Arimaa/Introduction to Strategy
Strategy is focused on long-term positions. A threat may create an advantage which can gradually be built upon, even if no captures happen for a while.
If he is not distracted by a camel or dog capture opportunity, Gold to move can easily stop the silver goal and threaten the advanced silver rabbit with capture. (Game)
The ultimate object of Arimaa is to get a friendly rabbit to goal. However, an advanced rabbit is a goal threat only when there is a substantial opening in the goal line. Even an apparent goal path can often be closed easily, although a weak opponent might not notice that he has left such a path open.
Until stronger pieces have established a viable goal path, it is a mistake to regard a rabbit advance as progress toward a goal. A quick rabbit advance may be costly, since an advanced rabbit can never retreat. Defending a rabbit from capture is often untenable, as an elephant has more important things to do, and any other defender could be captured itself.
In short, going for an early goal is a poor strategy which can quickly set one back. Nevertheless, a goal path must eventually be cleared somehow.
Because the gold elephant was decentralized, Silver was able to fork a gold dog. (Game)
While a game can finish with minimal captures or even no captures, capture threats are important. A piece is captured only when it is on a trap square with no friendly piece beside it; there are many ways to prevent a capture. If nothing else, the defending elephant can camp out beside a trap where there is a capture threat; since nothing can dislodge an elephant, its friendly pieces can never be captured in a trap it stays next to.
The key to progress is to make strong threats around two different traps. The enemy elephant can only defend one trap, and any other defender or rescuer could itself be at risk.
The simplest double threat is a fork between one's home traps. If a piece can be flipped in the center, it may be doomed to such a fork. This is one of many reasons both elephants might stay near the center. Although any piece can unfreeze a friend, an elephant can do so without putting itself at risk.
A rabbit near the center could be an easy target for a fork, since rabbits can't retreat homeward. This is one reason rabbits often do not begin in the middle. A piece might be dragged up a flank, but this would not in itself force a capture, as it would create a threat in only one trap. Many flank pulls are not worth the time they use up, though certain threats can be game-changing; if an elephant is stuck defending its camel, neither piece can counter the enemy camel elsewhere.
In this game, the silver camel has been taken hostage.
In the diagram, Gold has taken the silver camel hostage, threatening to capture it in c3 if the silver elephant leaves. The c4 cat could not defend the hostage alone, as the cat could itself be captured if the trap had no other silver defender. Since an elephant beside its home trap could normally pull a non-elephant enemy piece into the trap, this type of hostage can only be defended by an elephant or by a team of well-placed weaker pieces. A solid camel hostage will make the forces asymmetrical: with the gold elephant holding the silver camel hostage and the silver elephant defending it, the gold camel is the strongest free piece. Until something changes, there is not even a threat to a gold horse. With the gold camel and horse both active in the east, Gold might soon overload Silver's defenses. Having the strongest free piece is a large advantage, if that piece is well-positioned and supported by other pieces.
Without a strong alignment, holding a hostage can be costly. An elephant deadlock at one's home trap is a potential space disadvantage, since the opponent can safely advance pieces toward the deadlocked trap, but the home elephant is not available to ensure safe advances of its own friendly pieces. A home hostage-holder often can't easily leave, as the former hostage might then team up with its elephant to force captures in the trap, clearing space for a goal. In fact, the defending elephant often has better prospects for leaving; its friendly pieces might swarm the trap and soon defend it independently. That could be a devastating turn of events for a hostage-holder, as the enemy elephant would become the strongest free piece. To prevent an easy rotation by the defender, a hostage-holder should usually have an additional strong piece standing guard.
Given such costs, one must be selective about hostage-taking. Generally speaking, it is no good for an elephant to hold a horse hostage while the enemy camel is elsewhere. Conversely, it is usually fine for an elephant to defend a horse hostage held by the enemy elephant, as the opponent would have to tread carefully to avoid offering a horse trade or even a camel-for-horse trade.
A camel could take a horse hostage, but a hostage-holding camel might be vulnerable to the "defending" elephant. To maintain a hostage position, a non-elephant hostage-holder may need supporting pieces. A solid horse-by-camel hostage can be quite effective, however, if the hostage-holder's own elephant is free.
Silver has taken control of the c3 trap, creating a large problem for Gold.
If a piece cannot be taken as a strong hostage, it can safely advance along with its elephant. If the enemy camel can be cut off from one wing, a horse might quickly advance on that wing. In the game shown, the silver horses advanced with impunity because the gold camel was far away; Gold could have decentralized his elephant to hostage a silver horse, but that would have been a bad move overall.
To own a trap square is to be safe from capture therein while the opponent is not. A trap attack entails an attempt to gain ownership of an away trap and thus threaten several quick captures. Here, Silver has a strong attack on c3, where he can clean up unless the gold elephant moves to c4, which would leave the a6 dog to be captured in c6. An elephant can usually defend against a trap attack, but then will not be available elsewhere.
Seeing his overall weakness in the west, Gold looked east and counterattacked f6, but this was too late; Silver captured two gold pieces in c3 and then forced a rabbit through to goal. Even had the gold elephant defended c3, Gold's long-term prospects would have been bleak; more silver pieces could have advanced in the west, and the silver elephant likely could have gone elsewhere while a team of weaker silver pieces forced the gold elephant to stay beside c3. A strong trap attack will create a space advantage, capture threats, and potential goal threats. Had Gold attacked f6 sooner, a capture race might have ensued.
Home and away games
There are two basic plans: try to take control of an away trap, or aim to create capture threats at home. Since rabbits can't retreat, they can be pulled out gradually. Rabbit pulling was once routine, but fell out of favor as trap attacks caught on. One who simply chases and drags pieces may quickly find a home trap under siege. Homeward pulling has its place, but should perhaps not be one's main strategy.
Instead of thinking in terms of home and away play, one should think about the whole board. For a while, any possible move could be met with a solid defense or counterattack. The object is to attain the stronger overall position.
The gold camel is in little danger of getting stuck against the edge, as it could be unfrozen from above or from below. (Game)
The elephants are extremely important, but cannot do everything at once. A recurring theme in Arimaa strategy is elephant mobility. Sometimes an elephant gets blockaded, but more often it is restricted by the cost of leaving a particular trap. Before getting into a position that will require one's elephant to stay put, one must consider the opposing elephant's situation. If one elephant is even slightly more free than the other, this can snowball, since it affects how free other pieces are.
In the opening, camel mobility is of first concern. If a camel becomes stuck against the edge, even in home territory, the effect may be similar to that of a camel hostage. Sometimes a horse quickly advances on a flank, potentially threatening attack but also providing a way of escape for a friendly piece which might get stuck below it. Rabbits may likewise advance on the flanks to keep stronger pieces mobile.
Strategy vs. tactics
Gold has a far superior board, but will lose the game unless he immediately occupies b2. (Game)
Though strategy is vital, tactics should be considered first. A goal wins the game regardless of the rest of the board; a strong position may mean nothing if one forgets to defend goal. Beyond that, one must watch for hanging pieces and false protection. If a player is careless in this regard, the opponent might quickly gain ground.