possibility, it may be that the gold camel should stay home on defense when Gold has the silver camel hostage. Imagine that the gold camel were at home in the diagram at right, lurking on d2 for example. Once the silver elephant left the f3 trap, the gold camel could confront the new silver defenders. Silver would then have to scramble to prevent multiple captures.
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. Likewise, the gold camel isn't really a free piece, because it needs to lurk around in order to keep the silver elephant committed to defending c3.
As it turns out, the gold horses are suddenly the strongest free pieces. Gold can't yet force a capture at home, but he can use both horses to take over an enemy trap (most likely f6), threatening captures and ultimately goals. Silver might then move his elephant to the defense of that trap, and further threaten one or both of the gold horses with capture, but in that case Gold will stand to gain even more than that in c3 and f3. Gold's upper hand traces back to the camel hostage.
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.
Camel hostage value
When Gold is holding a camel hostage, both sides are usually keen to advance on opposite wings. Gold wants to advance on the non-hostage wing in order to secure material and goal threats, using the strongest free piece as necessary. Meanwhile, Silver wants to advance on the hostage wing in order to rotate out her elephant. The value of the hostage depends on the outcome of this race, and therefore on the initial positions of the pieces. The hostage will tend to be worth more if the gold camel is already on the non-hostage wing, and less if gold pieces (particularly the horse) are stuck behind the hostage.
Another plan available to Silver is to abandon the camel and seek compensation elsewhere. It is typically hard for Gold to make use of the hostage without exposing a horse to capture. Since a camel is worth approximately a horse and cat as an initial trade (see Relative Value of Pieces) it is not usually worth giving up more than a cat to get a camel hostage. On the other hand, if the opponent is well-positioned for a quick elephant rotation, the hostage can be of negative value.
Other hostage patterns
At right (game) Gold is holding a double hostage of the silver camel and horse. A double hostage is worth significantly more than a simple camel hostage, for two reasons. Firstly, since more material is threatened, the silver elephant will find it harder to abandon the hostages and get adequate compensation. Secondly, with the g2 horse unable to fight for control of f3, it will be difficult for Silver to rotate out the elephant. Note also how the horse contributes to the blockade preventing the camel from escaping.
One tactical resource available to Silver in this position is to occupy g4 with a weak piece. If the silver elephant then leaves, the gold elephant would not be able to stay on g3 while capturing a hostage, so the second hostage might escape. Gold must take this into account; for example, it may not be possible for Gold to advance his camel unsupported.
In this game, Gold has a high hostage. This type of pattern is less common than an ordinary camel hostage, since more pieces are required to maintain it. In this case, the hostage is unstable, as the silver horse can erode the blockade on b4 and then unfreeze the camel. If a high hostage can be maintained, it is more valuable than an ordinary hostage because the gold elephant remains centralised, making it harder for Silver to share control of c3.
A central camel hostage often results in the loss of the camel, since if the hostage-taker has good control of their home traps, the camel can simply be forked between them. In the example at right (game), the blockade on d2 prevents the camel from escaping, and the silver elephant can cover only one of c3 and f3. Such hostages are therefore more in the realm of tactics than strategy. TODO: find better example.