Arimaa/Playing The Game

From Wikibooks, the open-content textbooks collection

Arimaa is played on a chessboard with four squares distinguished as trap squares, namely c3, f3, c6, and f6 in algebraic chess notation. The two players, Gold and Silver, each control sixteen pieces: these are, in order from strongest to weakest, one elephant, one camel, two horses, two dogs, two cats, and eight rabbits. The pieces may be represented by the chess king, queen, rooks, bishops, knights, and pawns respectively.

The objective of the game is to move a rabbit of one's own color onto the home rank of the opponent. Thus Gold wins by moving a gold rabbit to the eighth rank, and Silver wins by moving a silver rabbit to the first rank. However, because it is difficult to usher a rabbit to the goal line while the board is full of pieces, an intermediate objective is to capture opposing pieces by pushing or pulling them into the trap squares.

The game begins with an empty board. Gold places the sixteen gold pieces in any configuration on the first and second ranks. Silver then places the sixteen silver pieces in any configuration on seventh and eighth ranks. The diagram at right shows one possible initial placement.

After the pieces are placed on the board, the players alternate turns, starting with Gold. A turn consists of making one to four steps. With each step a friendly piece may move into an unoccupied square one space left, right, forward, or backward, except that rabbits may not step backward. The steps of a turn may be made by a single piece or distributed between several pieces in any order. A turn must make a net change to the position. Thus one may not, for example, take one step forward and one step back with the same piece, effectively passing the turn.

The second diagram, from the same game as the initial position above, helps illustrate the remaining rules of movement.

A player may use two steps of a turn to dislodge an opposing piece with a stronger friendly piece which is adjacent. For example, a friendly dog may dislodge an opposing rabbit or cat, but not a dog, horse, camel, or elephant. The stronger piece may pull or push the adjacent weaker piece. When pulling, the stronger piece steps into an empty square, and the square it came from is occupied by the weaker piece. The silver elephant on d5 could step to d4 (or c5 or e5) and pull the gold horse from d6 to d5. When pushing, the weaker piece is moved to an adjacent empty square, and the square it came from is occupied by the stronger piece. The gold elephant on d3 could push the silver rabbit on d2 to e2 and then occupy d2. Note that the rabbit on d2 can't be pushed to d1, c2, or d3, because those squares are not empty.

Friendly pieces may not be dislodged. Also, a piece may not push and pull simultaneously. For example the gold elephant on d3 could not simultaneously push the silver rabbit on d2 to e2 and pull the silver rabbit from c3 to d3. An elephant can never be dislodged, since there is nothing stronger.

A piece which is adjacent to a stronger opposing piece is frozen, unless it is also adjacent to a friendly piece. Frozen pieces may not be moved by the owner, but may be dislodged by the opponent. A frozen piece can freeze another still weaker piece. The silver rabbit on a7 is frozen, but the one on d2 is able to move because it is adjacent to a silver piece. Similarly the gold rabbit on b7 is frozen, but the gold cat on c1 is not. The dogs on a6 and b6 do not freeze each other because they are of equal strength. An elephant cannot be frozen, since there is nothing stronger, but an elephant can be blockaded.

A piece which enters a trap square is captured and removed from the game unless there is a friendly piece adjacent. Silver to move could capture the gold horse on d6 by pushing it to c6 with the elephant on d5. Also a piece on a trap square is captured if all adjacent friendly pieces move away. Thus if the silver rabbit on c4 and the silver horse on c2 move away, voluntarily or by being dislodged, the silver rabbit on c3 will be captured.

Note that a piece may voluntarily step into a trap square, even if it is captured thereby. Also, the second step of a pulling maneuver may be completed, even if the piece doing the pulling is captured on the first step. For example, Silver to move could step the silver rabbit from f4 to g4, step the silver horse from f2 to f3, which captures the horse, and still pull the gold rabbit from f1 to f2 as part of the horse's move.

In the diagrammed position, if it were Gold's turn to move, Gold could win in three steps: The dog on a6 can push the rabbit on a7 to a8, and when the dog is on a7, it unfreezes the rabbit on b7, which can step to b8 for the victory.

There are several ways for the game to end apart from a rabbit reaching its goal. (The frequency of each in the first thousand rated human vs. human games on the Arimaa server is shown in parentheses.)

• (1.3%) If, at the beginning of a player's turn, no steps are possible because all friendly pieces are frozen or blockaded, the player whose turn it is loses.
• (0.2%) If the same position occurs three times with the same player to move, the player whose turn caused it to occur the third time loses. Only positions at the end of each turn are considered by this rule, not positions at the end of each step. (This rule originally did not consider side to move, but Syed changed it to be more like the chess repetition rule on May 28, 2005.)
• (0.0%) If all sixteen rabbits are captured, the game is a draw. (In elimination tournaments where a draw would be inconvenient, Syed has ruled that a player who captures all eight opposing rabbits wins the game, although as of December, 2006, it has been a moot point.)

Finally, if an opposing rabbit is dislodged onto its goal line and dislodged off within the same turn, the game continues.

← Overview · Introduction to Tactics →

← Overview · Arimaa · Introduction to Tactics →