Arimaa/Introduction to Tactics
In Arimaa, a tactic is usually a one- or two-turn plan which can be calculated precisely. With up to four steps per turn, plans which aim more than a turn ahead are usually impossible to calculate exactly, and therefore generally belong to the realm of strategy. This is in contrast to chess, where one can often limit the opponent's options enough to have a precise three-turn plan.
The essential tactics are those that bring a friendly rabbit to goal, capture an enemy piece, or thwart the opponent's plan for a goal or capture. If neither side can achieve victory or capture in a single turn, one might work toward doing so in the next turn; the opponent could then counter, perhaps bringing in reinforcements to strengthen a weak area. This quickly gets out of tactics and into strategy.
A rabbit might reach goal within one turn, even if the path appears blocked by a trap square and/or opposing pieces. At left, the gold rabbit on b5 can step to victory via b6, c6, c7, and c8. The rabbit is safe on the trap due to the gold dog on c5, and is never frozen because it is always next to a friendly piece on the way to goal. The rabbit will theoretically be frozen once it reaches c8, but Gold will have won regardless.
Pulling away an opposing piece may allow a blocked rabbit to advance. If the gold cat on h7 moves to h6 while pulling the silver rabbit from g7 to h7, the gold rabbit on g6 can then reach goal in the turn's final two steps. The gold camel on f6 is lost when the rabbit advances, but reaching goal is worth any sacrifice. Beginners often incline more toward pushing than pulling, but note that a push is ineffectual here. If the gold cat pushes the silver rabbit, the cat will itself block the friendly rabbit, which can't then reach goal in the turn's final two steps.
Near a depleted goal line, an enemy rabbit is a constant threat. Silver to move could push the gold horse on b3 to c3 with the silver camel moving from b4 to b3. This would unfreeze the silver rabbit on b2, which could then step to victory via a2 and a1. Occasionally a blocked and frozen rabbit can be unblocked and unfrozen at the same time. Silver to move could slide the silver elephant from g3 to f3, pulling the gold rabbit from g2 to g3; the newly unfrozen f2 rabbit could then step to the vacated g2 and then to g1, winning the game. The silver elephant would be lost on the third step, but since Silver wins immediately, the elephant loss is of no consequence. With the silver rabbit beginning the turn blocked in all directions and also frozen, this one-turn goal is very easy to overlook.
In the above position, each side to move can win the game, but pretend that Silver does not have a one-turn goal. Silver would then have to stop both Gold goal threats. Fortunately, this can be done in four steps. To block the eastern goal, Silver must occupy g8 and still also occupy f8, since moving the f8 rabbit to g8 would open a different goal path. To stop the western goal, Silver can likewise block it, or can use the b4 camel to push the b5 rabbit to a5.
Suppose Gold had to stop Silver's goals. The f1 dog could push the rabbit into the trap, which it couldn't easily get out of (per the rules it couldn't step itself to f4, and if the silver elephant stepped away, a silver piece in the trap would be lost.) To stop the western goal in two steps, the c2 horse must push the rabbit to a2; any other two-step option would still allow the silver camel to unfreeze the rabbit and get it to goal within four steps. If the b2 rabbit were the only silver goal threat, Gold could capture it in four steps, since Silver is currently not defending c3.
A non-elephant piece next to a trap is vulnerable. With Gold to move in the position at right, the gold elephant can step from d5 to c5 to b5, and then push the b6 dog into the c6 trap. Since there is no other silver piece next to the trap, this captures the silver dog, in one turn.
Sometimes one may need to push aside an obstructing piece to get at a vulnerable piece. With Gold to move, the g6 camel can push the g7 cat to h7; now on g7, the gold camel can push the f7 horse to f6, capturing it in a turn where one friendly piece pushed two different enemy pieces.
A piece on a trap square will be captured if its sole defender is dislodged. Silver to move could step the silver elephant from d4 to c4, then to b4, and then dislodge the b3 dog, capturing the c3 horse.
Since it is two squares away from an unprotected trap, the g2 cat can be captured in four steps. The dog could end the capture on any of three squares: f4 (after two pulls via f3), f2 (after two pushes via g2 or two pulls via f3) or g3 (via g4, with a pull followed by a push). The latter maneuver, where a piece returns to its initial square after moving an opposing piece two squares, is known as a flip.
Often, the best defense against capture is to move away the threatened piece. By defending the c3 trap, the silver elephant is protecting the b3 cat, but there is currently a better solution that does not tie down either piece. The silver elephant could step to b4, unfreezing the b3 cat, which could then step to a3 and then to a4.
Other than that, the simplest capture defense is to station one's elephant next to a trap square. Since an elephant can't be dislodged, no friendly piece can be captured in that trap until the elephant chooses to leave. At left, no gold piece can be captured in c6, and no silver piece can be captured in c3, unless the respective elephant moves away.
A non-elephant can sometimes defend a trap alone, but that is usually precarious. The enemy elephant may lose something if it moves away from a different trap, but if it captures a stronger piece in return it was worth it. If any non-elephant is the sole defender of a particular trap, it must keep a constant eye on all enemy pieces stronger than itself.
Two non-elephant pieces can defend a trap together; this is called mutual protection. Since a trap's four key squares are not right next to each other, four steps are not enough for any single attacker to dislodge one defender and capture the other. At left, Silver has defended the c6 trap with a dog on b6 and a rabbit on c7. Even if the gold elephant started on b5, it could not immediately capture anything in c6. Gold could at most dislodge the dog to set up a capture threat for the following turn, but then Silver could add another defender, such as the d7 horse.
Instead of adding a second defender to a trap, one can sometimes obstruct the path of an attacking piece. The gold camel on g6 can't capture the silver horse on f7, because the silver cat on g7 is in the way, and the silver rabbits on h7 and g8 prevent the cat from being pushed. Gold could pull the cat to g6, but that would only make it a second defender of the northeast trap. The silver pieces on f7, g7, h7 and g8 form a phalanx blocking the gold camel.
One counter-intuitive way to block an enemy's path is to station a friendly piece on a trap square in front of another friendly piece. The silver elephant could push the gold cat to d3, but that would temporarily give the c3 trap two gold defenders, making it impossible for Silver to capture anything in the final two steps. This only works because there is nothing else to immediately threaten the c2 dog; if it were dislodged with the cat still on c3, the cat would be lost.
In the southeast, Silver to move can step the g3 camel into the trap, where it is safe due to the silver dog on f2, and then capture the gold horse by pulling it into the trap. Gold to move could prevent this: if the horse steps to e2 and then back to e3 while pulling the f2 dog to e2, and then the f1 dog steps to f2, the gold horse and dog mutually protect the trap. This four-step maneuver is called a pull and replace.
A last resort capture defense is scattering, i.e. retreating threatened pieces away from a trap to the edges and corners of the board. Scattering may only delay captures, if the weak pieces have no safe place to go. Furthermore, scattering away from a home trap may leave a hole through which an opposing rabbit can march to goal. On the other hand, delaying captures may buy time to make progress elsewhere on the board. Scattering is most effective when one has strong threats of their own in enemy territory, and could reach goal first.
More capture patterns
It is easy to become too confident about one's defense. At right, Silver has two pieces next to the northwest trap, but Gold has a stronger piece next to each, and thus has a one-turn capture. First the gold elephant can push the silver dog from b6 to c6, and then the newly unfrozen gold cat can push the silver rabbit from c7 to c8, capturing the dog. If Gold prefers to capture the rabbit instead, he can pull the dog away, and then push the rabbit into c6. This situation, where one defender can be dislodged and the other captured, is known as false protection. Such a capture is only possible if there are two attackers, each adjacent to a weaker defender.
Around the northeast trap, the silver camel cannot push the gold dog into the trap, since the horse is in the way. However, Silver can play a split capture: the camel pushes the dog to g6, then the horse pulls the dog into the trap.
In the southwest corner, Gold has calculated that even if the silver elephant pushes the gold rabbit from b4 to a4, the b3 horse cannot be pushed. This is correct but insufficient, because the silver elephant may still pull the gold horse from b3 to b4, capturing the gold camel on c3.
The southeast shows that a weak enemy piece in a trap square may not prevent a one-turn capture. The f3 dog can simply step east or west, leaving three steps for the f4 horse to enter the trap square and pull the gold dog from f2 to f3, capturing it. If instead a gold piece were on f3, Silver wouldn't have a one-turn capture.
The fork threatens a single frozen piece with capture in two different traps. It is a basic two-turn tactic: a piece is pushed onto a square between traps, and is then captured in one or the other, unless the defender can do some heavy-lifting in between. In the diagram at left, from this game, Gold has threatened to capture the silver dog in either c3 or f3. Silver to move would need one step to defend the c3 trap with the elephant, and three steps to defend the f3 trap with the cat. Unfortunately for Silver, the gold rabbit on e4 is threatening to reach goal next turn, and cannot be frozen in place since it is next to the gold elephant; Silver must spend at least one step defending goal, and the silver dog is lost.
Against a weak opponent, a fork can be a way to make a quick capture. If all non-elephant pieces are still in their home territory, and then the gold elephant flips a silver piece into Gold territory, that piece is well on its way to being hopelessly forked. A weak opponent may even lose more pieces while trying to defend the forked piece. A skilled opponent, however, can usually prevent a fork, although that requires a bit more foresight than other tactical defenses; the key is to not leave a piece where it could be flipped directly to a place where it couldn't be rescued from a fork threat. Between skilled opponents, capture via a fork may happen later in the game, when pieces are more scattered and therefore vulnerable.
The fence is a less common two-turn capture tactic. A piece is brought next to an unprotected trap, and hemmed in on two sides. The piece may be unfrozen from a third side, but would have nowhere to go, as the trap is on the fourth side. In the diagram at right, from this game, Gold has fenced the silver horse next to the c3 trap. Silver is to move, but can't prevent the capture of the horse. The silver elephant could unfreeze the fenced horse by moving to c5 (incidentally capturing the gold rabbit in c6), but the unfrozen silver horse can't then escape, as its only available move would be suicide. Furthermore, the gold pieces prevent the silver elephant from reaching d3, c2, or b3 in four steps, and no other silver piece is close enough to defend the c3 trap.
Limitations of tactics
When both players understand these tactics, it will be difficult for either to achieve immediate material gain, since it is easy enough to prevent a one- or two-turn capture if you recognize the threat. In this game, shown at left, Silver has just flipped the gold camel from e3 to e5, and is threatening to capture it in f6. Besides defending the camel immediately, Gold must not let it get forked between c6 and f6. Even if the camel escapes, the b5 horse could be threatened. Despite these tactical ideas, the game ended without a single capture. Although this is unusual, captures in Arimaa are much less common than in chess.
After becoming acquainted with the most basic Arimaa tactics, you should turn your attention to long-term strategy, which will in turn open up more tactical possibilities.