Arimaa/Playing The Game

Rules

Like classic chess, Arimaa is played on an 8×8 grid. The two players, Gold and Silver, control sixteen pieces each (listed in descending order of strength):

Piece	Elephant	Camel	Horse	Dog	Cat	Rabbit
Number	1	1	2	2	2	8
Symbols

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

The players begin by setting up their pieces however they choose on their home rows. Highlighted are the four trap squares.

If Arimaa is played using a chess set, the pieces may be represented by the king, queen, knights, bishops, rooks, and pawns respectively. Unlike their chess counterparts, however, Arimaa pieces move only in cardinal directions (North, East, South and West), and step one square at a time. The relative strength of each piece lies in its power to push, pull, or immobilize weaker enemy pieces. There are four trap squares on which a piece can potentially be lost — these are the squares designated as c3, f3, c6, and f6 when classified by rank and file.

The game begins with an empty board. Gold arranges his pieces on the first and second ranks, in whatever configuration he chooses — Arimaa pieces do not have fixed starting positions. Silver then arranges her pieces on the seventh and eighth ranks.

A piece steps from square to square. Rabbits can step left, right, or forward. All other pieces can step left, right, forward, or backward. Diagonals have no place in the rules of Arimaa.

A turn (or move) consists of one to four steps. The steps in a turn can be used on four different pieces, all on the same piece, or any combination. After the setup phase is completed, the players alternate turns with Gold going first.

A player may not pass a turn, and must always make a net change to the position. Thus one cannot, for example, move the same piece forward and backward and leave it at that. Furthermore, a turn may not result in a position identical to one which the same player has created twice before.

The game's main objective is to get a rabbit across the board; the opponent's home rank is the goal line.

Freezing

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

The second diagram portrays a position which could occur later in a game.

A piece which is adjacent to a stronger enemy piece is frozen, unless it is also adjacent to a friendly piece. While frozen, a piece may not be moved by its owner. The silver elephant on d5 freezes the gold horse on d6. The frozen gold horse itself freezes a silver rabbit on e6, but the rabbit would be unfrozen if the f7 dog stepped west. The dogs on a6 and b6 do not freeze each other, as they are of equal strength.

Pushing and pulling

A piece can pull or push a weaker enemy piece which is next to it, provided an empty square allows for the necessary movement.

In a pull, a piece steps onto an adjacent empty square and drags the weaker enemy piece onto the square from which it came. The silver elephant on d5 could step east, west, or south and pull the gold horse from d6 to d5. In a push, the weaker enemy piece is moved onto an adjacent empty square, and the piece which pushed it moves onto the square it had occupied. The gold elephant on d3 could push the silver rabbit on d2 to e2 and then occupy d2. A push or pull uses two steps, since two pieces are moved.

Note that the rabbit on d2 can't be pushed to d1, c2, or d3, because those squares are already occupied. Remember also that a piece can only push or pull a weaker enemy piece — for example, a dog may dislodge an enemy rabbit or cat, but not a dog, horse, camel, or elephant. Although a rabbit may not retreat toward its home row, it can nonetheless be pushed or pulled in that direction. For example, the gold rabbit on g3 could not itself step back to g2, but the silver horse could take a step right and then pull it down.

A piece may not push and pull simultaneously — for example, the gold elephant could not dislodge the d2 and c3 rabbits in one move. No push can occur if there is no empty square for a piece to be pushed onto, and no pull can occur if there is no empty square for the pulling piece to step onto. Strong pieces can sometimes be limited by teams of weaker pieces.

A frozen piece can be pushed or pulled by the opponent. A non-frozen piece can also be pushed or pulled — an adjacent friendly piece does not protect against this. For example, the d1 cat does not protect the c1 cat from being pushed to b1 or pulled to c2. Whether a piece is frozen is unrelated to whether it can be dislodged.

Captures

In Arimaa, a capture can only occur on a trap square. A piece which enters a trap square is removed from the board unless there is a friendly piece next to that trap. The silver elephant could capture the gold horse by pushing it from d6 to c6. The silver rabbit on c3 is still alive because of the c4 rabbit and c2 horse — the c3 trap has two silver defenders. If all friendly defenders left or got dislodged, a piece still on a trap square would be lost.

A piece may voluntarily step into a trap square, even if it is lost thereby. The second step of a pulling maneuver may be completed, even if the pulling piece is lost on the first step. For example, Silver to move could step the silver horse from f2 to f3, losing the horse, and still pull the gold rabbit from f1 to f2 as part of the horse's move.

End of the game

An Arimaa game cannot end in a draw. There are three different ways to win:

• Goal: Gold wins by moving a gold rabbit onto the eighth rank, and Silver wins by moving a silver rabbit onto the first rank. As the principal object of the game, goal is normally how a game is won.
• Elimination: One can win by capturing the last remaining enemy rabbit.
• Immobilization: One can win by creating a position that leaves the opponent with no legal move. This could involve a large blockade.

If one side's move directly brings about a winning condition for the opponent, the opponent wins, except under these rare circumstances:

• If a move brings about goal or elimination for both sides, the one who made the move wins.
• Goal or elimination wins the game even if one's pieces are technically left immobilized. Immobilization is only checked at the start of a turn.
• If a rabbit is dislodged onto its goal line and then dislodged off within the same turn, as occurred on 83g of this game, the game continues.

Setting up

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

Gold has used the classic 99of9 setup; Silver has switched the dogs and cats.

The finer points of initial piece placement will be explored later, but a beginner just needs a flexible setup that denies the opponent an easy attack plan. Strong pieces start in the front row, as they must take the lead in clearing a path for a rabbit to goal.

In the diagram at right, Gold has chosen a classic symmetric setup. The elephant is placed in the center so that it can quickly reach any part of the board. The camel is placed in the center as well, so that it could defend either home trap and potentially punish an enemy horse advance on either wing. Rabbits are kept out of the center; since rabbits can't retreat, a rabbit pulled up in the middle might block its own friendly pieces. For the same reason, rabbits are not placed directly behind the traps.

The gold horses will quickly step forward, to assert control of Gold's home traps; one horse or the other might then advance in hopes of creating a threat. Beginning back and center, the gold dogs may soon move up. The gold cats might stay in place for a while, guarding the traps from behind and thus protecting other gold pieces from a quick capture at home.

Since Silver goes second, she can take Gold's setup into account when deciding on her own. Note that the silver elephant is not placed directly opposite the gold elephant. If both elephants started on the same file, Gold could advance his elephant four squares and temporarily fence in the silver elephant.

Silver has also used a symmetric setup, only switching the dogs and cats. Gold has chosen "cats behind the traps, dogs back", while Silver has used "dogs behind the traps, cats back". The pieces guarding their home traps from behind are potentially vulnerable to capture themselves — Silver stands to lose a dog in the opening if she's not careful. As long as another silver piece is next to the trap, however, a dog behind that trap strengthens Silver's control of it, since dogs cannot be pushed aside by enemy dogs. A dog might later advance through the trap and be replaced by a cat or rabbit.

A player who uses a non-symmetric setup may intend to move quickly on one wing.

Notation

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

One can play Arimaa without learning the standard notation for moves. For brevity's sake, however, examples will sometimes use the notation rather than spell out each individual step.

Each step is notated as ⟨piece⟩⟨initial square⟩⟨direction⟩.

• ⟨piece⟩ is a single letter:
  • E for Elephant
  • M for caMel
  • H for Horse
  • D for Dog
  • C for Cat
  • R for Rabbit
  Upper case is used for the gold pieces, and lower case for the silver pieces.
• ⟨initial square⟩ is a two-character square name as in chess notation (e.g. e4).
• ⟨direction⟩ can be n, e, s, or w for north, east, south, or west. This is always from Gold's point of view. In addition, the special direction x indicates that the piece is captured.

Suppose Gold is to move in the diagram. The false protection capture of the silver elephant is described as Mb4e db3n cd3e ec3x Hd4s. The northeastern goal is Eg7s rh7w Rh6n Rh7n, or equivalently, Eg7s rh7w Rh6nn. Consecutive steps by the same piece may be condensed, with only the initial square given.

When an actual game is cited, a turn is referred to by a number and "g" (gold) or "s" (silver). 1g and 1s are the setups, 2g is Gold's first regular turn, and 2s is Silver's first regular turn.

While this notation may seem verbose, each step must be accounted for with no ambiguity.