Arimaa

Arimaa is played on an 8×8 board with four trap squares. There are six kinds of pieces, ranging from elephant (strongest) to rabbit (weakest). 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 colour 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 (elimination) or by depriving the opponent of legal moves (immobilization). 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 (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. 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 (so that it will no longer support pieces at f3), 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 (their frequency is indicated in parentheses): • 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. (In competition, in order to avoid drawn games, the player who captures the eight opposing rabbits wins the game.) If an opposing rabbit is dislodged onto its winning rank and then dislodged again off that rank during the same turn, the game continues. ==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. 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. Trap squares The four trap squares (located at c3, f3, c6, and f6) define Arimaa's unique capturing system. Arimaa requires deliberately maneuvering opponents into these traps by pushing or pulling a weaker piece. Any piece occupying a trap square immediately perishes unless a friendly piece stands adjacent to provide support. This system creates several tactical opportunities and threats. Before finalizing any move, it is imperative to analyze all four trap squares and how all pieces nearby can be captured or protected. Two pieces positioned next to the same trap can provide mutual protection. If one gets pushed into the trap, the other keeps it alive. However, there are cases of false protection when both supporting pieces are frozen by stronger enemy pieces nearby. Then an opponent can separate them and claim the trap. The most common beginner mistakes are trap blunders which occur when players fail to notice an opponent can capture their piece on the following turn. Developing trap awareness prevents costly losses and reveals opportunities to threaten enemy pieces. The freeze mechanic When your piece stands adjacent to a stronger opponent piece without friendly support nearby, it becomes frozen and cannot move independently. However, positioning any friendly piece, even a rabbit, adjacent to the frozen piece restores its mobility. This creates interesting tactical dynamics. Stronger pieces can lock down multiple enemy pieces simultaneously through strategic positioning. Conversely, advancing pieces in groups rather than isolation prevents them from becoming easy freeze targets. The freeze mechanic particularly impacts rabbit advancement since an enemy cat can halt your rabbit's progress, forcing you to spend extra movement steps bringing supporting pieces forward. Rabbit Management Though winning requires getting just one rabbit across, managing all eight rabbits demands careful attention. Advancing too many rabbits early creates congestion, blocking your stronger pieces, and leaves the rabbits vulnerable to easy capture. Conversely, advancing too few rabbits leaves you with less opportunities for victory. The current recommended approach involves advancing one or two rabbits along the board edges where they're harder to intercept. Keep stronger pieces ahead of advancing rabbits for protection. Rabbits wandering alone become easy targets for enemy pulls into trap squares. Early in the game, maintain most rabbits on your back rank, forming a defensive wall. As stronger pieces leave the board through captures, rabbits gain mobility. In the mid-game and endgame, when there is less material on the board, one must be alert for "rocket rabbits" which can rush forward. A rabbit on your fourth rank can sprint directly to victory in a single four-step turn if unopposed. Thus, to prevent goal blunders near the endgame, players must keep all passed rabbits (rabbits that have advanced into the fourth rank or beyond) in mind and make sure to block them or push them back. Avoiding open columns is one key element of preventing enemy rabbits from making a goal. Other tactics "Danglers" are non-elephant pieces that advance beyond your third rank alone and without support. These pieces become vulnerable to enemy pulls toward their side of the board. Avoid creating danglers by advancing pieces past the third row unless you have a plan to support them. "Hostage-taking" occurs when you freeze or block an enemy piece near a trap, and threaten to capture it within four steps. This forces your opponent to commit a piece that is as strong as the hostage taker piece, just to guard the hostage. This tactic ties up two of the opposing pieces with just one piece. Furthermore, a "hostage fork" is when a piece is taken hostage in between two traps, and can taken out of the game from either direction in four move steps. This can be used to draw your opponent to bring up other pieces to save the hostage, which can then be taken hostage or blocked as well. "Framing" is where you trap an opponent's piece on a trap square, blocking its escape routes with other pieces. The framed piece survives only through a friendly guard, which itself becomes pinned in place. This is a good way to tie up your opponent's stronger pieces by framing a weaker one. Trap control involves positioning two or more strong pieces around enemy trap squares, dominating that board region. Sometimes trading control of a trap square on one's own side to gain control of an opponent's trap proves advantageous, especially when you have an advanced rabbit nearby. This allows you to better clear the route for your passed rabbit. == Patent and registered trademark ==

United States USPTO Patent no. 6,981,700 (“No. 6,981,700”) was filed on October 3, 2003, and granted on January 3, 2006, to Omar Syed, who also holds the registered trademark for the name “Arimaa”. Syed, however, stated that his objective is not to restrict the non-commercial use of the trademark, and therefore he released a license called the “Arimaa Public License,” with the intention of “making Arimaa a game in the public domain as much as possible, while still protecting its commercial use.” The items covered by the license are the patent and the registered trademark. ==Annual tournaments==

World Championship Each year since 2004 the Arimaa community has held a World Championship tournament. As part of the conditions of the prize, the computer program must run on standard, off-the-shelf hardware. The algorithm combined traditional alpha–beta pruning (changing sides every 4 ply) with heuristic functions manually written while analysing human expert games. After DeepMind's AlphaZero mastered Go, Chess, and Shogi simply by playing itself, Omar Syed announced a $10,000 prize for the creation of such an Arimaa bot which could win a 10-game match against Sharp. This has not yet been done. ==See also==