Arimaa/Camel Hostage

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The position at right is a basic example of a camel hostage. If the silver elephant left the trap, Gold could capture the silver camel by flipping or pulling it onto c3. For now, Silver can only defend with 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 stop Silver from capturing a gold piece in that trap. A hostage piece is usually held two squares away from a trap, so that the hostage-holder can be next to the trap.

If Silver ever abandons her 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.

Note:
In Arimaa, the strength and function of a piece depend on which other pieces remain. For instance, if each side has lost a camel and a horse, the remaining horses are the unique second strongest pieces on each side, and so have essentially the role that the camels had initially. In that case, a horse hostage would amount to a camel hostage.

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The gold elephant is holding the silver camel hostage.

Use of free pieces[edit]

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 the elephant 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.

Multi-piece defense[edit]

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The silver elephant has regained mobility, so Gold has no advantage from holding a camel hostage.

When the opponent has the strongest free piece, it is important to change that as soon as possible. Fortunately, an elephant defending a camel hostage can sometimes be freed without even losing the camel. When one's elephant defends an away trap, pieces can safely advance toward it. This often allows one to rotate the elephant out of hostage defense, replacing it with two weaker defenders supported by other friendly pieces. 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 lurking on d2; the e3 dog, and thus the f4 dog and g2 camel, would not be safe unless the silver elephant stayed nearby.

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This hostage position makes the eastern gold horse the strongest free piece.

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-placed 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 left the c3 trap, Silver would soon wipe out Gold's western forces. If the silver elephant left its current position, the gold camel could go west or north and do tremendous damage. The silver camel obviously isn't free, and the gold camel currently can't go anywhere without quickly being confronted by the silver elephant, which could safely leave e3 if the gold camel advanced. The silver horses are not free, as they are defending the silver camel and each other. The western gold horse is not totally free, as it is stopping Silver from strengthening her defense of c3, which would give the silver elephant more freedom.

The eastern gold horse is the strongest free piece. One way or another, it can soon create a second threat that will tie Silver's hands. The f2 dog could advance and help the horse attack f6; a gold cat or rabbit should then replace the dog on f2. The silver elephant might go north and make multiple captures, but the position assures that Gold could win any material exchange. Even if both silver horses escaped, Gold could capture the silver camel and then get his elephant to wherever it was needed, since Silver would have lost time getting her horses to safety.

This example and the next show that an elephant not directly defending a hostage can still be restricted by it. Rather than freeing the defending elephant, an elephant rotation sometimes just ties up more material in the hostage position.

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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. Silver might be tempted to move her camel south to attack c3, but then the gold elephant could safely go south also, becoming the strongest free piece. Silver might do better to send the c2 horse east, where it would be the strongest local piece and could work toward a goal threat.

Camel hostage value[edit]

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. Holding a hostage is useless if one plays passively, so a camel hostage-holder may have to offer what amounts to a horse-for-camel trade; the hostage value is thus related to the value of such a trade. A camel is estimated to be worth a horse and cat as an initial trade, so one might say that a solid camel hostage is worth a cat. This should be kept in mind if one has to choose whether to take a hostage or do something else.

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.

Elephant rotation[edit]

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This is typical of a successful elephant rotation; the formerly defending elephant is now elsewhere, the hostage camel remains safe, and the hostage-holding elephant cannot afford to leave the trap. The a4 rabbit assures that the silver dog could step right back to c4 were it pulled to b4. The c3 rabbit strengthens Silver's trap control, but its main purpose is to blockade the trap so that no gold piece can move through it. If not for the c3 rabbit, the gold elephant could push the horse to e3, perhaps threatening it in f3 if the overall position allowed for that. Also, an advanced piece in a trap can stop an enemy piece from advancing through that trap.
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Here a gold rabbit forms part of the blockade. Since rabbits can't step backward, they can sometimes be used against their own friendly pieces. This is why players often do not place a rabbit behind a trap; if pushed or pulled onto c3, a gold rabbit can't step back to c2.

Gold can try to clear space by pushing the camel to b1 and sliding the c3 rabbit to b3. This is a possible advantage of holding a hostage on b2; the hostage can be buried if necessary.

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The horse on the trap makes this a strong position for Gold. If the silver elephant leaves the trap, Silver will have to block the c3 horse on both d3 and c4; if the gold horse got onto either square with the silver elephant elsewhere, Gold could then capture any silver defender and then the silver camel. On the other hand, if the gold horse goes to c4 while the silver elephant is still nearby, Silver might threaten the gold horse in c6 and still protect c3.

Silver might consider flipping the gold horse away, but Gold could occupy d2 and e3 to prevent this.

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This is likely a poor hostage for Gold. The silver elephant has rotated out, and is now operating elsewhere as the strongest free piece. Unless Silver is very weak on the rest of the board, she could easily defend against anything the gold elephant might try. The a2 and b2 gold rabbits are key to Silver's position; if b2 could be cleared, Gold could pull the c2 horse to b2, taking a double hostage, and Silver would need to bring in another defender.

If the gold camel could reach and dislodge the c2 horse, things might change dramatically; Gold would then have three capture threats in c3, and could perhaps threaten a piece in f3 if Silver defended c3. If the c2 horse is safe, this is a strong position for Silver, but if the gold camel is nearby and the silver elephant is far away, this could soon become a strong position for Gold.

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A hostage held by a c2 elephant alters the usual alignment, since c2 is typically held by a weak piece. With the gold elephant on c2, another strong gold piece will likely have to protect b3. Here the gold horse is effectively stuck, since it is the only thing keeping the silver dog off of b3. This type of hostage may therefore be weak.

If d3 and d2 were unoccupied, the gold elephant could move to d3 and pull the silver camel to d2, perhaps resulting in a strong central hostage. Silver can usually prevent such maneuvers.

Other hostage patterns[edit]

Double hostage[edit]

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A double hostage is stronger than a simple camel hostage.

At right (game) Gold holds 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 left, any capture the gold elephant could make would land it on a square other than g3, so the second hostage could escape or be defended again after an exchange. Realizing that Silver could complicate things by stepping a rabbit or cat to g4, Gold should take care not to expose his camel to quick capture, as he might only get an even camel trade, leaving Silver with a potential goal threat which might lead to a southeastern elephant deadlock more favorable to Silver.

High hostage[edit]

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Gold has an unstable but valuable high hostage.

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.

Central hostage[edit]

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In this game, Silver can force the capture of the gold camel.

Here Silver is holding a central camel hostage. If the hostage-holder has good control of both home traps, a central hostage is very valuable because of forking tactics: Silver can play ed6s Md7s cc8s df6e, forking the camel, and Gold cannot defend both c6 and f6. Such hostages are therefore more in the realm of tactics than strategy; here Silver gave up a horse for the central hostage, and came out ahead. If the camel capture cannot be forced, the value of a central hostage might be similar to that of an ordinary hostage.