Arimaa/Introduction to Strategy/Other Hostages
As long as an elephant is not blockaded, it retains a theoretical freedom to roam the board. There are, however, fine distinctions in exactly how free an elephant is. A whole spectrum of positional features may limit an elephant's field of operation; enemy pieces can block an elephant's access to certain squares, or an elephant may need to stay beside one trap, to prevent significant material loss and/or an enemy goal.
Both elephants start out free, but differences in elephant mobility soon emerge. In Arimaa, tiny advantages often snowball; a more mobile elephant can pose increasingly tricky defensive puzzles for a less mobile elephant. As the game progresses, an elephant can become more and more committed to the defense of a particular trap. When an elephant can't afford to leave a trap, that elephant has clearly lost mobility.
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 defending elephant will lose some mobility, but it could also threaten or isolate the hostage-taking piece, perhaps limiting the enemy elephant's mobility as well.
Not all hostages are good
|The horse hostage does not benefit Silver, since the gold camel is more free than the silver camel. (from this game).|
An elephant holding a camel hostage is only one example of a whole class of positions where a frozen piece is held in danger of capture, committing the opponent to defense. However, not all such positions are effective. Suppose, for example, that an elephant holds a horse hostage instead. This commits the opposing elephant to defense, true, but who has the strongest free piece? The defending elephant can't leave without losing a horse, but the hostage-holding elephant often can't leave either, because the newly-freed horse would cooperate with the formerly-defending elephant to wreak havoc at that trap.
In this diagram, Silver is holding a hostage, but neither elephant wishes to leave the northeast trap square. Indeed, the gold elephant is closer to the center, and is thus a greater threat to the silver camel than the silver elephant is to the gold camel. Since the gold camel has more freedom of movement, Gold may make progress despite having a horse held hostage. Essentially, the inactivity of one gold horse is insufficient compensation for the decentralisation of the silver elephant and for Silver's poor alignment.
In some cases, such a 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. Unless the silver camel comes east, the gold elephant should stay on e6; if e6 and e7 were clear, the silver elephant could pull the gold horse onto e7 with a threat to fork it between traps.
Gold can treat this position somewhat like a camel hostage position, with pieces advancing on the hostage wing to replace the gold elephant in defending the horse. The difference from a camel hostage is that Silver does not have the strongest free piece, which means that there is more time to achieve an elephant rotation. It would be less straightforward for Gold were the gold horse held on h6 with the silver horse on g7: the silver elephant would be able at any time to leave the area while the silver horse blocked the gold horse away from sharing control of f6. In this case, Gold should still be able to make progress by actively using his camel, for instance in an attack on c6.
The right piece to hold a horse hostage is a 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, which could quickly 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 be worth more than a camel hostage, but this depends on the hostage-taker's ability to make quick threats.
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. If Silver had time for these maneuvers, Gold's hostage might in fact be an advantage for Silver.
The second diagram shows a similar position, but with the horse 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, here Silver is threatening to capture the camel by false protection. On the other hand, from b2 the horse can be pushed to b1, where it remains stuck.
In the third diagram, the silver elephant has no easy way to approach the gold camel. As long as Gold retains control of the b3 square, 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 hostage dog isn't 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 like to send his elephant after the gold camel, but in practice will probably have to try to capture the h5-rabbit before this is feasible.
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 the friendly 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 mean time.