Arimaa/Introduction to Strategy
Strategy is focused on long-term positions. A one- or even two-turn goal threat is a tactic, but a plan to clear space for an eventual goal is a strategy. A capture threat is a tactic, but a plan to make captures easier is a strategy. A move to save a threatened piece is a tactic, but a plan to keep one's advanced pieces safe is a strategy.
The ultimate object of Arimaa is to get a rabbit to goal. This requires that space be cleared, but not necessarily via captures; a game can finish with all pieces remaining. The question is how to best begin. Should one immediately try to rip a hole in the goal line and then march a rabbit through? If one side goes for a quick goal and the other doesn't, which side is better off?
It is best not to treat the whole game as a race. Defending one's home territory is important; a player who neglects home defense will tend to lose to one who prioritizes it. Getting a rabbit to goal will likely require several intermediate steps, although one might get an early goal if a careless opponent leaves a hole open.
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. Remember that an advanced rabbit can't retreat, and thus is 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, strong capture threats are usually needed to move things along. 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 piece which tries to prevent a capture might be captured itself.
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 easier to forcibly 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. Using his camel, Gold can make a threat in the east, overloading Silver's defences. Having the strongest free piece is often a large advantage.
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. However, holding a hostage can be costly. If the elephants are deadlocked at one's home trap, that is a 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 can't simply leave, as the former hostage could 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; if its friendly pieces do advance toward the trap, they might eventually defend it without the elephant.
For these and other reasons, one should be selective about hostage-taking. 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 take a long-term horse hostage. A camel could take a horse hostage, but a hostage-holding camel might be vulnerable to the "defending" elephant. Even if taking a hostage would give one the strongest free piece, one must consider how quickly that could change, and what could be accomplished in the meantime.
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 the elephant. If the enemy camel begins decentralized, a horse should probably advance on the other wing, and the elephant should try to stay between its advanced horse and the enemy camel. In the game shown, the silver horses advanced with impunity because the gold camel was far away.
Trap control concerns one's ability to make capture threats and defend against capture threats in a particular trap. Advanced pieces can create capture threats in both home and away traps. Here, Silver threatens a gold dog in c6, and many gold pieces in c3. Gold is not currently threatening capture anywhere; the c7 rabbit and f7 cat are potential targets, but Silver could easily add a second defender to either trap, and/or stop an attacking gold piece. If the a6 dog weren't frozen, it actually could capture the c7 rabbit in one turn and set the stage for more captures in c6, so Silver shouldn't get complacent. However, Gold is the one with problems, as Silver can make multiple captures in c3 unless the gold elephant moves to c4. That would leave the a6 dog to be captured in c6. By taking control of c3 and still sharing control of c6, Silver has established two strong capture threats.
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 camel could have countered anything the gold camel did. Away trap control creates a space advantage, capture threats, and potential goal threats. Had Gold taken control of f6 sooner, there might have been a capture race.
Home and away games
If pieces cannot safely advance on a wing, the opponent might pull them in order to threaten capture. There are therefore two basic plans: advance pieces with the aim of controlling an away trap, or pull enemy pieces homeward with the aim of hostaging or outright capturing them. Since rabbits cannot retreat, they could in principle be pulled out gradually over several turns. 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 find ways to use the pulled pieces to his advantage. Homeward pulling has its place, but should perhaps not be one's main strategy.
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.