Arimaa/Introduction to Tactics
A tactic is a narrow plan. A precise multi-turn plan would account for every possible move by the opponent, which is difficult when the opponent has thousands of options. Sometimes, however, one can severely limit the opponent's viable options. If a move creates a one-turn goal threat, the opponent must stop the goal or else lose the game. If a move creates a capture threat that if executed would give one a large material lead, the opponent must either stop the capture or somehow mitigate it, perhaps by capturing a piece in return.
Tactics can be offensive or defensive; a defensive tactic may slow things down considerably. When nothing big is imminent, plans may be more general, with each side aiming for a strong long-term position. This gets out of tactics and into strategy.
Each side to move has a one-turn goal on each wing.
At left, the gold rabbit on b5 can step to victory via b6, c6, c7, and c8. The rabbit is never frozen, as it is always next to the b7 cat or c5 dog, which also allows the rabbit to move through the c6 trap. The rabbit will theoretically be frozen once it reaches c8, but Gold will have won regardless.
Even if a rabbit's path is blocked, there may be a four-step goal. If the gold cat on h7 moves to h6 while pulling the silver rabbit from g7 to h7, the gold rabbit on g6 can step to goal. 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 be on g7, blocking its own rabbit with only two steps remaining.
Near a depleted goal line, an enemy rabbit is a constant threat. By pushing the b3 horse to c3, the silver camel would occupy b3 and unfreeze the b2 rabbit, which could then step to victory via a2 and a1. Occasionally a rabbit can be unblocked and unfrozen with one pull. 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 is lost on the third step, but that doesn't matter since Silver has won. With the f2 rabbit beginning the turn blocked and 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 and thus must defend. There are a few ways to stop each gold goal individually, but Silver has only four steps to stop both. To block the eastern goal, Silver must close the path to g8 without opening a different one-turn goal path. This could be accomplished by stepping the h8 cat to g8, leaving three steps for the western defense. In those three steps, the b4 camel or d6 horse could capture the c5 dog and freeze the b5 rabbit. If Silver had only two steps for western defense, the b5 rabbit could be pushed west, or the goal path could be blocked.
Suppose Gold had to stop Silver's goals. The simplest solution is Ee3nww Rh1w, which would freeze and threaten the silver camel while also keeping the f2 rabbit frozen, since unfreezing it would no longer be worth an elephant sacrifice by Silver. If Gold had only two steps for western defense, he couldn't freeze the silver camel, but could impede it.
Even if a goal can be stopped, a one-turn goal threat will force the opponent to use up steps on defense, unless he has a one-turn goal of his own. A move which creates a goal threat is typically part of a multi-turn plan, either to force goal or to force something else that the opponent won't have time to stop. One should always be aware of possible goal paths on both sides, so as not to be caught off guard or miss an opportunity.
Gold to move has one-turn captures in c6, f6, and f3; Silver to move has a one-turn capture in c3.
A piece adjacent to a trap is said to be a defender of that trap. A non-elephant acting as its side's sole defender of a trap is often vulnerable. With Gold to move in the position at right, the gold elephant can take two steps west 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.
One can sometimes 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 her elephant two squares west and then dislodge the b3 dog, capturing the c3 horse.
The g3 dog can capture the g2 cat in four steps, either by pushing it twice (cg2w Dg3s cf2nx Dg2w), pulling it twice (Dg3w cg2n Df3s cg3wx), or flipping it (Dg3n cg2nwx Dg4s). A flip is a pull and then a push, with the flipped piece moving two squares and the flipping piece returning to its original square.
Sometimes, the best way to stop a capture is to move the threatened piece. The silver elephant protects the b3 cat from capture in c3, but neither piece needs to be tied down. The silver elephant could step west and thereby unfreeze the b3 cat, which could then step to a3 and then to a4.
Other than that, stationing one's elephant next to a trap square is the simplest capture defense. 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 this is usually precarious, as the defender itself could be captured. Such a piece must keep a constant eye on all enemy pieces stronger than itself. The opponent may lose something if he moves his elephant, but if he captures more than he lost, it was worth it.
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. A phalanx blocks the gold camel from g7, thus the f7 horse is currently safe even though it is Silver's only direct defender of the f6 trap.
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. Gold has stuffed c3; the silver elephant could push the gold cat to d3, but that would temporarily give the c3 trap two gold defenders, preventing any capture in Silver's final two steps. Occupying c3 only works because no silver piece immediately threatens the c2 dog; if it were dislodged with the cat still on c3, the cat would be lost.
The f2 dog allows the g3 camel to safely step into the trap, and then capture the gold horse with a pull. Gold to move could prevent this with He3sn df2w Df1n, a pull and replace that would give the trap a second gold defender.
If defending a trap is not feasible, threatened pieces might scatter away from it. It may not be possible to get every piece to safety, but even delaying captures may buy time to make progress elsewhere. One scattering pieces away from a home trap should try to block the goal line, as enemy rabbits can easily advance toward an undefended trap.
More capture patterns
Although not immediately obvious, a one-turn capture is possible in each trap.
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.
In the northeast, 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, 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.
In the southeast, the f3 dog can 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 there.
In this game, the gold elephant has forked the silver dog between the c3 and f3 traps.
The fork is a basic multi-turn tactic, in which a piece is threatened with capture in two different traps. In the diagram, Gold has threatened to capture the silver dog in either c3 or f3. There is currently no chance for the dog to escape, so Silver would have to defend both traps in order to save it. Silver to move would need one step to defend c3 with the elephant, and three steps to defend f3 with the cat. Unfortunately for Silver, the gold rabbit on e4 is threatening to reach goal next turn, and cannot be frozen in place as it is next to the gold elephant. Silver must spend at least one step defending goal, and the silver dog is lost.
Generally speaking, a solid fork is most likely to occur between the forker's home traps; any other fork would tend to be easier to escape. From the start of the game, each side must be wary of allowing the opposing elephant to flip a piece into the centre, as that can lead to a strong fork. As defenses thin, forks become a greater potential threat in all areas of the board.
Use this link to make moves on the board.
Solution: ed3n Rc4w ed4w cb7s. Silver forks the camel between c3 and c6, blockading b5 so the camel cannot go west. The gold camel has no effective way to escape, and Gold has no effective way to defend both traps at once; Gold could put a rabbit or horse on d3, but the silver elephant could pull that piece into the trap, capturing it while retaining the camel fork.
The silver horse on c4 has been fenced in; Silver to move can't save it.
The fence is a less common multi-turn 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 save the horse. The silver elephant could move to c5 and unfreeze the fenced horse (while also capturing the gold rabbit in c6), but the unfrozen silver horse couldn't then escape, as its only available move would be suicide. Silver can't defend the trap, as no silver piece can reach d3, c2, or b3 in four steps; gold pieces block the silver elephant from doing so.
Solution: ef4nw Hg5w hg6s blocks the gold elephant out of e6, fences the gold horse on f5, and clears g6 so that the f6 rabbit can step east. The gold elephant can still pull the e6 dog, capturing the f6 rabbit, but in any event Silver can capture the fenced horse.
A fence may be valuable even if the fenced piece can be defended. At right, the silver elephant can go to d3 to defend the horse, but Gold can then frame the horse with hc4s Ed4w Hb4s. In other cases, Gold might keep the fenced piece on c4 as a hostage, while blockading c3 to stop the piece from advancing.
Limitations of tactics
Gold to move can avoid any capture.
Tactics alone can't accomplish much, if the opponent understands them. The position at left may look promising for Silver, but Gold went on to win without losing a single piece until the end.
The next thing to learn is basic long-term strategy, which can help one get a whole-board advantage and overwhelm the opponent's defenses.