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 gold elephant must be next to the trap, to prevent the silver elephant from capturing a gold piece in that trap. A hostage is usually not held right next to a trap, as that would prevent the hostage-holder from protecting the trap.
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. The silver camel obviously can't defend any trap, and the silver elephant can only defend one trap at a time. This makes the gold camel a grave threat in the east.
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; Silver would be happy with an even camel trade. Gold might think his elephant could capture the silver camel and still protect his own camel. However, if the gold camel advanced, the silver elephant went east, and then the gold elephant captured the silver camel, 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 a blocked or frozen piece.
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 threaten captures in f6, his own camel will likely have to advance in the east, since a silver horse could defend a trap from a gold horse. 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 (remember, rabbits can't retreat homeward). 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. It might seem best for Silver to protect the camel instead of a weak piece, but consider that Gold can repeat this again and again if there is nothing to stop the camel and horse in the east.
Realizing that Gold is poised to take control, what should Silver do? Silver needs to free her elephant. In this case, Silver could trade her camel 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.
Gold to move 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, the arrival of the silver dogs has freed the silver elephant to roam. Suddenly the tables have turned and Silver's elephant is the strongest free piece. This is a bad position for a hostage-holder, made worse by the advanced silver rabbits, which would surely reach goal if the gold elephant left. Gold is strategically lost.
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.
In this game, diagrammed at left, Gold cannot force a capture in either c3 or f3, despite holding the silver camel hostage and having two strong gold pieces on the other wing. The well-positioned silver elephant prevents any capture in f3, while also protecting the silver horses from the gold camel.
Who has the strongest free piece now? If the gold elephant leaves the c3 trap, Silver will soon wipe out Gold's western forces. As things are, however, the silver elephant isn't totally free either; if it returns to its home territory, the silver horses will be vulnerable to the gold camel. Likewise, the gold camel isn't really free, as it currently can't go anywhere without quickly being confronted by the silver elephant, which could safely leave e3 if the gold camel advanced. The elephants, camels, and silver horses are basically in a stalemate.
As it turns out, the gold horses are the strongest free pieces. Gold can't yet force a capture at home, but he could create strong second threats in enemy territory. The two gold horses could work side-by-side, but there is an even better option which allows Gold to keep a horse on each wing: the f2 dog could advance and help the gold horse attack f6 (a gold cat or rabbit would replace the dog on f2). The silver elephant might then move to the defense of f6, and perhaps even capture both the dog and horse, but Gold could capture even more in c3 and f3; the silver horses might both escape, but that would give Gold time to capture the camel and still protect his advanced pieces. Gold's upper hand traces back to the camel hostage.
|Each side currently has an elephant, camel, and horse tied up in this hostage position. (game)|
Though the position at right may appear hopeless for Silver, neither side has a clear advantage in free pieces. Despite having rotated out of direct hostage defense, the gold elephant is not free, as it is the only thing between its northeastern army and the silver camel. Of the four horses, the silver horse on c2 may be the most free; if it moves east, the pressure will be on Gold.
Camel hostage value
When Gold holds the silver camel hostage in the southwest, Silver likely wants to advance pieces in the west while Gold wants to advance in the east. Gold wants to create a second threat using the strongest free piece, while Silver wants 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. Such a camel hostage will tend to be worth more if the gold camel is already on the non-hostage wing, and less if a strong gold piece is stuck behind the hostage. Ideally, the free camel and a friendly horse will work together on the non-hostage wing, while the other friendly horse will be active on the hostage wing, preventing a successful elephant rotation. This is not the only alignment for an effective hostage, but the free pieces are always key, and there is limited time to maneuver them.
If Silver is not well-positioned for an elephant rotation, she might abandon her camel and seek compensation elsewhere. It is often hard to make use of a camel hostage without exposing a friendly horse to capture, so the value of a camel hostage is related to the value of a horse-for-camel trade. A camel is estimated to be worth a horse and cat as an initial trade, so one might say that a camel hostage is worth a cat when the board is full, and less after even material has been traded. Occasionally, one must actually decide whether to save a weak piece or take a hostage.
If Silver is well-positioned for a quick elephant rotation, a hostage might be 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. With three strong silver pieces tied up, Silver's counterplay options are quite limited. Unless Gold is reckless in the west, Silver cannot hope to abandon the hostages and remotely make up for a camel and horse loss. With Gold's large advantage in free pieces, elephant rotation would also be quite difficult for Silver. The silver camel can't escape, due to a phalanx which the frozen g2 horse is part of.
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. If the silver elephant moved west and threatened a gold piece, Gold might only capture one piece in return, despite having held a double-hostage. Realizing that Silver could complicate things by stepping a rabbit or cat to g4, Gold should be careful not to expose his camel to quick capture, since he might only get an even camel trade, and then would have 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 has the advantage of the attacking elephant remaining centralised.
A central camel hostage is essentially a camel fork. In the example at right (game), the d2 and c3 phalanxes prevent the camel from escaping, and the silver elephant can't defend both c3 and f3. Such hostages are therefore more in the realm of tactics than strategy. TODO: find better example.