Arimaa/Introduction to Strategy/Camel Hostage
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. For now, Silver can't defend with less than the elephant, because any other silver defender could itself be captured in c3, unless there were two weaker silver defenders securely in place, which would require some work.
The hostaged camel is not held right next to the trap, because then it would help Silver control the trap, while the gold elephant would not defend the trap. In this case, that would allow Silver to capture the gold cat.
If Silver ever abandons his camel, the gold elephant should then pull it into the trap, finishing on c4 or d3, near the action. It is thus important that the gold cat remain on c2.
For now, Gold's elephant is tying up Silver's elephant and camel both, leaving Gold's camel unopposed as the strongest free piece. While things stay this way, 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 its camel.
Use of Free Pieces
As the strongest free piece, Gold's own camel is key to his advantage. However, that does not mean the camel should simply march forward. Imagine in the above diagram that instead of the horse, the gold camel were on a6. Silver to move could send her 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.
Even if the gold camel advanced on the other wing, it would have to be careful. Gold might advance his camel expecting that, if the silver elephant went east, the gold elephant could take care of everything. However, the silver elephant would have a head start while the gold elephant captured the silver camel, and other silver pieces could temporarily block the gold elephant's path to e6 or f5; Gold can't just assume his elephant could get there in time to save an advanced piece. Remember also that an advanced piece can retreat only if it is not frozen.
Usually, at least one horse should advance first. Besides protecting the friendly camel, advanced horses can also protect weaker pieces. The gold horse on the west wing is 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 Silver 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 the camel hostage, Gold wants to make a strong second threat and force the silver elephant to choose which to defend against. If Gold wants to take over an away trap, his own camel will likely have to advance in the east. Another option is to keep the gold camel where it is, and use the eastern gold horse to drag weaker pieces down for capture in f3. As long as the camel hostage remains in place, the silver horses are the strongest silver pieces which could defend f3, but that would be difficult with the gold camel right there. Indeed, the gold camel could hostage a weak piece much as the gold elephant is hostaging the silver camel, and the silver elephant couldn't defend both. If Silver doesn't abandon her camel, find some other way to defend it, or find such a way to defend f3, Gold can do this over and over, decimating Silver's forces.
Realizing that Gold is poised to take control, what should Silver do? Silver needs to free her elephant. In this case, Silver could give up her 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. That is a material loss for Silver, but not a bad deal considering the position she was in. Alternatively, Silver could use her horse to unfreeze her camel, which could then push the gold dog aside, burrowing the camel so that it could not be captured in one turn. This is an option only because Gold has left b2 empty; gold pieces on a1, a2, and b2 would form a phalanx, fencing 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.
If it's Gold turn, Gold can prevent Silver from doing either of those things. To fence in the silver camel, Gold could simply advance the b1 rabbit to b2, but a better option would be to slide the a2 dog to b2, the a1 rabbit to a2, and the b1 rabbit to a1; that way, the dog isn't blocked in. On the fourth step, the a6 horse could move to a7, precluding an immediate camel-for-horse trade.
When the enemy has the strongest free piece, it is crucial to free one's own elephant within a few turns. Depending on the balance of forces near the trap, this can sometimes be done without giving up the camel; if two weaker pieces can defend the trap, the elephant can leave. 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.
Such a scenario highlights one advantage of keeping the friendly camel home on defense while holding a camel hostage. Imagine that the gold camel were at home in the diagram at right, lurking on d2 for example. The e3 dog, and thus the f4 dog and g2 camel, would not be safe unless the silver elephant stayed nearby.
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.
Camel hostage value
When Gold is holding a silver camel hostage in Gold's home territory, 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.
If Silver is not well-positioned for an elephant rotation, she might abandon her camel and seek compensation elsewhere. For Gold, the hostage value depends on what compensation Silver could get, and what the resulting position would look like. It is typically hard to make use of a camel hostage without exposing a friendly horse to capture. Since a camel is estimated to be worth 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. If the board is full, and Gold takes a camel hostage but gives up a cat in the process, and then Silver abandons her camel but captures an enemy horse in return, material is basically even. If this sequence happens after material has already been exchanged, Silver likely comes out ahead, and thus the hostage was a net loss for Gold even though he captured the silver camel.
If Silver is well-positioned for a quick elephant rotation, a hostage is likely of negative value for Gold. One should not aim to take a camel hostage if the opponent could defend it without their elephant.
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 option for Silver is to occupy g4 with a weak piece. If the silver elephant then leaves, any capture the gold elephant could make would land it on a square other than g3, so the second hostage might escape. Gold must take this into account; for example, if Gold advanced his camel and then it was threatened, Gold might only get an even camel trade, despite having held a double-hostage. Gold would further have to deal with an enemy horse moving through his own back row, now with no camel to threaten it.
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 quick capture of the camel; 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.