Arimaa
Arimaa is a two-player strategy board game that was designed to be playable with a standard chess set and difficult for computers while still being easy to learn and fun to play for humans. It was invented between 1997 and 2002 by Omar Syed. Arimaa is a complex abstract strategy game and after decades of play, a body of theory has developed among high level players, along with a few books on the game. Arimaa has also developed a community on the internet, where tournaments are played.
An Indian-American computer engineer trained in artificial intelligence, Omar Syed was inspired by Garry Kasparov's defeat at the hands of the chess computer Deep Blue to design a new game. His goal was to make a game that 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. The name "Arimaa" is "Aamir" spelled backwards plus an initial "a". In 2002, Omar Syed published the rules of Arimaa and had them patented in 2003, and the name Arimaa became a registered trademark. Arimaa sets were developed and sold by Z-man Games beginning in 2009.
Syed also established the [|Arimaa Challenge] to promote the game. A prize of USD 10,000 would be available each year until 2020 to reward the first program, running on a standard consumer computer, capable of defeating a high-level human player in a match of six games or more. Beginning in 2004, the Arimaa community held three annual tournaments: a [|World Championship], a [|Computer Championship], and the Arimaa Challenge. After eleven years of human dominance, the 2015 challenge was won decisively by the 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.
Rules
Arimaa is played on an 8×8 board with four trap squares. There are six kinds of pieces, ranging from elephant to rabbit. Stronger pieces can push or pull weaker pieces, and stronger pieces freeze weaker pieces. Pieces can be captured by dislodging them onto a trap square when they have no orthogonally adjacent pieces.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. These may be represented by the king, queen, rooks, bishops, knights, and pawns respectively when one plays using a chess set.
Objective
The main object of the game is to move a rabbit of one's own color onto the home rank of the opponent, which is known as a goal. 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 them into the trap squares.The game can also be won by capturing all of the opponent's rabbits or by depriving the opponent of legal moves. Compared to goal, these are uncommon.
Setup
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 the seventh and eighth ranks. Diagram 1 shows one possible initial placement.Movement
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 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 among several pieces in any order.A turn must make a net change to the position. Thus one cannot, for example, take one step forward and one step back with the same piece, effectively passing the turn and evading zugzwang. Furthermore, one's turn may not create the same position with the same player to move as has been created twice before. This rule is similar to the situational super ko rule in the game of Go, which prevents endless loops, and is in contrast to chess where endless loops are considered draws. The prohibitions on passing and repetition make Arimaa a drawless game.
Pushing and pulling
The second diagram, from the same game as the initial position above, helps illustrate the remaining rules of movement.A player may use two consecutive steps of a turn to dislodge an opposing piece with a stronger friendly piece which is adjacent in one of the four cardinal directions. For example, a player's 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 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.
Freezing
A piece which is adjacent in any cardinal direction 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.Capturing
A piece which enters a trap square is captured and removed from the game unless there is a friendly piece orthogonally adjacent. Silver could move to capture the gold horse on d6 by pushing it to c6 with the elephant on d5. A piece on a trap square is captured when 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 thereby captured. Also, the second step of a pulling maneuver is completed even if the piece doing the pulling is captured on the first step. For example, Silver could step the silver rabbit from f4 to g4, and then step the silver horse from f2 to f3, which captures the horse; the horse's move could still pull the gold rabbit from f1 to f2.
Other endgame conditions
In addition to bringing a rabbit to the final rank, there are other ways to end a game :- Immobilization: if, at the beginning of its turn, a player cannot make any step because all of its pieces are frozen or blocked, that player loses the game.
- Repetition: if the same position occurs three times, the player who causes the repetition by ending their turn loses the game.
- Draw: if all sixteen rabbits are captured, the game is a draw.
Strategy and tactics
Arimaa presents players with the deceptively simple objective of advancing one rabbit to the opposite edge of the board. Beneath this straightforward goal lies numerous tactical and strategic considerations. Strategically, it is important to maintain balanced piece distribution across the board. Concentrating all your strong pieces on one side leaves the opposite trap square vulnerable to takeover. Keep open communication lines between your pieces, avoiding isolated columns that allow enemy rabbits to slip through uncontested.Material considerations matter less in Arimaa than in similar games like Chess. Sacrificing pieces to advance a rabbit into an unstoppable position is a sound strategy. It is also important to avoid complete immobilization of your pieces. If all your pieces become frozen or boxed in with no legal moves, you lose immediately.
For beginning insights into good play, see the Arimaa Wikibook. Karl Juhnke, twice Arimaa world champion, has written a book titled Beginning Arimaa which gives an introduction to Arimaa tactics and strategies. Also Jean Daligault, six time Arimaa world champion, wrote Arimaa Strategies and Tactics which is geared towards those who have started playing Arimaa and want to improve their game.
Piece strength and the elephant
Understanding the strength ladder is fundamental to Arimaa strategy. The elephant reigns supreme. While it cannot be captured, its true value lies in how it is deployed. An aggressive elephant can dominate the board, forcing weaker enemy pieces to scatter or face removal through trap squares. Alternatively, a defensive elephant creates protected corridors for your rabbits by freezing any opponent piece that threatens your advance. Maintaining central control with your elephant by positioning it near the board's center four squares allows rapid response to threats across all four trap squares.An important tactic is limiting the mobility of the opponent's elephant, and ideally, performing an elephant blockade. This is done by completely surrounding an elephant with multiple pieces on all four sides so it cannot push its way out. The corners are particularly deadly for elephants since they can be more easily blockaded with a smaller number of pieces.
Since the camel is the second-strongest piece it should be protected vigilantly. Losing the camel significantly weakens a player's tactical options. One powerful tactic is taking an opponent's camel hostage with a centrally located elephant. A hostage camel significantly weakens the enemy position.