Arimaa/Introduction to Strategy/Early Ideas

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Direct Goal Is Impossible[edit]

37px-Arimaa board.jpg
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Gold has no way to make progress with the h6 rabbit.

The most direct strategy in Arimaa is to advance a rabbit and some strong pieces, attempting to rip a hole in the opponent's defenses through which the rabbit can reach goal. If both players try to do this, the game turns into a race. Each player in a race must judge how many steps to spend delaying the opposing rabbit, and how many steps to use furthering their own rabbit.

Before long, however, the Arimaa community discovered that if one player tries to force goal in the opening while the other player defends, advantage accrues to the defender. With the entire defending army still at home, the pieces support each other, and thus can prevent an attacker from simply displacing enough pieces to get a rabbit to goal. Meanwhile, the attacking rabbit is vulnerable to capture in the defender's home traps. In the diagram at right, the h6-rabbit is no threat to goal, but the rabbit itself is in danger of capture in f6. Furthermore, rabbits can't retreat, so the h6-rabbit can't save itself. Finally, if the gold elephant advances to g6 to protect the h6-rabbit, the elephant will be blockaded.

Two threats[edit]

Realizing the futility of forcing an early goal, top Arimaa players next turned to capturing pieces as the most plausible strategy. However, that was not straightforward either. Suppose Gold threatens a silver piece with capture in f3. The silver elephant can camp out by that trap, and Gold can never capture anything there: the silver elephant defends other silver pieces, and can't itself be pushed or pulled. In order to make progress, Gold must create threats around two different traps.

For this reason, each player wants to be the first to make two strong threats. This could be as simple as forking one enemy piece between two traps; any non-elephant piece must be careful about advancing in the center. It is tempting to send one's elephant hunting and just keep everything else at home, but a skilled opponent could make that very slow, while developing more sophisticated threats of their own.

When one's elephant defends an away trap, it can likely protect any friendly pieces advanced on that wing; such pieces can't be captured in the protected trap, and if they were pulled toward the center, the elephant could help them retreat (unless they were rabbits, but even then it would take the opponent a few turns to drag a rabbit across the board, with the only gain being a rabbit capture.) With the gold elephant on e6, the silver camel in the west, and the gold camel in the east, the gold camel could advance and then either drag silver pieces down to f3, or team up with the elephant to make captures in f6. However, the silver elephant could attack the advanced gold camel, neutralizing its threats while also setting the stage for two strong threats by Silver. The gold elephant protects its camel from capture, but without other gold pieces already in place to support the camel, the silver elephant can hold it against the side of the board. To prevent capture, the gold elephant must stay beside the trap. With both elephants and the gold camel tied up in the northeast, the silver camel is the strongest free piece. Silver now has one strong threat in the camel hostage, and her own camel can create a second threat, which only the tied-up gold pieces could defend against.

A note on the functions of pieces[edit]

In Arimaa, the strength and function of a piece depends on what pieces remain on the board. For instance, if each side has lost a camel and a horse, the remaining horses are the unique second strongest pieces on each side, and so have essentially the role that the camels had initially. When the following sections discuss strategic features such as camel hostages, it should be borne in mind that the actual pieces involved may differ if exchanges have taken place.

Camel Hostage