Arimaa/Print version

From Wikibooks, open books for an open world
< Arimaa
Jump to: navigation, search


Arimaa is a two-player abstract strategy board game that can be played using the same equipment as chess.

Note: current version of this book can be found at http://en.wikibooks.org/wiki/Arimaa

Table of Contents

  1. Overview
  2. Playing The Game
  3. Introduction to Tactics
  4. Introduction to Strategy
  5. Relative Value of Pieces
  6. Advanced Tactics
  7. Positioning for an Attack
  8. Lone Elephant Attacks
  9. Elephant and Camel Attacks
  10. Elephant and Horse Attacks
  11. Elephant and Minor Piece Attacks
  12. Multi-Piece Swarming Attacks
  13. Camel and Horse Attacks
  14. Double-Trap Attacks
  15. Initial Piece Placement
  16. Other Attacking Ideas
  17. Arimaa Challenge History
  18. Sample Games
  19. Glossary
  20. Resources
  21. GNU Free Documentation License

Overview

Arimaa is a two-player board game invented by Omar Syed, a computer engineer trained in artificial intelligence. Inspired by Garry Kasparov's defeat at the hands of the chess computer Deep Blue, Syed wanted to design a new game which would be difficult for computers to play well, but would have rules simple enough for his four-year-old son Aamir to understand. In fact, "Arimaa" is "Aamir" spelled backwards plus an initial "a". In 2002 Syed published the rules to Arimaa and announced a $10,000 prize, available through 2020, for the first computer program to win matches against top-ranked human players. David Wu's bot Sharp accomplished this in 2015.

Arimaa was specifically designed so that it could be played using a chess set—an 8×8 board is used, and each player has sixteen pieces, in a 1-1-2-2-2-8 distribution. It can also be played online at the arimaa.com gameroom. In 2009, Z-Man Games began producing a commercial Arimaa set. Only one face-to-face tournament has taken place, but about 900 games are played online every week. Omar Syed has hosted various events in the gameroom:

  • The World Championship is an annual tournament for human players. Jean Daligault of France has won the championship six times, in 2007, 2009, 2010, 2011, 2013, and 2014. Matthew Brown won it in 2015, 2016, and 2017.
  • From 2004 to 2015, the Computer Championship matched the top Arimaa bots in an elimination tournament. David Fotland's program Bomb placed first from 2004 to 2008. Jeff Bacher's Clueless prevailed in 2009. Mattias Hultgren's Marwin won in 2010 and 2012. David Wu's Sharp triumphed in 2011, 2014, and 2015. Ricardo Barreira's Ziltoid was victorious in 2013.
  • The Arimaa Challenge took place following the Computer Championship. The top two bots were available to play during a "screening" period. A human could play two games against each of these two bots; the bot with the better record in those matches advanced to the Challenge. That bot faced three ultimate human defenders, who were selected beforehand and hadn't played in the screening. If this bot could win three-game matches against all three human defenders, its developer would win the $10,000 prize. Humans dominated until 2015, when Sharp defeated Jean Daligault, Lev Ruchka, and Matthew Brown.

In addition to these events, the 1st Arimaa Online Festival was organized for 11 September 2010. This event included Arimaa matches, a strategy workshop, and an interview with Omar Syed.

United States Patent number 6,981,700 for Arimaa was filed on the 3rd of October 2003, and granted on the 3rd of January 2006. Omar Syed also holds a trademark on the name "Arimaa". Syed has released an experimental license called "The Arimaa Public License", with the declared intent to "make Arimaa as much of a public domain game as possible while still protecting its commercial usage". Items covered by the license are the patent and the trademark.

Playing The Game

Understanding gameplay

Arimaa, like chess, is played on an 8×8 square board. The two players, Gold and Silver, control sixteen pieces each: one elephant (Elephant), one camel (Camel), two horses (Horse), two dogs (Dog), two cats (Cat), and eight rabbits (Rabbit), 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 must all step from square to square. 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.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The players begin by setting up their pieces however they choose on their home rows. Highlighted are the four trap squares.


37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png


The game begins with an empty board. Gold arranges their pieces on the first and second ranks, in whatever 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.

The 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. It is no easy task, however, to get a rabbit past an opposing army of stronger pieces—a player must out-maneuver the other army while at the same time keeping all enemy rabbits at bay.

The second diagram, portraying a position which could occur later in a game, helps illustrate the remaining rules of movement.

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 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.

Although most games conclude with a rabbit reaching goal, there are two other circumstances which can bring about an end.

  • Complete immobilization. If upon their turn a player has no legal move available, that player loses.
  • Loss of all rabbits. A player can win by capturing the last remaining enemy rabbit, even if they sacrifice their own last rabbit in the same turn.

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

Setting up

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.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Gold has used the 99of9 setup; Silver has switched the dogs and cats.


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 defender.

Notation

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png

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
    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.

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 goal in the north-east is Eg7s rh7w Rh6n Rh7n, or, equivalently, Eg7s rh7w Rh6nn.

Although this notation is rather verbose, proposed replacements have not become standard.

Introduction to Tactics

In Arimaa, a tactic is usually a one- or two-turn plan which can be calculated precisely. Since there are up to four steps per turn, plans which aim farther than two turns ahead are usually impossible to calculate exactly, and therefore generally belong to the realm of strategy. This is in contrast to chess, where positions can be precisely calculated more than two turns ahead.

The most basic tactics to master are those that bring a friendly rabbit to goal or capture an enemy piece within four steps. If a player can't achieve victory or capture in a single turn, the opponent may bring in reinforcements which change the situation dramatically. Such contingencies require strategic rather than tactical planning.

One-turn goal

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png


Most simply, a rabbit may be able to reach goal within one turn, even if the path appears blocked by a trap square and/or opposing pieces. At left, the gold rabbit on b5 can step to victory via b6, c6, c7, and c8. The rabbit is safe on the trap due to the gold dog on c5, and is never frozen because it is always next to a friendly piece on the way to goal. The rabbit will theoretically be frozen once it reaches c8, but Gold will have won regardless.

Pulling away an opposing piece may allow a blocked rabbit to advance. At left, if the gold cat on h7 moves to h6 while pulling the silver rabbit from g7 to h7, the gold rabbit on g6 can then reach the goal in the turn's final two steps. The gold camel on f6 is lost when the rabbit advances, but reaching the goal is worth any sacrifice. Many beginners seem to prefer pushing over pulling, but note that a push is ineffectual in this case. If the gold cat pushes the silver rabbit, the cat will itself be in the way of the friendly rabbit, which won't then have time to reach the goal in the same turn.

Near the goal line, a rabbit which is frozen but not blocked is a constant threat. Silver to move could push the gold horse on b3 to c3 with the silver camel moving from b4 to b3. This would unfreeze the silver rabbit on b2, which could then step to victory via a2 and a1. Occasionally a blocked and frozen rabbit may be unblocked and unfrozen at the same time. Silver to move could pull the gold rabbit from g2 to g3 with the silver elephant sliding from g3 to f3, unfreezing the silver rabbit on f2, which could then step to the vacated g2 and then to g1, winning the game. The silver elephant would be lost as soon as the silver rabbit stepped away, but since Silver wins immediately, the elephant loss is of no consequence. With the silver rabbit beginning the turn blocked in all directions and also frozen, this one-turn goal is very easy to overlook.

One-turn capture

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png


A non-elephant piece acting as its side's sole defender of a trap is itself vulnerable. With Gold to move in the position at right, the gold elephant can step from d5 to c5, then to b5, and then push the b6 dog into the c6 trap. Since there is no other silver piece next to the trap, this captures the silver dog, in one turn.

Sometimes one may need to push aside an obstructing piece to get at a vulnerable piece. With Gold to move, the g6 camel could push the silver cat on g7 to h7; now on g7, the gold camel can push the silver horse on f7 to f6, capturing it in a turn where one friendly piece pushed two different enemy pieces.

A piece on a trap square with only one adjacent friendly piece is extremely vulnerable. Silver to move could capture the gold horse on c3 by stepping the silver elephant from d4 to c4, then b4, and then dislodging the gold dog on b3.

A piece which is two squares away from an undefended trap could be captured in four steps, if a stronger enemy piece is next to it. If it is Gold's turn, the g3 dog can capture the g2 cat. The dog could end the capture on any of three squares: f4 (after two pulls via f3), f2 (after two pushes via g2 or two pulls via f3) or g3 (via g4, with a pull followed by a push). The latter maneuver, where a piece returns to its initial square after moving an opposing piece two squares, is known as a flip.

Capture defense

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png


The simplest capture defense is to station an elephant next to a trap square. Since nothing can dislodge an elephant, nothing can be captured in that trap until the elephant voluntarily moves away. At left, no gold pieces can be captured in the northwest trap as long as the gold elephant remains on c5. If all stronger enemy pieces are tied up elsewhere, a single piece such as a horse may defend a trap alone, but must beware of a changing situation which liberates any stronger opposing piece to move nearer and threaten it.

The next simplest capture defense, mutual protection, is to station two or more pieces next to a trap. This allows weaker pieces with numerical superiority to defend against one, and sometimes two strong attackers. However, mutual protection cannot defend against three attackers because they can surround three sides of a trap. At left, Silver has defended the c6 trap with a dog on b6 and a rabbit on c7. If Gold pushes the dog away, there will not be enough steps left to capture the rabbit. Gold to move can at most set up the threat of a capture for the following turn, which gives Silver time to defend.

Sometimes one may wish to defend a trap without bringing a second piece adjacent to it. In this case one can obstruct the path of the attacking piece with friendly pieces. The gold camel on g6 can't capture the vulnerable silver horse on f7, because the silver cat on g7 is in the way, and the silver rabbits on h7 and g8 prevent the cat from being pushed. Gold could pull the cat to g6, but that would only make it a second defender of the northeast trap. The silver pieces on f7, g7, h7 and g8 form a phalanx blocking the gold camel.

One counter-intuitive way to block an enemy's path is to station a friendly piece on a trap square in front of another friendly piece. The silver elephant could push the gold cat to d3, but that would temporarily give the c3 trap two gold defenders, making it impossible for Silver to capture anything in the final two steps. This only works because there is nothing else to immediately threaten the c2 dog; if it were dislodged with the cat still on c3, the cat would be lost.

In the southeast, Silver is threatening to capture the e3 horse by stepping the g3 camel into the trap, where it is safe due to the silver dog on f2, then returning while pulling the horse. Gold can defend by pulling the f2 dog to e2 (with the horse returning to e3) and then occupying f2 with the f1 dog, after which the gold horse and dog mutually protect the trap. This four-step maneuver is called a pull and replace.

A last resort capture defense is scattering, i.e. retreating threatened pieces away from a trap to the edges and corners of the board. Scattering usually only delays captures, because the weak pieces can be frozen and eventually pulled into the trap which has been stripped of its defense. Furthermore, scattering away from a home trap may leave a hole through which an opposing rabbit can march to the goal. On the other hand, delaying captures may buy time to make progress elsewhere on the board. This defensive technique is most often useful late in the game when defenders are few (which makes mutual protection less feasible) and goal threats are imminent (which leaves less time to hunt down fleeing pieces).

More capture patterns

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png


After one has learned the basic ways of defending a trap square, one may be lured into a false sense of security by an illusion of defense. At right, Silver has two pieces next to the northwest trap, but since both pieces can be dislodged, Gold has a one-turn capture. First the gold elephant on b5 can push the silver dog from b6 to c6, and then the newly unfrozen gold cat on b7 can push the silver rabbit from c7 to c8, capturing the dog. Alternatively Gold can capture the rabbit by pushing or pulling the dog away from b6, then pushing the rabbit from c7 into c6. This situation, where a one-turn capture is possible despite the presence of two defenders adjacent to the trap, is known as false protection. It is only possible if there are two attackers, one adjacent to each defender.

Around the northeast trap, the silver camel cannot push the gold dog into the trap, since the horse is in the way. However, Silver can play a split capture: the camel pushes the dog to g6, then the horse pulls the dog into the trap.

In the southwest corner, Gold has calculated that even if the silver elephant pushes the gold rabbit from b4 to a4, the gold horse on b3 is safe from a push. This is correct but insufficient, because the silver elephant may still pull the gold horse from b3 to b4, capturing the gold camel on c3.

The situation around the southeast trap demonstrates that an enemy piece in a trap square provides less protection than a friendly one. The f3 dog may voluntarily step east or west, leaving three steps for the f4 horse to enter the trap square and pull the gold dog from f2 to f3, capturing it. If instead a gold piece were on f3, Silver wouldn't have a one-turn capture, since pushing or pulling that gold piece would place it on e3, g3, or f4, temporarily giving the trap two gold defenders.

The fork

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The gold elephant has forked the silver dog between the c3 and f3 traps.


The fork threatens a single frozen piece with capture in two different traps. It is the most basic of the two-turn tactics: on the first turn an enemy piece is threatened, and on the second turn it is captured unless the enemy can defend both traps. In the diagram at left, from this game, Gold has threatened to capture the silver dog in either c3 or f3. Silver to move would need one step to defend the c3 trap with the elephant, and three steps to defend the f3 trap with the cat. Unfortunately for Silver, the gold rabbit on e4 is threatening to reach goal next turn, so Silver must spend at least one step defending the goal, and the silver dog is lost.

Forks resulting in immediate material gain are more common later in the game when fewer defenders are available, but even if both relevant traps can be defended, holding a hostage near one or two traps can be an effective strategy to commit enemy pieces to defensive positions.

The fence

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The silver horse on c4 has been fenced in; Silver to move can't save it.


The fence is a less common two-turn capture tactic. A piece is brought next to a trap, and hemmed in on two sides. The piece may be unfrozen from a third side, but then its only direction of retreat would be into the trap. In the diagram at right, from this game, Gold has fenced the silver horse next to the c3 trap. Silver is to move, but can't prevent the capture of the horse. The silver elephant could indeed unfreeze the fenced horse by moving to c5 (incidentally capturing the gold rabbit in c6), but the unfrozen silver horse can't then escape, as its only available move would be suicide. Furthermore, the gold pieces prevent the silver elephant from reaching d3, c2, or b3 in four steps, and no other silver piece is close enough to defend the c3 trap.

Limitations of tactics

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
With Gold to move, there are no forced captures, despite tactical threats.


When one's opponent understands these tactics, there are not many ways to achieve immediate material gain. Until one side can gain a long-term advantage, most threats can be neutralized. In this game, shown at left, Silver has just flipped the gold camel from e3 to e5, and is threatening to capture it in f6. Besides defending the camel immediately, Gold must take care not to allow it to be forked between c6 and f6. The b5 horse could also be threatened in the near future. Despite these tactical ideas in the position, the game ended without a single capture. Although this is unusual, captures in Arimaa are much less common than in chess.

After becoming acquainted with the most basic Arimaa tactics, you should turn your attention to long-term strategy, which will better enable you to get into positions where tactics are of use.

Introduction to Strategy

Arimaa strategy involves straightforward concepts which overlap in complex ways. Very different styles of play remain popular; some players are very aggressive, quickly advancing piece after piece with the aim of controlling the entire board. Others tend to play a "home game", initially sending few pieces to enemy territory. However you prefer to play, it is best to understand any strategy which an opponent might use against you.

If you are playing Arimaa bots, you may have already defeated the weakest ones just by using basic tactics. Each strategy you learn will get you further up the bot ladder. There's no need to study all the subsections right away; just understanding basic concepts could take you far. Later, you could revisit this material to learn how to build on an advantage or turn around a disadvantage. As you progress up the bot ladder, you'll need deeper and deeper strategies.

Initial Setup

Understanding gameplay

Arimaa, like chess, is played on an 8×8 square board. The two players, Gold and Silver, control sixteen pieces each: one elephant (Elephant), one camel (Camel), two horses (Horse), two dogs (Dog), two cats (Cat), and eight rabbits (Rabbit), 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 must all step from square to square. 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.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The players begin by setting up their pieces however they choose on their home rows. Highlighted are the four trap squares.


37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png


The game begins with an empty board. Gold arranges their pieces on the first and second ranks, in whatever 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.

The 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. It is no easy task, however, to get a rabbit past an opposing army of stronger pieces—a player must out-maneuver the other army while at the same time keeping all enemy rabbits at bay.

The second diagram, portraying a position which could occur later in a game, helps illustrate the remaining rules of movement.

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 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.

Although most games conclude with a rabbit reaching goal, there are two other circumstances which can bring about an end.

  • Complete immobilization. If upon their turn a player has no legal move available, that player loses.
  • Loss of all rabbits. A player can win by capturing the last remaining enemy rabbit, even if they sacrifice their own last rabbit in the same turn.

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

Setting up

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.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Gold has used the 99of9 setup; Silver has switched the dogs and cats.


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 defender.

Notation

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png

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
    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.

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 goal in the north-east is Eg7s rh7w Rh6n Rh7n, or, equivalently, Eg7s rh7w Rh6nn.

Although this notation is rather verbose, proposed replacements have not become standard.

Early Ideas

Direct Goal Is Impossible

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Gold has no way to make progress with the h6 rabbit.

The most straightforward strategy in Arimaa is to advance a rabbit and some strong pieces, attempting to rip a hole in the opponent's defenses through which the rabbit can reach goal. If both players try to do this, the game turns into a race. Each player in a race must judge how many steps to spend delaying the opposing rabbit, and how many steps to use furthering their own rabbit.

Before long, however, the Arimaa community discovered that if one player tries to force goal in the opening while the other player defends, advantage accrues to the defender. With the entire defending army still at home, the pieces support each other, and thus can prevent an attacker from simply displacing enough pieces to get a rabbit to goal. Meanwhile, the attacking rabbit is vulnerable to capture in the defender's home traps. In the diagram at right, the h6-rabbit is no threat to goal, but the rabbit itself is in danger of capture in f6. Furthermore, rabbits can't retreat, so the h6-rabbit can't save itself. Finally, if the gold elephant advances to g6 to protect the h6-rabbit, the elephant will be blockaded.

Two threats

Realizing the futility of forcing an early goal, top Arimaa players next turned to capturing pieces as the most plausible strategy. However, that was not straightforward either. Suppose Gold threatens a silver piece with capture in a home trap. The silver elephant can camp out by that trap, and Gold can never capture anything there: the silver elephant defends other silver pieces, and can't itself be pushed or pulled. In order to make progress, Gold must create threats around two different traps.

For this reason, each player wants to be the first to make two strong threats. This could be as simple as forking one enemy piece between two traps; any non-elephant piece must be careful about advancing in the center. It is tempting to send one's elephant hunting and just keep everything else at home, but a skilled opponent could make that very slow, while developing more sophisticated threats of their own.

When one's elephant defends an away trap, it can likely protect any friendly pieces advanced on that wing; such pieces can't be captured in the protected trap, and if they were pushed toward the center, the elephant could help them retreat (unless they were rabbits, but even then it would take the opponent a few turns to drag a rabbit across the board, with the only gain being a rabbit capture.) With the gold elephant on e6, the silver camel in the west, and the gold camel in the east, the gold camel could advance and quickly create capture threats in both f3 and f6. Since these threats depend on the camel, however, the silver elephant can stop both, by attacking the camel. The gold elephant protects its camel from capture, but without other gold pieces already in place to support the camel, the silver elephant can hold it against the side of the board. To prevent capture, the gold elephant must stay beside the trap. With both elephants and the gold camel tied up in the northeast, the silver camel is the strongest free piece. Silver now has one strong threat in the camel hostage, and her own camel can help create a second threat, which only the tied-up gold pieces could defend against.

A note on the functions of pieces

In Arimaa, the strength and function of a piece depends on what pieces remain on the board. For instance, if each side has lost a camel and a horse, the remaining horses are the unique second strongest pieces on each side, and so have essentially the role that the camels had initially. When the following sections discuss strategic features such as camel hostages, it should be borne in mind that the actual pieces involved may differ if exchanges have taken place.

Camel Hostage

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The gold elephant is holding the silver camel hostage.


In the position at right, the gold elephant is holding the silver camel hostage. The camel is frozen, so it can't escape, and on any turn Gold could flip or pull it into the c3 trap. To preserve the camel, Silver must station his elephant next to the c3 trap. For now, Silver can't defend with less than the elephant, because any other silver defender could itself be captured in c3, unless there were two weaker silver defenders securely in place, which would require some work.

The hostaged camel is not held right next to the trap, because then it would help Silver control the trap, while the gold elephant would not defend the trap. In this case, that would allow Silver to capture the gold cat.

If Silver ever abandons his camel, the gold elephant should then pull it into the trap, finishing on c4 or d3, near the action. It is thus important that the gold cat remain on c2.

For now, Gold's elephant is tying up Silver's elephant and camel both, leaving Gold's camel unopposed as the strongest free piece. While things stay this way, Gold can dominate the other side of the board. The silver camel obviously can't defend f3, and at present the silver elephant can't defend f3 without losing its camel.

Use of Free Pieces

As the strongest free piece, Gold's own camel is key to his advantage. However, that does not mean the camel should simply march forward. Imagine in the above diagram that instead of the horse, the gold camel were on a6. Silver to move could send her elephant to b6, setting the stage for an even camel trade, which would be a disappointing outcome for Gold. Since the camel captures would each use all four steps of a turn, neither elephant could come back and save its own camel.

Even if the gold camel advanced on the other wing, it would have to be careful. Gold might advance his camel expecting that, if the silver elephant went east, the gold elephant could take care of everything. However, the silver elephant would have a head start while the gold elephant captured the silver camel, and other silver pieces could temporarily block the gold elephant's path to e6 or f5; Gold can't just assume his elephant could get there in time to save an advanced piece. Remember also that an advanced piece can retreat only if it is not frozen.

Usually, at least one horse should advance first. Besides protecting the friendly camel, advanced horses can also protect weaker pieces. The gold horse on the west wing is not attacking so much as it is defending the c6 trap. The hostage camel keeps Silver's elephant next to the c3 trap, but it can still dart around as long as it is on c4, d3, or even c2 at the end of a turn. This mobility could allow the silver elephant to dislodge a small gold piece and gradually move it up. If Silver could get a weak gold piece into silver territory, and Gold had nothing there to protect it, that gold piece would soon be lost while the silver camel would remain safe. The gold horses are prepared to defend the c6 and f6 traps, short-circuiting any such shenanigans by Silver. The gold horse in the west must keep some distance from the silver elephant, to avoid being frozen on c5 and then captured in two steps.

While holding the camel hostage, Gold wants to make a strong second threat and force the silver elephant to choose which to defend against. If Gold wants to take over an away trap, his own camel will likely have to advance in the east. Another option is to keep the gold camel where it is, and use the eastern gold horse to drag weaker pieces down for capture in f3. As long as the camel hostage remains in place, the silver horses are the strongest silver pieces which could defend f3, but that would be difficult with the gold camel right there. Indeed, the gold camel could hostage a weak piece much as the gold elephant is hostaging the silver camel, and the silver elephant couldn't defend both. If Silver doesn't abandon her camel, find some other way to defend it, or find such a way to defend f3, Gold can do this over and over, decimating Silver's forces.

Realizing that Gold is poised to take control, what should Silver do? Silver needs to free her elephant. In this case, Silver could give up her camel in exchange for a horse: if the silver elephant moves to b6, and the silver camel is then captured, Silver can pull the gold horse from a6 into c6, capturing it in return. That is a material loss for Silver, but not a bad deal considering the position she was in. Alternatively, Silver could use her horse to unfreeze her camel, which could then push the gold dog aside, burrowing the camel so that it could not be captured in one turn. This is an option only because Gold has left b2 empty; gold pieces on a1, a2, and b2 would form a phalanx, fencing in any a3 hostage. Burrowing the camel would only be a delaying tactic by Silver, since the camel would hardly be free, but it would allow the silver elephant to leave c3 temporarily.

If it's Gold turn, Gold can prevent Silver from doing either of those things. To fence in the silver camel, Gold could simply advance the b1 rabbit to b2, but a better option would be to slide the a2 dog to b2, the a1 rabbit to a2, and the b1 rabbit to a1; that way, the dog isn't blocked in. On the fourth step, the a6 horse could move to a7, precluding an immediate camel-for-horse trade.

Active Defense

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The silver elephant has regained mobility, so Gold has no advantage from holding a camel hostage


When the enemy has the strongest free piece, it is crucial to free one's own elephant within a few turns. Depending on the balance of forces near the trap, this can sometimes be done without giving up the camel; if two weaker pieces can defend the trap, the elephant can leave. In this game, diagrammed at right, Gold is strategically lost because the arrival of the silver dogs has freed the silver elephant to roam, whereas the gold elephant must stay put to prevent an immediate goal. Suddenly the tables have turned and Silver's elephant is the strongest free piece.

Such a scenario highlights one advantage of keeping the friendly camel home on defense while holding a camel hostage. Imagine that the gold camel were at home in the diagram at right, lurking on d2 for example. The e3 dog, and thus the f4 dog and g2 camel, would not be safe unless the silver elephant stayed nearby.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Gold must now attack Silver's home traps

The most active defense against a camel hostage is to bring up pieces either numerous enough or strong enough to contest both enemy traps. In this game, diagrammed at left, Gold can't make a capture in either c3 or f3, despite holding the silver camel hostage. The gold camel would like to help regain control of c3, but the silver elephant is well-positioned in the way.

Who has the strongest free piece now? The silver elephant is more free than the gold elephant, but it isn't totally free, because if it crosses back to the silver side of the board, the gold camel will smash across into the silver horses around c3. Likewise, the gold camel isn't really a free piece, because it needs to lurk around in order to keep the silver elephant committed to defending c3.

As it turns out, the gold horses are suddenly the strongest free pieces. Gold can't yet force a capture at home, but he can use both horses to take over an enemy trap (most likely f6), threatening captures and ultimately goals. Silver might then move his elephant to the defense of that trap, and further threaten one or both of the gold horses with capture, but in that case Gold will stand to gain even more than that in c3 and f3. Gold's upper hand traces back to the camel hostage.

Camel hostage value

When Gold is holding a silver camel hostage in Gold's home territory, both sides are usually keen to advance on opposite wings. Gold wants to advance on the non-hostage wing in order to secure material and goal threats, using the strongest free piece as necessary. Meanwhile, Silver wants to advance on the hostage wing in order to rotate out her elephant. The value of the hostage depends on the outcome of this race, and therefore on the initial positions of the pieces. The hostage will tend to be worth more if the gold camel is already on the non-hostage wing, and less if gold pieces (particularly the horse) are stuck behind the hostage.

If Silver is not well-positioned for an elephant rotation, she might abandon her camel and seek compensation elsewhere. For Gold, the hostage value depends on what compensation Silver could get, and what the resulting position would look like. It is typically hard to make use of a camel hostage without exposing a friendly horse to capture. Since a camel is estimated to be worth a horse and cat as an initial trade (see Relative Value of Pieces), it is not usually worth giving up more than a cat to get a camel hostage. If the board is full, and Gold takes a camel hostage but gives up a cat in the process, and then Silver abandons her camel but captures an enemy horse in return, material is basically even. If this sequence happens after material has already been exchanged, Silver likely comes out ahead, and thus the hostage was a net loss for Gold even though he captured the silver camel.

If Silver is well-positioned for a quick elephant rotation, a hostage is likely of negative value for Gold. One should not aim to take a camel hostage if the opponent could defend it without their elephant.

Other hostage patterns

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
A double hostage is stronger than a simple camel hostage


At right (game) Gold is holding a double hostage of the silver camel and horse. A double hostage is worth significantly more than a simple camel hostage, for two reasons. Firstly, since more material is threatened, the silver elephant will find it harder to abandon the hostages and get adequate compensation. Secondly, with the g2 horse unable to fight for control of f3, it will be difficult for Silver to rotate out the elephant. Note also how the horse contributes to the blockade preventing the camel from escaping.

One option for Silver is to occupy g4 with a weak piece. If the silver elephant then leaves, any capture the gold elephant could make would land it on a square other than g3, so the second hostage might escape. Gold must take this into account; for example, if Gold advanced his camel and then it was threatened, Gold might only get an even camel trade, despite having held a double-hostage. Gold would further have to deal with an enemy horse moving through his own back row, now with no camel to threaten it.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Gold has an unstable but valuable high hostage

In this game, Gold has a high hostage. This type of pattern is less common than an ordinary camel hostage, since more pieces are required to maintain it. In this case, the hostage is unstable, as the silver horse can erode the blockade on b4 and then unfreeze the camel. If a high hostage can be maintained, it is more valuable than an ordinary hostage because the gold elephant remains centralised, making it harder for Silver to share control of c3.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
This central hostage will result in the capture of the camel


A central camel hostage often results in the quick capture of the camel; if the hostage-taker has good control of their home traps, the camel can simply be forked between them. In the example at right (game), the blockade on d2 prevents the camel from escaping, and the silver elephant can cover only one of c3 and f3. Such hostages are therefore more in the realm of tactics than strategy. TODO: find better example.

Elephant Blockade

Strongest free piece revisited

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The silver elephant has no legal move, so the gold elephant is the strongest free piece.

Not long after discovering the camel hostage strategy, human players discovered that some bots could be lured into an elephant blockade by the offer of a free piece for capture. Later it was discovered that the bot may squirm to try to free its elephant, and in the process get jammed all the way against an edge of the board.

In this game, diagrammed at right, Gold has lost a cat while Silver has a full army, but Silver is nonetheless completely lost. Not only is there no empty square for the silver elephant to step into, there is no empty square into which it can push its tormentors. The gold elephant and camel will keep an eye on the silver camel and horses respectively. Gold can ward off any attempts to break the silver elephant out of its prison, while herding silver pieces at will into the f3 trap. This is a much more decisive advantage than a camel hostage. Silver has no plausible lines of play in this case.

Rotation

Most elephant blockades, however, are not as hugely advantageous as that one. It is a rare opponent who will voluntarily move his elephant to the edge of the board when a blockade is looming. The diagram below left, from this game, shows a slightly less advantageous situation with the blockaded elephant one square away from the edge of the board.


37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The gold elephant is blockaded, but the game is not over.

Here the gold elephant can't move, true, but nine silver pieces are required to maintain the blockade, including both the silver elephant and camel. Indeed, if all the pieces involved in the blockade stayed put, the strongest free piece would actually be the gold camel.

As it happens, however, Silver can undertake a rotation (or replacement) of the pieces participating in the blockade. When it comes to being in the way, a weak piece serves just as well as a strong one. Silver to move can free his camel for duty in only four steps, while maintaining the blockade: camel h6 south, rabbit h7 south, rabbit h8 south, and rabbit g8 east. The gold elephant can't make use of g8 to dig its way to freedom without getting smothered against the edge, so Silver can fill in that hole next move. Thus Silver needs only one turn to equal Gold for having the strongest free piece.

Furthermore, if Gold plays passively, Silver can continue to rotate pieces, freeing his elephant as well in two or three more turns. Because of this threat, it is very important that Gold not remain passive. Gold must immediately begin preparing a rescue mission to erode the blockade from the side, or even from the front if the silver elephant tries to leave. This will necessarily expose gold pieces to danger, but at least it puts some play into the position. For Gold to hang back is to await execution.

Note that even if Silver manages to rotate the elephant out of the blockade, it will require a few more pieces to maintain than a blockade on the edge. Furthermore those pieces will protrude one square further, making them slightly easier targets for would-be blockade busters. Still, the blockade is quite advantageous to Silver.

When rotation is impossible

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Silver has blockaded the gold elephant, but would gladly give up the blockade to take the Gold camel hostage.


The diagram at right, from this game in the 2006 Arimaa World Championship, features an elephant blockaded one step further from the edge of the board, which is correspondingly less advantageous. Indeed, it is no longer realistic for Silver to expect to be able to free his elephant by rotating blockaders appropriately. True, the f6 trap is participating in the blockade at the moment, but Gold might bring a piece to f5 or e6, allowing the gold elephant to step to freedom, so Silver must soon occupy at least the latter squares.

An elephantless blockade would require silver pieces on g8, f7, g7, h7, e6, h6, f5, g5, h5, and g4. Not only are ten pieces necessary, but the bubble of blockaders also presents a large surface area for Gold to assail, extending within two steps of Gold's home trap at f3. Silver would be too busy warding off threats to the blockade to ever start capturing pieces with his freed elephant.

Since Silver can't rotate his elephant out of this blockade in practice, it does not give him the strongest free piece like an ideal blockade does. Yet the blockade is not worthless. Its value is that, although both Gold and Silver have a free camel, the silver camel is more free.

Suppose that Silver, while maintaining the blockade, were to use his camel to attack the c3 trap. Gold could defend c3 with his own camel, but couldn't endanger the attacking silver camel. In contrast, if Gold were to attack c6 with his camel, Silver would have the option of giving up the blockade to cross wings and take the gold camel hostage. (This principle recurs again and again in the study of elephant mobility.)

This difference of freedom pegs the value of the blockade to Silver at somewhat less than a camel hostage. Silver certainly can't expect to get more out of the position, because if Gold is willing to give up his camel as a hostage, he can frustrate anything else Silver might undertake. Indeed, the gold camel can probably break the blockade at any time if it is willing to expose itself. On the other hand, Silver can't necessarily force Gold to expose his camel. Gold can play in the west as well as hovering in the east making threats to break the blockade. If Silver has trouble generating a threat in the west while maintaining the blockade in the east, he may be forced to give up the blockade for an advantage smaller than a camel hostage.

Partial blockades

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
A partial elephant blockade makes the gold camel the strongest free piece.


Because of the difficulty of blockading an elephant in the centre of the board, complete elephant blockades are uncommon in games between strong players. Partial blockades, keeping the elephant from accessing an important area of the board, are more frequent. In this position (see game), Silver has a horse hostage, which ideally would make the silver elephant the strongest free piece. In this case, however, the elephant is blockaded away from the centre of the board; the strongest free piece is in fact the gold camel. Note that the blockade is not complete: the elephant can escape through the c6 trap. This maneuver would take several moves, allowing the gold camel to capture a piece in the meantime. Furthermore, it would disrupt Silver's defense of c6, probably allowing Gold to share control of the trap.

The Center

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The gold elephant is cut off from the center.


A more subtle, positional aspect to elephant mobility is the ability of the elephant to access the areas of most importance at the current stage of the game. From the centre four squares of the board the elephant has access to all four traps, so as a general rule it is better for the elephant to be centrally located. Also, a centralized elephant is almost impossible to blockade. On the other hand, in order to attack or defend a trap, an elephant must decentralize itself at least to one of the eight squares in the ring around the center, and perhaps further if it is hunting down a fleeing piece. The possibilities available to an elephant in the center usually remain mere possibilities until the elephant leaves the center to pursue one of them.

It is occasionally possible to station a clump of friendly pieces in the center of the board, which can cut off the opposing elephant's ability to switch wings at will. In the diagram at right, from this game, Gold is losing because the gold elephant can't access the f3 trap.

This strategy must be used with great caution, however, because if the opponent is able to erode the dividing wall, there will probably not be time to retreat all of the participating pieces to safety. At right, if the gold elephant could break through the wall, some silver piece would likely perish in f3. In general, pieces other than the elephant should stay out of the center. It is asking for trouble to give the opposing elephant a target in the center where that elephant wants to be anyway.

Elephant Mobility

As long as an elephant is not blockaded, it retains a theoretical freedom to roam the board. There are, however, fine distinctions in exactly how free an elephant is. A whole spectrum of positional features may limit an elephant's field of operation; enemy pieces can block an elephant's access to certain squares, or an elephant may need to stay beside one trap, to prevent significant material loss and/or an enemy goal.

Both elephants start out free, but differences in elephant mobility soon emerge. In Arimaa, tiny advantages often snowball; a more mobile elephant can pose increasingly tricky defensive puzzles for a less mobile elephant. As the game progresses, an elephant can become more and more committed to the defense of a particular trap. When an elephant can't afford to leave a trap, that elephant has clearly lost mobility.

Other than the elephants, any piece can potentially be taken hostage, and often the elephant is the only friendly piece which can feasibly protect it. The defending elephant will lose some mobility, but it could also threaten or isolate the hostage-taking piece, perhaps limiting the enemy elephant's mobility as well.

Not all hostages are good

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The horse hostage does not benefit Silver, since the gold camel is more free than the silver camel. (from this game).

An elephant holding a camel hostage is only one example of a whole class of positions where a frozen piece is held in danger of capture, committing the opponent to defense. However, not all such positions are effective. Suppose, for example, that an elephant holds a horse hostage instead. This commits the opposing elephant to defense, true, but who has the strongest free piece? The defending elephant can't leave without losing a horse, but the hostage-holding elephant often can't leave either, because the newly-freed horse would cooperate with the formerly-defending elephant to wreak havoc at that trap.

In this diagram, Silver is holding a hostage, but neither elephant wishes to leave the northeast trap square. Indeed, the gold elephant is closer to the center, and is thus a greater threat to the silver camel than the silver elephant is to the gold camel. Since the gold camel has more freedom of movement, Gold may make progress despite having a horse held hostage. Essentially, the inactivity of one gold horse is insufficient compensation for the decentralisation of the silver elephant and for Silver's poor alignment.

In some cases, such a hostage might be converted to a frame, or passed off to the silver camel, freeing the silver elephant. If Silver were better positioned for that, it would be urgent for Gold to prevent a solid frame or horse-by-camel hostage. Unless the silver camel comes east, the gold elephant should stay on e6; if e6 and e7 were clear, the silver elephant could pull the gold horse onto e7 with a threat to fork it between traps.

Gold can treat this position somewhat like a camel hostage position, with pieces advancing on the hostage wing to replace the gold elephant in defending the horse. The difference from a camel hostage is that Silver does not have the strongest free piece, which means that there is more time to achieve an elephant rotation. It would be less straightforward for Gold were the gold horse held on h6 with the silver horse on g7: the silver elephant would be able at any time to leave the area while the silver horse blocked the gold horse away from sharing control of f6. In this case, Gold should still be able to make progress by actively using his camel, for instance in an attack on c6.

Horse hostages

Arimaa board sw55.jpg
Arimaa-border.png
a5 b5 c5 d5 e5
a4 b4 c4 d4 e4
a3 b3 c3 d3 e3
a2 b2 c2 d2 e2
a1 b1 c1 d1 e1
Arimaa-border.png


Arimaa board sw55.jpg
Arimaa-border.png
a5 b5 c5 d5 e5
a4 b4 c4 d4 e4
a3 b3 c3 d3 e3
a2 b2 c2 d2 e2
a1 b1 c1 d1 e1
Arimaa-border.png


Arimaa board sw55.jpg
Arimaa-border.png
a5 b5 c5 d5 e5
a4 b4 c4 d4 e4
a3 b3 c3 d3 e3
a2 b2 c2 d2 e2
a1 b1 c1 d1 e1
Arimaa-border.png

The right piece to hold a horse hostage is a camel. Ideally this ties the opposing elephant to defence, while the friendly elephant is free to roam. However, the situation is often unstable because the "defending" elephant can attack the hostage-holding camel, which could quickly turn the tables. Thus the camel needs friendly supporting pieces, to keep the advantage long enough for the friendly elephant to make a strong second threat. A good horse hostage can be worth more than a camel hostage, but this depends on the hostage-taker's ability to make quick threats.

These diagrams illustrate different positions for a horse-by-camel hostage. In the first diagram, the gold piece on a4 is necessary for the hostage to be effective: pulling the gold camel to b4 would be a waste of time, as it could simply return to b3. It may take Silver several turns to break this hostage, which should allow Gold to gain a large advantage elsewhere. Note that the b2 cat allows capture of the hostage in case the silver elephant goes to b4. Also, Gold should leave d3 clear; if d3 were occupied by any gold piece, the silver elephant could then afford to move to b4, since the only one-turn capture would end with the gold camel on c4, where it would be threatened in c6.

Without the gold horse on a4, the hostage would be weak. With ec4w eb4e Mb3n ha3e, Silver could have her elephant on c4 and her horse on b3, with the gold camel frozen on b4. Not only could Silver then threaten captures in c3, but she could also flip the gold camel to c5, with a threat to capture it in c6. If Silver had time for these maneuvers, Gold's hostage might in fact be an advantage for Silver.

The second diagram shows a similar position, but with the horse on b2 rather than a3. This means that the horse can more directly join the trap control fight if the camel is dislodged—for instance, here Silver is threatening to capture the camel by false protection. On the other hand, from b2 the horse can be pushed to b1, where it remains stuck.

In the third diagram, the silver elephant has no easy way to approach the gold camel. As long as Gold retains control of the b3 square, the hostage is fairly secure. This can be the strongest type of horse hostage, provided there are enough pieces to maintain it.

In all of these cases, the side defending the hostage should consider bringing more pieces into the local fight. For instance, in the last example Silver would have a strong position if she could bring a horse to b3, dislodging the gold dog. In the first, the silver camel might be able to attack the a4 horse, which would weaken the hostage pattern.

Cat and Dog Hostages

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
In this game, Silver's position would be much stronger if its camel were free and a silver horse held the gold dog hostage.


A smaller piece may also make a valuable hostage. In this example, the silver camel holds a gold dog hostage next to the c6 trap. The silver elephant is free to pull gold pieces toward the f6 trap. The gold elephant can't defend c6 and f6 at the same time.

However, the situation is less than ideal for Silver, for two reasons. First, the silver cat on c6 means that the hostage dog isn't threatened with one-turn capture. If the gold elephant leaves, it will take five steps for Silver to capture the hostage dog, giving the gold elephant that much more mobility. Second, the gold rabbit on h5 gives the gold camel more freedom to advance without fear of being taken hostage by the silver elephant. Silver would like to send his elephant after the gold camel, but in practice will probably have to try to capture the h5-rabbit before this is feasible.

In general, the advantage of a small piece hostage over a horse hostage is twofold. First, the smaller piece can be held hostage by a horse, sparing both the friendly elephant and the friendly camel for other duty. Second, it is easier to frame a small piece than to frame a horse. In the diagrammed position, Silver would have a greater advantage if the c7-camel were swapped with the g6-horse. Then the silver camel could defend the f6 trap while the silver elephant either hunted for a second piece to drag for capture, or assisted in framing the hostage dog. As it stands, the silver elephant can't help frame the c8-dog, because of the damage the gold camel would do in the mean time.

Race Positions

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
The players are racing to capture pieces as quickly as possible.


Race positions occur when the two elephants each take control of an opposing trap as in this game diagrammed at right. In a race position, both elephants are clearly free, so elephant mobility is of secondary importance. The critical issue is which elephant can do more damage more quickly.

Race positions are rare because they typically require one player to have misjudged the position in a costly way. The player who is going to lose the race shouldn't have raced in the first place. The ultimate loser will wish he could go back to the move on which he used his elephant to attack rather than defend.

By the same token, however, it is important to know how to play in a race position, so as to be able to judge beforehand whether or not to race. One strategic point is that an elephant assisted by other pieces usually makes progress faster than an unaided elephant. Another point is that an advanced rabbit makes an attack much more potent by threatening to make goal, and may force the opposing elephant to break off its attack, wasting a couple of moves to cross over and defend.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Goal threats trump capture threats.

In the position at left, from this game in the 2006 Arimaa World Championship, Silver is on move. Each player is threatening goal. As soon as one player is forced to defend with his elephant, the game will essentially be over, because the other player will capture the little attacking pieces near the trap where the attack has just been abandoned. In other words, both players have staked the game on the outcome of this race.

Silver should consider using his camel to push the d6-rabbit back to d5. It may endanger the silver camel to bring it nearer to the gold elephant, but in a goal race it may be worth sacrificing a camel to buy time. Meanwhile if Gold ends Silver's goal threat by capturing the g3-rabbit, the silver elephant will respond by heading home for defense and capturing the gold f4-camel in f6. Therefore Gold would have to keep racing instead.

Because the cost of losing a race is so high, and because the side with more pieces committed usually makes progress faster, it is rare to respond to a complete loss of trap control by launching an all-out race. Instead, the defender might protect material with the elephant while building towards a slower counter-attack.

Trap Control

Each trap is either owned by one player or shared. To own a trap is to be safe from capture in it, and further to be able to capture opposing pieces in it. At the beginning of the game each player owns their two home traps (c3 and f3 for Gold, c6 and f6 for Silver), but this could change quickly as pieces advance. It is very valuable to take complete ownership of an enemy trap. An enemy trap usually has plenty of enemy pieces nearby, which might be captured in quick succession, in contrast to the laborious process of repeatedly prying loose a single enemy piece and dragging it all the way to a home trap for capture. When pieces are threatened in their own home trap, they might delay or avoid capture by scattering, but this is even better for an attacker, since it leaves a hole through which a rabbit might reach goal. Threatening to own an opposing trap is quite forcing: it limits the opponent's options to immediate defense or sharp counter-attack.

37px-Arimaa board.jpg
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5