Arimaa

Arimaa pieces do not have fixed starting positions. The players may choose any starting configuration they prefer, so long as all of their friendly counters are in the two rows nearest to them.

No. of Players

Two

Equipment

An Arimaa board is a simple 8x8 square grid with four special square cells marked differently to distinguish them as traps. Each player commences with sixteen pieces of five varieties of one color. The types of pieces, from strongest to weakest, are:

Elephant

Each player starts with one.

Camel

Each player starts with one.

Horse

Each player starts with two.

Dog

Each player starts with two.

Cat

Each player starts with two.

Rabbit

Each player starts with eight.

Note that the standard Chessmen could be substituted for the pieces described here. Here, the elephant may be represented by the king, camel by the queen queen, horses by the rooks, dogs by the bishops, cats by the knights, and rabbits by the pawns.

History

Arimaa was invented by Omar Syed, an Indian American computer engineer trained in artificial intelligence. Syed was inspired by Garry Kasparov's defeat at the hands of the chess computer Deep Blue to design a new game which could be played with a standard chess set, would be difficult for computers to play well, but would have rules simple enough for his then four-year-old son Aamir to understand. ("Arimaa" is "Aamir" spelled backwards plus an initial "a".)

Every year since 2004 and as of 2013, the Arimaa community has held three tournaments: a World Championship (humans only), a Computer Championship (computers only), and the Arimaa Challenge (human vs. computer).

Arimaa has won several awards including GAMES Magazine 2011 Best Abstract Strategy Game, Creative Child Magazine 2010 Strategy Game of the Year, and the 2010 Parents' Choice Approved Award. It has also been the subject of several research papers.

Objective

There are three ways to win the game:

  1. Move a rabbit of your color to the eighth row of the board.

  2. Capture all enemy rabbits.

  3. Deprive the opponent of legal moves.

Play

The game begins with a vacant board. Gold arranges their pieces on their first and second ranks, in any configuration they choose—Arimaa pieces do not have fixed starting positions. Silver then arranges their pieces on the seventh and eighth ranks. The diagram at right shows opening setups which are fairly common.

Once the pieces are on the board, Gold and Silver alternate turns, starting with Gold. A turn consists of one to four steps—each player is allowed four steps per turn and must take at least one, but can choose to pass on any of the rest. The steps of a turn can be distributed however the player chooses—four different pieces can each take one step, one piece can take four steps, two pieces can each take two steps, etc. A turn must make a net change to the position—one may not, for example, simply take one step left and one step right with the same piece, effectively passing the turn. A player who has ended two different turns on an identical position may not end another turn with that same position, no matter how far apart the turns are. As a further safeguard against indefinite loops of pieces moving back and forth, rabbits are prohibited from retreating homeward. Elephants, camels, horses, dogs, and cats may each step left, right, forward, or backward; rabbits may only step left, right, or forward.

A piece can pull or push a weaker enemy piece which is next to it, provided there is an empty square allowing 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. 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. A push or pull uses two steps, since two pieces are moved. 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 on d3 could not push the silver rabbit from d2 to e2 and at the same time pull the other silver rabbit from c3 to d3.

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, but may still be pushed or pulled by the opponent. 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. An elephant cannot be frozen per se, just as it cannot be pushed or pulled since there is nothing stronger. However, if enough enemy pieces are utilized against it, an elephant can be blockaded so that it has nowhere to go—this is possible because only one piece can be pushed at a time, regardless of relative 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.

A piece which enters a trap square is removed from the game 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—however, if the silver pieces protecting the c3 trap were to leave their positions, either voluntarily or by being dislodged, the silver rabbit on c3 would be lost.

Note that 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 piece doing the pulling is captured on the first step. For example, Silver to move could step the silver horse from f2 to f3, which would be suicide for 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 enemy rabbit from a7 to a8. Now on a7, the gold dog unfreezes its own rabbit on b7, which can then step to b8 for the victory.

Note that an adjacent friendly piece does not protect against pulling or pushing. For example, on Silver's turn, their horse on c2 could push the gold cat from c1 to b1, or pull it to c2, even though the gold cat has a friendly piece next to it on d1.

Finally, if an enemy piece dislodges a rabbit onto its goal line and dislodges it off within the same turn, the game continues.

Strategy

Variations

Sources

  1. The icons for the pieces are the work of WIkimedia Commons user Nathan Hwang (aka The Novice Oof) and are licensed under the Creative Commons Attribution 3.0 Unported license.