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; 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.

A hostage piece is usually held two squares away from a trap, so that it cannot function as a defender of the trap. A hostage-holder typically stays right next to the trap, to keep shared control of that 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. The gold camel is thus 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 camels had initially. On a depleted board, a horse hostage may amount to a camel hostage, and dogs may function as horses would in a camel hostage position.

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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. Gold has wisely advanced a horse ahead of it; had the gold camel simply marched forward, Silver might well have gotten an even camel trade, as the silver elephant could have had a head start east while Gold captured the silver camel. Silver could have then frozen the gold camel and also impeded the gold elephant's path to e6 or f5. An even camel trade would be a disappointing outcome for one who had held a camel hostage.

Advanced horses can also protect weaker pieces. The western gold horse might attack later, but right now it is in effect defending the c6 trap. Although restricted by the hostage, the silver elephant can move between c4, d3, and c2, needing only to finish each turn on one of those squares. Such mobility could allow the silver elephant to dislodge a small gold piece and eventually deliver it to the c6 or f6 trap. The gold horses are prepared to defend those traps. The western gold horse 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 that Silver cannot defend against without giving up her camel. A silver horse can defend against a gold horse, so the gold camel will ultimately have to make such a threat. If Gold wants to play it safe, he can keep his camel at home 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 silver elephant defends the silver camel, horses are the strongest silver pieces which could defend f3, but that would be difficult with the gold camel right there. Indeed, Gold could take a second hostage, and Silver would struggle to defend both. It might seem best for Silver to protect the camel at the expense of a weak piece, but consider that Gold can repeat this again and again if there is nothing to stop the gold camel and horse in the east.

Realizing that Gold is poised to take control, what should Silver do? Silver must free her elephant. In this case, Silver to move 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 play hb5ws Da2e ma3s, unfreezing and burrowing her 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 not free it, but would buy Silver time, as Gold would then need two turns just to reestablish a solid camel hostage.

Gold to move can stop 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, this must be changed before he can capitalize. When the gold camel is active, the silver elephant cannot perpetually defend a hostaged silver camel. Fortunately, it might not need to. While one's elephant defends an away trap, friendly 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.

A hostage will often backfire when the hostage-holder has no other strong piece in the area. Were a gold horse or camel nearby, silver dogs likely could not hold both e3 and f4, especially with the silver elephant elsewhere.


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Gold has just freed his elephant, but still has a fight ahead.

On 28g of this game, Gold completed an elephant rotation just in time. Silver had a strong attack in the southwest, but the silver strength concentrated there made the northeastern rotation easier for Gold. Gold had no goal threat and no piece on f6, so the silver elephant had some degree of freedom. Meanwhile, Silver's western goal threat remained formidable; Gold's elephant rotation hardly sealed the game.


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

On 13g of this game, Gold held the silver camel hostage and was strong on both wings, yet could not force a capture in c3 or f3. The well-placed silver elephant prevented 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 southwestern forces. If the silver elephant left e3, the gold camel could go west or north and do tremendous damage. The silver camel obviously isn't free, and the gold camel 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 a potential Silver swarm of c3, which could give the silver elephant more freedom.

The eastern gold horse is the strongest free piece; Gold can soon create an away threat that will force captures somewhere. A double-horse attack on c6 is one option for Gold, but a faster option is to advance the f2 dog and threaten to have it occupy f7, which would constitute a strong attack on f6; a gold cat or rabbit should replace the dog on f2. The silver elephant might go north and make multiple captures, but Gold could more than make up for that by sending his camel west. Even if both silver horses escaped, Gold could capture the silver camel and minimize his own losses, as 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 free 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, horse, and dog tied up in this hostage position. (game)

In the position at left, the silver elephant has been blockaded. Gold appears to have pulled off an ideal elephant rotation, yet neither side has a clear advantage in free pieces. The gold elephant is not actually free, as it is the only thing between its northeastern army and the silver camel. Silver might 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. Such a threat would be stronger if the second silver horse were free; having a friendly horse blocked in weakens a hostage-holder's position.

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. For Gold, a camel hostage will tend to be worthwhile if two strong gold pieces are already on the non-hostage wing, and Silver is not well-developed on the hostage wing. 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 the hostage-holder's free pieces cannot quickly accomplish something, the hostage may be weak.

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. The purpose of a camel hostage is to tie down the enemy elephant and camel, thus freeing one's own camel and/or horse to attack. If the enemy elephant quickly becomes free while one's own elephant remains effectively stuck, this has backfired badly.

Rotation strength[edit]

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This is typical of a successful elephant rotation; a team of silver pieces has freed the silver elephant and cornered the gold elephant. The a4 rabbit assures that the silver dog could step right back to c4 were it pulled to b4. The c3 rabbit blockades the trap; if c3 were clear, the gold elephant could push the horse to e3, perhaps threatening it in f3 if the overall position allowed for that. The gold elephant must stay beside the trap, as Silver could quickly goal if space were cleared.
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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.

The gold elephant has some mobility, as Silver does not yet have a strong goal threat in this quadrant. Gold could push the camel to b1 and slide the c3 rabbit to b3, clearing space for further maneuvers. This is a possible advantage of holding a hostage on b2; the hostage could be buried if necessary.

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The gold horse in the trap makes rotation difficult for Silver. If the silver elephant leaves, Silver will have to keep the gold horse off of c4 or d3; if the gold horse got onto either square with the silver elephant elsewhere, the silver camel likely could not be saved unless the silver elephant returned.

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

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The trap is clear, but the gold elephant can't move through it, as the trap currently has no other gold defender. The silver elephant has left the quadrant, but may still be nearby; how free it is depends on the rest of the board. Gold could become very strong if he could threaten the silver dog or horse, as those pieces and the silver camel could potentially fall like dominoes. Once again, the a4 rabbit ensures that the silver dog could return to c4 if pulled to b4. The a2 and b2 gold rabbits are also key to Silver's position; if Gold could clear b2, the silver horse would not be safe on c2, from where it could be pulled to b2. That would give Gold a double hostage and also allow a gold defender to occupy c2.

If the silver horse and dog are safe, this is a strong position for Silver. 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, b3 may be vulnerable. Here the gold horse may not be able to stop an elephant rotation, as Silver could occupy b3 and b4 if the gold horse stepped east. A hostage held behind the trap 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, 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. Though not currently frozen, the silver camel can't escape, as h2 is blocked by a phalanx which includes the frozen g2 horse.

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, which would free and strengthen the southeastern silver horse. In fact, this horse could then help create a formidable goal threat.

High hostage[edit]

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Gold has an unstable but valuable high hostage. Game

A high hostage is held on the fourth or fifth rank. This is a relatively rare pattern, as it is tricky to maintain, but it is always good to have one's elephant centralized if possible. This high camel hostage is unstable, as the western silver horse can eventually reach b4 and unfreeze the camel. The gold horse on c5 could then be lost in c6, so this is a risky position for Gold. It may be easier to hold a high hostage on a depleted board, as Silver did in this endgame.

Central hostage[edit]

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A central hostage may face capture threats in two different traps.

A central hostage is held on the d- or e-file. If the hostage-holder has good control of both home traps, a central hostage can soon become a fork: Silver can play ed6s Md7s cc8s df6e, and Gold cannot defend both c6 and f6. This hostage position is more tactical than strategic; Silver gave up a horse to trap the gold camel. If the capture cannot be forced, the value of a central hostage might be similar to that of an ordinary hostage.