Arimaa/Playing The Game
Arimaa, like chess, is played on an 8×8 square board. The two players, Gold and Silver, control sixteen pieces each (listed in descending order of strength):
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, and step one square at a time. Diagonals have no place in the rules of Arimaa. The relative strength of each piece lies in its power to push, pull, or immobilize weaker enemy pieces. Four squares of the game board are distinguished as 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 main objective of the game is to get a rabbit to the other side of the board.
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. Gold moves first, but Silver can react to Gold's setup; these two advantages roughly cancel out. The diagram shows opening setups which are fairly common.
A piece steps from square to square. Most pieces can step left, right, forward, or backward. Rabbits can only step left, right, or forward.
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 his or her turn, and each turn must 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 second diagram, portraying a position which could occur later in a game, helps illustrate the remaining rules of movement.
A piece which is adjacent (in any cardinal direction) to a stronger enemy piece is frozen, unless it is also adjacent to a friendly piece. A piece which is frozen may not be moved by its owner. The silver rabbit on a7 is frozen, but the one on d2 is able to move because it is next to another 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, as they are of equal strength.
A frozen piece can freeze another still weaker piece just as it would otherwise. The silver elephant on d5 freezes the gold horse on d6, which itself freezes the silver rabbit on e6.
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.
To 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. To 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 (i.e. push or pull) 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. Likewise, no piece can push two pieces at once. Since even an elephant can only push one piece at a time, an elephant can sometimes be blockaded so that it has nowhere to go. This is the only way an elephant can be immobilized, since no piece can freeze it.
Whether a piece is frozen is independent of whether it can be dislodged — an adjacent friendly piece does not protect against pulling or pushing. For example, the d1 cat does not protect the c1 cat from being pushed to b1 or pulled to c2.
A piece which enters a trap square is removed from the board unless there is a friendly piece adjacent to the square. 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 silver rabbit on c4 as well as the silver horse on c2 — the trap has two silver defenders. If both defenders left or got dislodged, the silver rabbit on c3 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 captured 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
There are three victory conditions:
- Goal: the main objective of the game is to move any 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. This is by far the most common victory condition.
- Elimination: the game can be won by capturing all enemy rabbits.
- Immobilization: if the opponent has no legal move when it is their turn, they lose.
The following edge cases are rarely relevant:
- If both players achieve goal or elimination on the same move, the player who made the move wins.
- If immobilization occurs together with goal or elimination, the goal or elimination takes precedence. Intuitively, goal and elimination are checked at the end of a move, while immobilization is not checked until the start of the next move.
- If an enemy piece dislodges a rabbit onto its goal line and dislodges it off within the same turn, the game continues.
Gold arranges their pieces on the first and second ranks, and then Silver arranges their pieces on the seventh and eighth ranks. The finer points of initial piece placement will be explored later, but for now you just want a setup that gives you flexibility and denies the opponent an easy attack plan. Most or all rabbits should start in the back row — the strong pieces must take the lead in clearing a path for a rabbit to goal. Moreover, rabbits cannot retreat homeward, and thus could quickly be pulled up and captured if they began exposed.
The 99of9 setup (named for the player who popularized it) is optimal for beginners. In the diagram at right, Gold has chosen the classic 99of9 setup. The elephant is placed in the center so that it can quickly attack any part of the board. The camel is placed in the center as well, so that it can easily go to either wing depending on Silver's setup.
The gold horses will quickly move up, to assert control of Gold's home traps and then perhaps to attack Silver's traps. A rabbit is placed forward on each flank, because a2 and h2 tend to be safer places for rabbits than the centralized d1 and e1 would be.
Beginning back and center, the gold dogs will soon move up. As long as the gold cats remain behind the traps, they make it hard for Silver to capture a gold camel, horse, or dog in Gold's own home trap.
Since Silver goes second, they can take Gold's setup into account when deciding on their own. At right, note that the silver elephant is not placed directly opposite the gold elephant. If the silver elephant directly faced its gold counterpart, Gold could advance their elephant four squares and temporarily fence in the silver elephant.
Silver has used a variation of the 99of9 setup, 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 strategic difference is subtle. Silver's dogs are guarding their home traps, and thus are potentially vulnerable to capture themselves — Silver stands to lose a dog in the opening if he'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.
You may wonder why rabbits do not begin behind the home traps. Experienced players will sometimes do this, but the downside is that a rabbit could get pushed into a protected trap and then could never step back, creating a mess for the home player.
You can become a decent Arimaa player 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. You can learn the notation now or later.
A move is a sequence of steps, where 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
- ⟨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.
Consecutive steps by the same piece may be condensed, with the piece letter and initial square given just once.
Suppose Gold is to move in the diagram. The capture of the silver elephant is described as Mb4e db3n cd3e Hd4s ec3x. The northeastern goal is Eg7s rh7w Rh6n Rh7n, or equivalently, Eg7s rh7w Rh6nn.
Although this notation is rather verbose, proposed replacements have not become standard.