Arimaa/Introduction to Strategy
Strategy is focused on long-term positions. If a threat can be defended against, a tactic may become a strategy. Even if a goal cannot soon be forced, a goal threat may create a space advantage, by blocking enemy pieces and compelling them to defend goal. Even if a capture cannot be forced, a capture threat may compel the enemy elephant to stay beside a particular trap. By tying up enemy forces, one can build a whole-board advantage.
The ultimate object of Arimaa is to get a friendly rabbit to goal. This requires that space be cleared, but how? Should one immediately try to rip a hole in the goal line and then march a rabbit through? If one side attempts this, how should the other side respond?
It is best not to treat the whole game as a race. Until a fair amount of space has been cleared, forcing a goal is much harder than stopping a goal. Even if a goal path is opened, the defender can often close it easily. One might get a quick goal against a weak opponent, but a skilled opponent is usually attentive to home defense.
As long as there is no real opening in the goal line, it is futile to advance a rabbit for the purpose of reaching goal. Even if one is aiming for a space advantage, it must be remembered that an advanced rabbit can never retreat, and thus may be quite vulnerable to capture. Generally speaking, it would be extremely wasteful to use one's elephant to protect a rabbit.
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.
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. Since rabbits can't retreat, they are often not placed in the center.
Pieces on the flanks are less vulnerable to a fork. It is often easier to drag down a piece right against the edge, but from there it is harder to force capture if the defending elephant stands in between traps.
If both sides take care to prevent a fork, the threats will have to be more sophisticated.
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. Such a hostage can only be defended by an elephant or by a team of well-placed weaker pieces; here, the c4 cat could itself be captured if the trap had no other silver defender. 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. With the gold camel and horse both active in the east, Gold can soon overload Silver's defences. Having the strongest free piece is a large advantage, if that piece is well-positioned and supported by other pieces.
The risk of a hostage might make one reluctant to advance any piece other than the elephant. Also, one might jump at any chance to take an enemy piece hostage. Without an alignment such as this one, however, holding a hostage can be costly. If the elephants are deadlocked at one's home trap, that 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, which would clear 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.
For these and other reasons, one should be selective about hostage-taking. In general, a long-term hostage should only be held by a just-stronger piece; while the silver camel remains, the gold elephant must always be somewhat prepared to confront it, and thus should not be stuck in a corner while that camel is elsewhere. Conversely, it is usually fine for one's own elephant to defend a horse hostage held by the enemy elephant; if the elephants are deadlocked and both camels are elsewhere, there is no strongest free piece, but the hostage defender usually has a more centralized elephant, which might rotate out of hostage defense, or just trade its horse for the enemy camel if that camel is too aggressive.
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.
In this game, Silver is making threats in c3 and c6.
If a piece cannot be taken as a strong hostage, it can safely advance along with its elephant. If the enemy camel begins decentralized, a horse might advance on the other wing. In the game shown, the silver horses advanced with impunity because the gold camel was far away. Advanced pieces can create capture threats in both home and away traps.
Trap control concerns one's ability to make capture threats and defend against capture threats in a particular trap. A trap attack entails an attempt to control an away trap and thereby overload the opponent's defenses. If nothing else, an elephant could defend its home trap, but that would often give the attacker opportunities elsewhere. Here, Silver has a strong attack on c3, where he can make multiple captures unless the gold elephant moves to c4, which would leave the a6 dog to be captured in c6.
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 kept shared control of c3. Away trap control creates a space advantage, capture threats, and potential goal threats. Had Gold attacked f6 sooner, there might have been a capture race.
Home and away games
There are two basic plans: try to take control of an away trap, or aim to create a capture threat at home. Since rabbits cannot retreat, they are potentially quite vulnerable to capture in enemy traps, although dragging them down can be slow. Early in Arimaa's history, rabbit pulling was considered an important element of opening strategy.
It has become apparent, however, that early pulling cedes valuable space and time to the opponent, who might advance on the other wing or even use a pulled piece to his advantage. 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.
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.