Arimaa/Introduction to Strategy/Other Hostages
Other than the elephants, any piece can potentially be taken hostage, and often the elephant is the only friendly piece which can feasibly protect it. The value of such a hostage depends largely on which side is left with the strongest free piece.
|The horse hostage does not benefit Silver, since the gold camel is more free than the silver camel (from this game).|
Not all hostage positions are effective. Even with camel hostages, the hostage-holder is often more stuck than the defender, since the hostage could become an attacker if freed. This gets worse if an elephant holds a horse hostage instead, as in this diagram. If the silver elephant left the trap, the gold horse would likely help its elephant make captures, perhaps decimating Silver's eastern forces. Thus both elephants are basically stuck, but consider the overall position. Gold would gladly trade his horse for the silver camel, thus the silver camel must be careful, especially since it could be forked between c3 and f3. The gold camel is not at risk of anything like this; if the silver elephant left the northeast, Gold could likely make progress there before Silver could threaten the gold camel, which could easily be defended in the west. The camels are the strongest free pieces, but Gold's camel is more free, thus the hostage does not give Silver an overall advantage. When the enemy camel is still on the board, an elephant must be careful about what else it commits to.
As long as the gold elephant defends f6, it should stay on e6. If e6 and e7 were clear, the silver elephant could pull the gold horse onto e7 and then fork it between traps. That is a possible advantage of positioning a hostage-holder behind the trap.
In some cases, a horse-by-elephant hostage might be converted to a frame, or passed off to the silver camel, freeing the silver elephant. If Silver were better positioned for that, it would be urgent for Gold to prevent a solid frame or horse-by-camel hostage, which could make the silver elephant the strongest free piece.
Gold can treat this position somewhat like a camel hostage, advancing pieces on the hostage wing so that two weaker defenders can replace the gold elephant. This could be relatively easy, since Silver does not have the strongest free piece. After this, the gold elephant and camel might attack the c6 trap. Alternatively, the gold camel might go east to defend f3 against a counterattack.
A horse-by-elephant hostage may be effective if it makes one's own pieces stronger. In this game, each side has lost a camel and horse; Gold has the last remaining horse, but this is balanced by Silver's dog and rabbit advantage. The hostage makes the dogs the strongest free pieces, and thus Silver has the edge, being up two dogs to one.
When most pieces remain on the board, the right piece to hold a horse hostage is usually the camel. Ideally this ties the opposing elephant to defence, while the friendly elephant is free to roam. However, the situation is often unstable because the "defending" elephant can attack the hostage-holding camel, and thus turn the tables. Thus the camel needs friendly supporting pieces, to keep the advantage long enough for the friendly elephant to make a strong second threat. A good horse hostage can make one's own elephant the strongest free piece, a greater advantage than could be gained from a camel hostage.
These diagrams illustrate different positions for a horse-by-camel hostage. In the first diagram, the gold piece on a4 is necessary for the hostage to be effective: pulling the gold camel to b4 would be a waste of time, as it could simply return to b3. It may take Silver several turns to break this hostage, which should allow Gold to gain a large advantage elsewhere. Note that the b2 cat allows capture of the hostage in case the silver elephant goes to b4. Also, Gold should leave d3 clear; if d3 were occupied by any gold piece, the silver elephant could then afford to move to b4, since the only one-turn capture would end with the gold camel on c4, where it would be threatened in c6.
Without the gold horse on a4, the hostage would be weak. With ec4w eb4e Mb3n ha3e, Silver could have her elephant on c4 and her horse on b3, with the gold camel frozen on b4. Not only could Silver then threaten captures in c3, but she could also flip the gold camel to c5, with a threat to capture it in c6. Without a gold piece ensuring the friendly camel's mobility, Gold would have much more to lose than to gain here.
In the second diagram, the horse is on b2 rather than a3. This means that the horse can more directly join the trap control fight if the camel is dislodged. For instance, if the silver elephant moved to b4, it would then threaten to capture the camel due to false protection. On the other hand, Gold now has the option of pushing the horse to b1, which would make it even more difficult for Silver to free the hostage. If the silver elephant left, the horse could then be pulled back to b2.
In the third diagram, the silver elephant has no easy way to approach the gold camel. As long as Gold can safely occupy b3, the hostage is fairly secure. This can be the strongest type of horse hostage, provided there are enough pieces to maintain it.
In all of these cases, the side defending the hostage should consider bringing more pieces into the local fight. For instance, in the last example Silver would have a strong position if she could bring a horse to b3, dislodging the gold dog. In the first, the silver camel might be able to attack the a4 horse, which would weaken the hostage pattern.
Cat and dog hostages
|In this game, Silver's position would be much stronger if its camel were free and a silver horse held the gold dog hostage.|
A smaller piece may also make a valuable hostage. In this example, the silver camel holds a gold dog hostage next to the c6 trap. The silver elephant is free to pull gold pieces toward the f6 trap. The gold elephant can't defend c6 and f6 at the same time.
However, the situation is less than ideal for Silver, for two reasons. First, the silver cat on c6 means that the c8 dog isn't currently threatened with one-turn capture. If the gold elephant leaves, it will take five steps for Silver to capture the hostage dog, giving the gold elephant that much more mobility. Second, the gold rabbit on h5 gives the gold camel more freedom to advance without fear of being taken hostage by the silver elephant. Silver would probably have to capture the h5 rabbit before making any other threat in f6.
In general, the advantage of a small piece hostage over a horse hostage is twofold. First, the smaller piece can be held hostage by a horse, sparing both the friendly elephant and camel for other duty. Second, it is easier to frame a small piece than to frame a horse. In the diagrammed position, Silver would have a greater advantage if the c7 camel were swapped with the g6 horse. Then the silver camel could defend the f6 trap while the silver elephant either hunted for a second piece to drag for capture, or assisted in framing the hostage dog. As it stands, the silver elephant can't help frame the c8 dog, because of the damage the gold camel would do in the meantime.