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Table of Contents
- Playing The Game
- Introduction to Tactics
- Introduction to Strategy
- Camel Hostage
- Other Hostages
- Trap Control
- Distribution of Force
- Rabbit Advancement
- Elephant Blockade
- Race Positions
- Relative Value of Pieces
- Lone Elephant Attacks
- Advanced Tactics
- Sample Games
- Arimaa Challenge History
- GNU Free Documentation License
Arimaa (pronounced uh-ree-muh) 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 32-piece, 64-square board game that would be easier for humans than computers. His idea was to create a game with simple rules, but too much variation for a computer to keep track of. In 2002 Syed published the rules for Arimaa and announced a $10,000 prize, available annually through 2020, for the first computer program to win matches against top-ranked human players. David Wu's bot Sharp accomplished this in 2015.
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, although a bot-in-progress named "Dolores" appears promising.
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 various events have been hosted online:
- 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. Mathew Brown won it in 2015, 2016, and 2017. Karl "Fritz" Juhnke won it in 2005 and 2008.
- 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. At first, the winning bot played an eight-game match against a lone human defender. The format evolved: from 2007 onward, 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, where it faced three ultimate human defenders, who were selected beforehand and hadn't played in the screening. If this bot could win best-of-three 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 Mathew 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
Arimaa, like chess, is played on an 8×8 square board. The two players, Gold and Silver, control sixteen pieces each (listed in descending order of strength):
If Arimaa is played using a chess set, the pieces may be represented by the king, queen, knights, bishops, rooks, and pawns respectively. Unlike their chess counterparts, however, Arimaa pieces move only in cardinal directions, and step one square at a time. Diagonals have no place in the rules of Arimaa. The relative strength of each piece lies in its power to push, pull, or immobilize weaker enemy pieces. There are four trap squares on which a piece can potentially be lost — these are the squares designated as c3, f3, c6, and f6 when classified by rank and file.
The main objective is to get a rabbit across the board; the opponent's home rank is the goal line.
The players begin by setting up their pieces however they choose on their home rows. Highlighted are the four trap squares.
The game begins with an empty board. Gold arranges his pieces on the first and second ranks, in whatever configuration he chooses — Arimaa pieces do not have fixed starting positions. Silver then arranges her pieces on the seventh and eighth ranks. The diagram shows setups which are fairly common.
A piece steps from square to square. Most pieces can step left, right, forward, or backward. Rabbits can only step left, right, or forward.
A turn (or move) consists of one to four steps. The steps in a turn can be used on four different pieces, all on the same piece, or any combination. After the setup phase is completed, the players alternate turns with Gold going first.
A player may not pass a turn, which must make a net change to the position. Thus one cannot, for example, move the same piece forward and backward and leave it at that. Furthermore, a turn may not result in a position identical to one which the same player has created twice before.
The second diagram, portraying a position which could occur later in a game, helps illustrate the remaining rules of movement.
A piece which is adjacent (in any cardinal direction) to a stronger enemy piece is frozen, unless it is also adjacent to a friendly piece. A frozen piece may not be moved by its owner. The silver rabbit on a7 is frozen, but the one on d2 can move because it is next to another silver piece. Similarly the gold rabbit on b7 is frozen, but the gold cat on c1 is not. The dogs on a6 and b6 do not freeze each other, as they are of equal strength.
A frozen piece can freeze another still weaker piece just as it would otherwise. The silver elephant on d5 freezes the gold horse on d6, which itself freezes the silver rabbit on e6.
Pushing and pulling
A piece can pull or push a weaker enemy piece which is next to it, provided an empty square allows for the necessary movement.
To pull, a piece steps onto an adjacent empty square and drags the weaker enemy piece onto the square from which it came. The silver elephant on d5 could step east, west, or south and pull the gold horse from d6 to d5. To push, the weaker enemy piece is moved onto an adjacent empty square, and the piece which pushed it moves onto the square it had occupied. The gold elephant on d3 could push the silver rabbit on d2 to e2 and then occupy d2. A push or pull uses two steps, since two pieces are moved.
Note that the rabbit on d2 can't be pushed to d1, c2, or d3, because those squares are already occupied. Remember also that a piece can only push or pull a weaker enemy piece — for example, a dog may dislodge an enemy rabbit or cat, but not a dog, horse, camel, or elephant. Although a rabbit may not retreat toward its home row, it can nonetheless be pushed or pulled in that direction. For example, the gold rabbit on g3 could not itself step back to g2, but the silver horse could take a step right and then pull it down.
A piece may not push and pull simultaneously — for example, the gold elephant could not dislodge the d2 and c3 rabbits in one move. Likewise, no piece can push two pieces at once. Since even an elephant can only push one piece at a time, an elephant can sometimes be blockaded so that it has nowhere to go. This is the only way an elephant can be immobilized, since no piece can freeze it.
Whether a piece is frozen is independent of whether it can be dislodged — an adjacent friendly piece does not protect against pulling or pushing. For example, the d1 cat does not protect the c1 cat from being pushed to b1 or pulled to c2.
In Arimaa, a capture can only occur on a trap square. A piece which enters a trap square is removed from the board unless there is a friendly piece next to that trap. 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 c4 rabbit and c2 horse — the c3 trap has two silver defenders. If all friendly defenders left or got dislodged, a piece still on a trap square would be lost.
A piece may voluntarily step into a trap square, even if it is lost thereby. The second step of a pulling maneuver may be completed, even if the pulling piece is lost on the first step. For example, Silver to move could step the silver horse from f2 to f3, losing the horse, and still pull the gold rabbit from f1 to f2 as part of the horse's move.
End of the game
An Arimaa game cannot end in a draw. There are three different ways to win:
- Goal: The principal object of the game is to move any friendly rabbit all the way across the board. Thus Gold wins by moving a gold rabbit onto the eighth rank, and Silver wins by moving a silver rabbit onto the first rank. This is normally how a game is won.
- Elimination: One can win by capturing the last remaining enemy rabbit.
- Immobilization: One can win by creating a position that leaves the opponent with no legal move.
If one side's move directly brings about a winning condition for the opponent, the opponent wins, except under these rare circumstances:
- If a move brings about goal or elimination for both sides, the one who made the move wins.
- Goal or elimination wins the game even if one's pieces are technically left immobilized. Immobilization is only checked at the start of a turn.
- If a rabbit is dislodged onto its goal line and then dislodged off within the same turn, the game continues.
The finer points of initial piece placement will be explored later, but for now you just want a flexible setup that 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.
Gold has used the 99of9 setup; Silver has switched the dogs and cats.
In the diagram at right, Gold has chosen the 99of9 setup (named for the player who popularized it), which is good for beginners because of its simplicity and flexibility. 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.
The gold horses will quickly move up, to assert control of Gold's home traps; one or the other might then advance in a bid to take over Silver's home trap. 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, she can take Gold's setup into account when deciding on her own. At right, note that the silver elephant is not placed directly opposite the gold elephant. If both elephants started on the same file, Gold could advance his 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 she's not careful. As long as another silver piece is next to the trap, however, a dog behind that trap strengthens Silver's control of it, since dogs cannot be pushed aside by enemy dogs.
You may wonder why rabbits do not begin behind the home traps. Experienced players will sometimes do this, but the downside is that a rabbit could get pushed into a protected trap and then could never step back, creating a mess for the home player.
You can become a decent Arimaa player without learning the standard notation for moves. For brevity's sake, however, examples will sometimes use the notation rather than spell out each individual step. You can learn the notation now or later.
Each individual step is notated as ⟨piece⟩⟨initial square⟩⟨direction⟩.
- ⟨piece⟩ is a single letter:
- E for Elephant
- M for caMel
- H for Horse
- D for Dog
- C for Cat
- R for Rabbit
- ⟨initial square⟩ is a two-character square name as in chess notation (e.g. e4).
- ⟨direction⟩ can be n, e, s, or w for north, east, south, or west. This is always from Gold's point of view. In addition, the special direction x indicates that the piece is captured.
Suppose Gold is to move in the diagram. The false protection capture of the silver elephant is described as Mb4e db3n cd3e Hd4s ec3x. The northeastern goal is Eg7s rh7w Rh6n Rh7n, or equivalently, Eg7s rh7w Rh6nn. Consecutive steps by the same piece may be condensed, with only the initial square given.
Although this notation is rather verbose, proposed replacements have not become standard.
Introduction to Tactics
A tactic is a narrow plan. It's easy enough to plan one's own turn, but unless that turn ends the game, one must consider how the opponent could respond. Since each player's turn consists of up to four steps, and there are usually lots of pieces that could move, seeing even one turn ahead can be tricky. Sometimes, however, one can severely limit the opponent's viable options. If a move creates a one-turn goal threat, the opponent must stop the goal or else lose the game. If a move creates a capture threat that if executed would give one a large material lead, the opponent must either stop the capture or somehow mitigate it, perhaps by capturing a piece in return.
Tactics can be offensive or defensive; a defensive tactic may slow things down considerably. When nothing big is imminent, plans may be more general, with each side aiming for a strong long-term position. This gets out of tactics and into strategy.
Each side to move has a one-turn goal on each wing.
At left, the gold rabbit on b5 can step to victory via b6, c6, c7, and c8. The rabbit is never frozen, as it is always next to the b7 cat or c5 dog, which also allows the rabbit to move through the c6 trap. The rabbit will theoretically be frozen once it reaches c8, but Gold will have won regardless.
Even if a rabbit's path is blocked, there may be a four-step goal. If the gold cat on h7 moves to h6 while pulling the silver rabbit from g7 to h7, the gold rabbit on g6 can step to goal. The gold camel on f6 is lost when the rabbit advances, but reaching goal is worth any sacrifice. Beginners often incline more toward pushing than pulling, but note that a push is ineffectual here. If the gold cat pushes the silver rabbit, the cat will be on g7, blocking its own rabbit with only two steps remaining.
Near a depleted goal line, an enemy rabbit is a constant threat. By pushing the b3 horse to c3, the silver camel would occupy b3 and unfreeze the b2 rabbit, which could then step to victory via a2 and a1. Occasionally a rabbit can be unblocked and unfrozen with one pull. Silver to move could slide the silver elephant from g3 to f3, pulling the gold rabbit from g2 to g3; the newly unfrozen f2 rabbit could then step to the vacated g2 and then to g1, winning the game. The silver elephant is lost on the third step, but that doesn't matter since Silver has won. With the f2 rabbit beginning the turn blocked and frozen, this one-turn goal is very easy to overlook.
In the above position, each side to move can win the game, but pretend that Silver does not have a one-turn goal and thus must defend. There are a few ways to stop each gold goal individually, but Silver has only four steps to stop both. To block the eastern goal, Silver must close the path to g8 without opening a different one-turn goal path. This could be accomplished by stepping the h8 cat to g8, leaving three steps for the western defense. In those three steps, the b4 camel or d6 horse could capture the c5 dog and freeze the b5 rabbit. If Silver had only two steps for western defense, the b5 rabbit could be pushed west, or the goal path could be blocked.
Suppose Gold had to stop Silver's goals. The simplest solution is Ee3nww Rh1w, which would freeze and threaten the silver camel while also keeping the f2 rabbit frozen, since unfreezing it would no longer be worth an elephant sacrifice by Silver. If Gold had only two steps for western defense, he couldn't freeze the silver camel, but could impede it.
Even if a goal can be stopped, a one-turn goal threat will force the opponent to use up steps on defense, unless he has a one-turn goal of his own. A move which creates a goal threat is typically part of a multi-turn plan, either to force goal or to force something else that the opponent won't have time to stop. One should always be aware of possible goal paths on both sides, so as not to be caught off guard or miss an opportunity.
Gold to move has one-turn captures in c6, f6, and f3; Silver to move has a one-turn capture in c3.
A piece adjacent to a trap is said to be a defender of that trap. A non-elephant acting as its side's sole defender of a trap is often vulnerable. With Gold to move in the position at right, the gold elephant can take two steps west 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.
One can sometimes push aside an obstructing piece to get at a vulnerable piece. With Gold to move, the g6 camel can push the g7 cat to h7; now on g7, the gold camel can push the f7 horse to f6, capturing it in a turn where one friendly piece pushed two different enemy pieces.
A piece on a trap square will be captured if its sole defender is dislodged. Silver to move could step her elephant two squares west and then dislodge the b3 dog, capturing the c3 horse.
The g3 dog can capture the g2 cat in four steps, either by pushing it twice (cg2w Dg3s cf2nx Dg2w), pulling it twice (Dg3w cg2n Df3s cg3wx), or flipping it (Dg3n cg2nwx Dg4s). A flip is a pull and then a push, with the flipped piece moving two squares and the flipping piece returning to its original square.
Sometimes, the best way to stop a capture is to move the threatened piece. The silver elephant protects the b3 cat from capture in c3, but neither piece needs to be tied down. The silver elephant could step west and thereby unfreeze the b3 cat, which could then step to a3 and then to a4.
Other than that, stationing one's elephant next to a trap square is the simplest capture defense. Since an elephant can't be dislodged, no friendly piece can be captured in that trap until the elephant chooses to leave. At left, no gold piece can be captured in c6, and no silver piece can be captured in c3, unless the respective elephant moves away.
A non-elephant can sometimes defend a trap alone, but that is usually precarious. The enemy elephant may lose something if it leaves a different trap, but if it captures a stronger piece in return it was worth it. When a non-elephant is its side's sole defender of a particular trap, it must keep a constant eye on all enemy pieces stronger than itself.
Two non-elephant pieces can defend a trap together; this is called mutual protection. Since a trap's four key squares are not right next to each other, four steps are not enough for any single attacker to dislodge one defender and capture the other. At left, Silver has defended the c6 trap with a dog on b6 and a rabbit on c7. Even if the gold elephant started on b5, it could not immediately capture anything in c6. Gold could at most dislodge the dog to set up a capture threat for the following turn, but then Silver could add another defender, such as the d7 horse.
Instead of adding a second defender to a trap, one can sometimes obstruct the path of an attacking piece. A phalanx blocks the gold camel from g7, thus the f7 horse is currently safe even though it is Silver's only direct defender of the f6 trap.
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. Gold has stuffed c3; the silver elephant could push the gold cat to d3, but that would temporarily give the c3 trap two gold defenders, preventing any capture in Silver's final two steps. Occupying c3 only works because no silver piece immediately threatens the c2 dog; if it were dislodged with the cat still on c3, the cat would be lost.
The f2 dog allows the g3 camel to safely step into the trap, and then capture the gold horse with a pull. Gold to move could prevent this with He3sn df2w Df1n, a pull and replace that would give the trap a second gold defender.
If defending a trap is not feasible, threatened pieces might scatter away from it. It may not be possible to get every piece to safety, but even delaying captures can buy time to make progress elsewhere. One scattering pieces away from a home trap should try to block the goal line, as enemy rabbits can easily advance toward an undefended trap.
More capture patterns
Although not immediately obvious, a one-turn capture is possible in each trap.
It is easy to become too confident about one's defense. At right, Silver has two pieces next to the northwest trap, but Gold has a stronger piece next to each, and thus has a one-turn capture. First the gold elephant can push the silver dog from b6 to c6, and then the newly unfrozen gold cat can push the silver rabbit from c7 to c8, capturing the dog. If Gold prefers to capture the rabbit instead, he can pull the dog away, and then push the rabbit into c6. This situation, where one defender can be dislodged and the other captured, is known as false protection. Such a capture is only possible if there are two attackers, each adjacent to a weaker defender.
In the northeast, 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, Gold has calculated that even if the silver elephant pushes the gold rabbit from b4 to a4, the b3 horse cannot be pushed. 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.
In the southeast, the f3 dog can 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 there.
In this game, the gold elephant has forked the silver dog between the c3 and f3 traps.
The fork is a basic multi-turn tactic, in which a piece is threatened with capture in two different traps. In the diagram, Gold has threatened to capture the silver dog in either c3 or f3. There is currently no chance for the dog to escape, so Silver would have to defend both traps in order to save it. Silver to move would need one step to defend c3 with the elephant, and three steps to defend f3 with the cat. Unfortunately for Silver, the gold rabbit on e4 is threatening to reach goal next turn, and cannot be frozen in place as it is next to the gold elephant. Silver must spend at least one step defending goal, and the silver dog is lost.
Generally speaking, a solid fork is most likely to occur between the forker's home traps; any other fork would tend to be easier to escape. From the start of the game, each side must be wary of allowing the opposing elephant to flip a piece into the centre, as that can lead to a strong fork. As defenses thin, forks become a greater potential threat in all areas of the board.
Use this link to make moves on the board.
Solution: ed3n Rc4w ed4w cb7s. Silver forks the camel between c3 and c6, blockading b5 so the camel cannot go west. The gold camel has no effective way to escape, and Gold has no effective way to defend both traps at once; Gold could put a rabbit or horse on d3, but the silver elephant could pull that piece into the trap, capturing it while retaining the camel fork.
The silver horse on c4 has been fenced in; Silver to move can't save it.
The fence is a less common multi-turn tactic. A piece is brought next to an unprotected trap, and hemmed in on two sides. The piece may be unfrozen from a third side, but would have nowhere to go, as the trap is on the fourth side. 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 save the horse. The silver elephant could move to c5 and unfreeze the fenced horse (while also capturing the gold rabbit in c6), but the unfrozen silver horse couldn't then escape, as its only available move would be suicide. Silver can't defend the trap, as no silver piece can reach d3, c2, or b3 in four steps; gold pieces block the silver elephant from doing so.
Solution: ef4nw Hg5w hg6s blocks the gold elephant out of e6 and fences the gold horse on f5, while also making room for the f6 rabbit to step east. The gold elephant can still pull the e6 dog, capturing the f6 rabbit, but in any event Silver can capture the fenced horse.
A fence may be valuable even if the fenced piece can be defended. At right, the silver elephant can go to d3 to defend the horse, but Gold can then frame the horse with hc4s Ed4w Hb4s. In other cases, Gold might keep the fenced piece on c4 as a hostage, while blockading c3 to stop the piece from advancing.
Limitations of tactics
Gold to move can avoid any capture.
When both players understand these tactics, it will be difficult for either side to achieve immediate gain. The position at left may look promising for Silver, but Gold went on to win without losing a single piece until the end.
The next thing to learn is basic long-term strategy, which can help one get a whole-board advantage and overwhelm the opponent's defenses.
Introduction to Strategy
Strategy is focused on long-term positions. If no capture or goal can be forced, a tactic may become a strategy. A goal threat's value may lie in the space advantage it creates; enemy pieces forced to defend goal will not be a problem elsewhere. A capture threat may likewise tie enemy pieces to defense, if the opponent is unwilling to give up the threatened piece. By tying up enemy forces, one can build a whole-board advantage.
The ultimate object of Arimaa is to get a friendly rabbit to goal. This requires that space be cleared, but how? Should one immediately try to rip a hole in the goal line and then march a rabbit through? If one side attempts this, how should the other side respond?
It is best not to treat the whole game as a race. Until a fair amount of space has been cleared, forcing a goal is much harder than stopping a goal. Even if a goal path is opened, the defender can often close it easily. One might get a quick goal against a weak opponent, but a skilled opponent is usually attentive to home defense.
As long as there is no real opening in the goal line, it is futile to advance a rabbit for the purpose of reaching goal. A quick rabbit advance may be costly, since an advanced rabbit can never retreat. Generally speaking, it would be extremely wasteful to use one's elephant to protect a rabbit from capture.
In short, going for an early goal is a poor strategy which can quickly set one back. Nevertheless, a goal path must eventually be cleared somehow.
While a game can finish with minimal captures or even no captures, capture threats are important. A piece is captured only when it is on a trap square with no friendly piece beside it; there are many ways to prevent a capture. If nothing else, the defending elephant can camp out beside a trap where there is a capture threat; since nothing can dislodge an elephant, its friendly pieces can never be captured in a trap it stays next to.
The key to progress is to make strong threats around two different traps. The enemy elephant can only defend one trap, and any other defender or rescuer could itself be at risk.
The simplest double threat is a fork between one's home traps. If a piece can be flipped in the center, it may be doomed to such a fork. This is one of many reasons both elephants might stay near the center. Although any piece can unfreeze a friend, an elephant can do so without putting itself at risk. Since rabbits can't retreat, they are often not placed in the center.
Pieces on the flanks are less vulnerable to a fork. It is often easier to drag down a piece right against the edge, but from there it is harder to force capture if the defending elephant stands in between traps.
If both sides take care to prevent a fork, the threats will have to be more sophisticated.
In this game, the silver camel has been taken hostage.
In the diagram, Gold has taken the silver camel hostage, threatening to capture it in c3 if the silver elephant leaves. Such a hostage can only be defended by an elephant or by a team of well-placed weaker pieces; here, the c4 cat could itself be captured if the trap had no other silver defender. A solid camel hostage will make the forces asymmetrical: with the gold elephant holding the silver camel hostage and the silver elephant defending it, the gold camel is the strongest free piece. With the gold camel and horse both active in the east, Gold can soon overload Silver's defences. Having the strongest free piece is a large advantage, if that piece is well-positioned and supported by other pieces.
The risk of a hostage might make one reluctant to advance any piece other than the elephant. Also, one might jump at any chance to take an enemy piece hostage. Without an alignment such as this one, however, holding a hostage can be costly. If the elephants are deadlocked at one's home trap, that is a potential space disadvantage, since the opponent can safely advance pieces toward the deadlocked trap, but the home elephant is not available to ensure safe advances of its own friendly pieces. A home hostage-holder often can't easily leave, as the former hostage might then team up with its elephant to force captures in the trap, which would clear space for a goal. In fact, the defending elephant often has better prospects for leaving; its friendly pieces might swarm the trap and soon defend it independently. That could be a devastating turn of events for a hostage-holder, as the enemy elephant would become the strongest free piece.
For these and other reasons, one should be selective about hostage-taking. In general, a long-term hostage should only be held by a just-stronger piece; while the silver camel remains, the gold elephant must always be somewhat prepared to confront it, and thus should not be stuck in a corner while that camel is elsewhere. Conversely, it is usually fine for one's own elephant to defend a horse hostage held by the enemy elephant; if the elephants are deadlocked and both camels are elsewhere, there is no strongest free piece, but the hostage defender usually has a more centralized elephant, which might rotate out of hostage defense, or just trade its horse for the enemy camel if that camel is too aggressive.
A camel could take a horse hostage, but a hostage-holding camel might be vulnerable to the "defending" elephant. To maintain a hostage position, a non-elephant hostage-holder may need supporting pieces. A solid horse-by-camel hostage can be quite effective, however, if the hostage-holder's own elephant is free.
In this game, Silver is making threats in c3 and c6.
If a piece cannot be taken as a strong hostage, it can safely advance along with its elephant. If the enemy camel begins decentralized, a horse might advance on the other wing. In the game shown, the silver horses advanced with impunity because the gold camel was far away. Advanced pieces can create capture threats in both home and away traps.
Trap control concerns one's ability to make capture threats and defend against capture threats in a particular trap. A trap attack entails an attempt to control an away trap and thereby overload the opponent's defenses. If nothing else, an elephant could defend its home trap, but that would often give the attacker opportunities elsewhere. Here, Silver has a strong attack on c3, where he can make multiple captures unless the gold elephant moves to c4, which would leave the a6 dog to be captured in c6.
Seeing his overall weakness in the west, Gold looked east and counterattacked f6, but this was too late; Silver captured two gold pieces in c3 and then forced a rabbit through to goal. Even had the gold elephant defended c3, Gold's long-term prospects would have been bleak; more silver pieces could have advanced in the west, and the silver elephant likely could have gone elsewhere while a team of weaker silver pieces kept shared control of c3. Away trap control creates a space advantage, capture threats, and potential goal threats. Had Gold attacked f6 sooner, there might have been a capture race.
Home and away games
There are two basic plans: try to take control of an away trap, or aim to create a strong capture threat at home. Since rabbits can't retreat, they can be pulled out gradually; when they are eventually threatened on the other side of the board, their owner will have no good way to defend them. At least, that is how a rabbit-puller might think.
Although rabbit pulling was once considered an important element of opening strategy, it has become apparent that such pulling often cedes valuable space and time to the opponent. The time spent chasing and then dragging rabbits might be better spent building a space advantage, which may then allow one to make threats in both home and away traps.
Instead of thinking in terms of home and away play, one should think about the whole board. For a while, any possible move could be met with a solid defense or counterattack. The object is to attain the stronger overall position.
A recurring theme in Arimaa strategy is elephant mobility. Sometimes an elephant gets blockaded, but more often it is restricted by the cost of leaving a particular trap. Before getting into a position that will require one's elephant to stay put, one must consider the opposing elephant's situation. If one elephant is even slightly more free than the other, this can snowball, since it affects how free other pieces are.
Use of free pieces
As the strongest free piece, Gold's own camel is key to his advantage. Gold has wisely advanced a horse ahead of it; had the gold camel simply marched forward, Silver might well have gotten an even camel trade, as the silver elephant could have had a head start east while Gold captured the silver camel. Silver could have then frozen the gold camel and also impeded the gold elephant's path to e6 or f5. An even camel trade would be a disappointing outcome for one who had held a camel hostage.
Advanced horses can also protect weaker pieces. The western gold horse might attack later, but right now it is in effect defending the c6 trap. Although restricted by the hostage, the silver elephant can move between c4, d3, and c2, needing only to finish each turn on one of those squares. Such mobility could allow the silver elephant to dislodge a small gold piece and eventually deliver it to the c6 or f6 trap. The gold horses are prepared to defend those traps. The western gold horse 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 that Silver cannot defend against without giving up her camel. A silver horse can defend against a gold horse, so the gold camel will ultimately have to make such a threat. If Gold wants to play it safe, he can keep his camel at home and use the eastern gold horse to drag weaker pieces down for capture in f3 (remember, rabbits can't retreat homeward). As long as the silver elephant defends the silver camel, horses are the strongest silver pieces which could defend f3, but that would be difficult with the gold camel right there. Indeed, Gold could take a second hostage, and Silver would struggle to defend both. It might seem best for Silver to protect the camel at the expense of a weak piece, but consider that Gold can repeat this again and again if there is nothing to stop the gold camel and horse in the east.
Realizing that Gold is poised to take control, what should Silver do? Silver must free her elephant. In this case, Silver to move could trade her camel 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 play hb5ws Da2e ma3s, unfreezing and burrowing her 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 not free it, but would buy Silver time, as Gold would then need two turns just to reestablish a solid camel hostage.
Gold to move can stop 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.
The silver elephant has regained mobility, so Gold has no advantage from holding a camel hostage.
When the opponent has the strongest free piece, this must be changed before he can capitalize. When the gold camel is active, the silver elephant cannot perpetually defend a hostaged silver camel. Fortunately, it might not need to. While one's elephant defends an away trap, friendly pieces can safely advance toward it. This often allows one to rotate the elephant out of hostage defense, replacing it with two weaker defenders supported by other friendly pieces. In this game, diagrammed at right, the arrival of the silver dogs has freed the silver elephant to roam. Suddenly the tables have turned, and Silver's elephant is the strongest free piece. This is a bad position for a hostage-holder, made worse by the advanced silver rabbits, which would surely reach goal if the gold elephant left. Gold is strategically lost.
A hostage will often backfire when the hostage-holder has no other strong piece in the area. Were a gold horse or camel nearby, silver dogs likely could not hold both e3 and f4; at the very least, the silver elephant would have to stick around for a while.
Gold has just freed his elephant, but still has a fight ahead.
On 28g of this game, Gold completed an elephant rotation just in time. Silver had a strong attack in the southwest, but the silver strength concentrated there made the northeastern rotation easier for Gold. Gold had no goal threat and no piece on f6, so the silver elephant had some degree of freedom. Meanwhile, Silver's western goal threat remained formidable; Gold's elephant rotation hardly sealed the game.
This hostage position makes the eastern gold horse the strongest free piece.
On 13g of this game, Gold held the silver camel hostage and was strong on both wings, yet could not force a capture in c3 or f3. The well-placed silver elephant prevented any capture in f3, while also protecting the silver horses from the gold camel.
Who has the strongest free piece now? If the gold elephant left the c3 trap, Silver would soon wipe out Gold's southwestern forces. If the silver elephant left e3, the gold camel could go west or north and do tremendous damage. The silver camel obviously isn't free, and the gold camel can't go anywhere without quickly being confronted by the silver elephant, which could safely leave e3 if the gold camel advanced. The silver horses are not free, as they are defending the silver camel and each other. The western gold horse is not totally free, as it is stopping a potential Silver swarm of c3, which could give the silver elephant more freedom.
The eastern gold horse is the strongest free piece; Gold can soon create an away threat that will force captures somewhere. A double-horse attack on c6 is one option for Gold, but a faster option is to advance the f2 dog and threaten to have it occupy f7, which would constitute a strong attack on f6; a gold cat or rabbit should replace the dog on f2. The silver elephant might go north and make multiple captures, but Gold could more than make up for that by sending his camel west. Even if both silver horses escaped, Gold could capture the silver camel and minimize his own losses, as Silver would have lost time getting her horses to safety.
This example and the next show that an elephant not directly defending a hostage can still be restricted by it. Rather than free the defending elephant, an elephant rotation sometimes just ties up more material in the hostage position.
Each side currently has an elephant, camel, horse, and dog tied up in this hostage position. (game)
In the position at left, the silver elephant has been blockaded. Gold appears to have pulled off an ideal elephant rotation, yet neither side has a clear advantage in free pieces. The gold elephant is not actually free, as it is the only thing between its northeastern army and the silver camel. Silver might move her camel south to attack c3, but then the gold elephant could safely go south also, becoming the strongest free piece. Silver might do better to send the c2 horse east, where it would be the strongest local piece and could work toward a goal threat. Such a threat would be stronger if the second silver horse were free; having a friendly horse blocked in weakens a hostage-holder's position.
Camel hostage value
When Gold holds the silver camel hostage in the southwest, Silver likely wants to advance pieces in the west while Gold wants to advance in the east. Gold wants to create a second threat using the strongest free piece, while Silver wants 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. For Gold, a camel hostage will tend to be worthwhile if two strong gold pieces are already on the non-hostage wing, and Silver is not well-developed on the hostage wing. Ideally, the free camel and a friendly horse will work together on the non-hostage wing, while the other friendly horse will be active on the hostage wing, preventing a successful elephant rotation. This is not the only alignment for an effective hostage, but the free pieces are always key, and there is limited time to maneuver them. If the hostage-holder's free pieces cannot quickly accomplish something, the hostage may be weak.
If Silver is not well-positioned for an elephant rotation, she might abandon her camel and seek compensation elsewhere. Holding a hostage is useless if one plays passively, so a camel hostage-holder may have to offer what amounts to a horse-for-camel trade; the hostage value is thus related to the value of such a trade. A camel is estimated to be worth a horse and cat as an initial trade, so one might say that a solid camel hostage is worth a cat. This should be kept in mind if one has to choose whether to take a hostage or do something else.
If Silver is well-positioned for a quick elephant rotation, a hostage might be of negative value for Gold. The purpose of a camel hostage is to tie down the enemy elephant and camel, thus freeing one's own camel and/or horse to attack. If the enemy elephant quickly becomes free while one's own elephant remains effectively stuck, this has backfired badly.
|This is typical of a successful elephant rotation; a team of silver pieces has freed the silver elephant and cornered the gold elephant. The a4 rabbit assures that the silver dog could step right back to c4 were it pulled to b4. The c3 rabbit blockades the trap; if c3 were clear, the gold elephant could push the horse to e3, perhaps threatening it in f3 if the overall position allowed for that. The gold elephant must stay beside the trap, as Silver could quickly goal if space were cleared.|
|Here a gold rabbit forms part of the blockade. Since rabbits can't step backward, they can sometimes be used against their own friendly pieces. This is why players often do not place a rabbit behind a trap; if pushed or pulled onto c3, a gold rabbit can't step back to c2.
The gold elephant has some mobility, as Silver does not yet have a strong goal threat in this quadrant. Gold could push the camel to b1 and slide the c3 rabbit to b3, clearing space for further maneuvers. This is a possible advantage of holding a hostage on b2; the hostage could be buried if necessary.
|The gold horse in the trap makes rotation difficult for Silver. If the silver elephant leaves, Silver will have to keep the gold horse off of c4 or d3; if the gold horse got onto either square with the silver elephant elsewhere, the silver camel likely could not be saved unless the silver elephant returned.
Silver might consider flipping the gold horse away, but Gold could occupy d2 and e3 to prevent this.
|The trap is clear, but the gold elephant can't move through it, as the trap currently has no other gold defender. The silver elephant has left the quadrant, but may still be nearby; how free it is depends on the rest of the board. Gold could become very strong if he could threaten the silver dog or horse, as those pieces and the silver camel could potentially fall like dominoes. Once again, the a4 rabbit ensures that the silver dog could return to c4 if pulled to b4. The a2 and b2 gold rabbits are also key to Silver's position; if Gold could clear b2, the silver horse would not be safe on c2, from where it could be pulled to b2. That would give Gold a double hostage and also allow a gold defender to occupy c2.
If the silver horse and dog are safe, this is a strong position for Silver. If the gold camel is nearby and the silver elephant is far away, this could soon become a strong position for Gold.
|A hostage held by a c2 elephant alters the usual alignment, since c2 is typically held by a weak piece. With the gold elephant on c2, b3 may be vulnerable. Here the gold horse may not be able to stop an elephant rotation, as Silver could occupy b3 and b4 if the gold horse stepped east. A hostage held behind the trap may therefore be weak.
If d3 and d2 were unoccupied, the gold elephant could move to d3 and pull the silver camel to d2, perhaps resulting in a strong central hostage. Silver can usually prevent such maneuvers.
Other hostage patterns
A double hostage is stronger than a simple camel hostage.
At right (game) Gold holds a double hostage of the silver camel and horse. With three strong silver pieces tied up, Silver's counterplay options are quite limited. Unless Gold is reckless, Silver cannot hope to abandon the hostages and remotely make up for a camel and horse loss. With Gold's large advantage in free pieces, elephant rotation would also be quite difficult for Silver. Though not currently frozen, the silver camel can't escape, as h2 is blocked by a phalanx which includes the frozen g2 horse.
One option for Silver is to occupy g4 with a weak piece. If the silver elephant then left, any capture the gold elephant could make would land it on a square other than g3, so the second hostage could escape or be defended again after an exchange. Realizing that Silver could complicate things by stepping a rabbit or cat to g4, Gold should take care not to expose his camel to quick capture, as he might only get an even camel trade, which would free and strengthen the southeastern silver horse. In fact, this horse could then help create a formidable goal threat.
Gold has an unstable but valuable high hostage. Game
A high hostage is held on the fourth or fifth rank. This is a relatively rare pattern, as it is tricky to maintain, but it is always good to have one's elephant centralized if possible. This high camel hostage is unstable, as the western silver horse can eventually reach b4 and unfreeze the camel. The gold horse on c5 could then be lost in c6, so this is a risky position for Gold. It may be easier to hold a high hostage on a depleted board, as Silver did in this endgame.
A central hostage may face capture threats in two different traps.
A central hostage is held on the d- or e-file. If the hostage-holder has good control of both home traps, a central hostage can soon become a fork: Silver can play ed6s Md7s cc8s df6e, and Gold cannot defend both c6 and f6. This hostage position is more tactical than strategic; Silver gave up a horse to trap the gold camel. If the capture cannot be forced, the value of a central hostage might be similar to that of an ordinary hostage.
If a hostage is not a camel, there are further considerations. Would an elephant waste its strength by holding a horse or weaker piece hostage? If the hostage-holder is not an elephant, can the hostage position be kept intact?
This horse hostage does not benefit Silver, whose camel is very limited (from this game).
Not all hostage positions are effective. Even with camel hostages, the hostage-holder is often more stuck than the defender, since the hostage could become an attacker if freed. This gets worse if an elephant holds a horse hostage instead, as in this diagram. If the silver elephant left the northeast trap, the gold horse would likely help its elephant make captures, perhaps decimating Silver's eastern forces. Thus both elephants are basically stuck, but consider the overall position. Gold would gladly trade his horse for the silver camel, which if it came east might get forked between c3 and f3. The gold camel is more free to move around; if the silver elephant left the northeast, Gold could likely make progress there before Silver could threaten the gold camel, which could easily be defended. The camels are the strongest free pieces, but Gold's camel is more free, thus the hostage does not benefit Silver. Ultimately, this is an issue of alignment; decentralizing one's elephant on account of an enemy horse is highly questionable.
For now, the gold elephant is better placed on e6 than on f5. If e6 and e7 were clear, the silver elephant could pull the gold horse onto e7 and then fork it between traps. That is a possible advantage of positioning a hostage-holder behind the trap.
In some cases, a horse-by-elephant hostage might be converted to a frame or passed off to the silver camel. If Silver were better positioned for that, it would be urgent for Gold to prevent a solid frame or horse-by-camel hostage, which could free the silver elephant while the gold elephant remained stuck defending the horse.
Gold can begin to advance in the east, but should try to avoid having a second piece taken hostage while the gold elephant is still needed for defense, as that could make it more costly for the gold elephant to confront the silver camel.
This horse-by-elephant hostage makes the dogs the strongest free pieces.
A horse-by-elephant hostage may be effective on a depleted board. In this endgame, such a hostage tied up the three strongest remaining pieces. Up two-to-one in dogs, Silver can dominate the rest of the board. If a second gold horse or dog remained, this hostage would likely be weak.
The camel is usually the piece that should fight an enemy horse long-term. This may lead to a horse-by-camel hostage, which will ideally tie the opposing elephant to defense while the friendly elephant is free to roam. However, the "defending" elephant can often attack the hostage-holding camel, and thus turn the tables. If the hostage is defended by the enemy elephant, a hostage-holding camel will need friendly support. If a solid horse-by-camel hostage is feasible, it may be worth using considerable material on, since it can give one the only free elephant.
These diagrams illustrate different horse-by-camel hostage configurations, with Gold holding such a hostage in the southwest. A gold piece is always on a4, to keep the gold camel mobile if it is pulled to b4. In the first diagram, 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. As it is, this may be a solid hostage position for Gold, whose own elephant is the strongest free piece for the time being.
Without a gold piece securely on a4, the hostage would be weak. With ec4we Mb3n ha3e, Silver could have her elephant on c4 and her horse on b3; if the gold camel were frozen on b4, Silver would have strong capture threats in c3, and could also flip the gold camel to c5 with a threat to capture it in c6. The a4 square is thus crucial to such a hostage position, and Gold does well to have a horse on that square, as a weaker piece could be pulled away more easily.
In the second diagram, the hostage horse is on b2 rather than a3. This means that the silver horse can more directly join the trap control fight if the camel is dislodged. For instance, if the silver elephant moved to b4, it would then threaten to capture the camel due to false protection. On the other hand, Gold now has the option of pushing the horse to b1, which would make it even more difficult for Silver to free the hostage. If the silver elephant left, the horse could then be pulled back to b2.
In the third diagram, the silver elephant has no easy way to approach the gold camel. As long as Gold can hold b3, 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. 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 attack the a4 horse, weakening the hostage pattern.
Gold cannot save both horses. Game
While a horse-by-elephant hostage is usually a bad long-term strategy, it may be an effective tactic if the hostage-holder can make a quick second threat. Here, Silver took both gold horses hostage, and Gold did not have time to defend both traps.
Although up by a horse, Gold refused to give up his hostaged horse, leading to disaster below.
On 23s of this game, the silver camel took a gold horse hostage. The western silver dog and the silver rabbit behind it proved crucial, as they stopped Gold from retaking ownership of c3 and threatening multiple captures; the gold elephant then quickly returned north to defend the horse hostage, and Silver owned c3. Silver decimated Gold's forces around c3, all the while retaining the threat in c6. The gold elephant should have defended c3 and let the c8 horse be captured, as that capture would have only pulled Silver even in material.
Silver's horse-by-camel hostage allows silver dogs to control an away trap.
By tying up the gold elephant and horse, Silver's horse-by-camel hostage at right enabled silver dogs to control f3. This led to a relatively quick goal.
Gold holds a camel hostage in the east, and a double hostage in the center.
In this game, Gold's central horse-by-camel hostage stopped Silver from forcing a western goal; with the silver horse frozen and other silver pieces blocked from advancing, there was nothing to help the silver elephant counter Gold's defense. This would be a strong position for Silver if he could displace the gold camel, but Gold to move can blockade c3 and perhaps move toward a northwestern goal threat. With the southern forces tying each other down, the western gold horse is the strongest free piece; the silver elephant must stay beside c3, and cannot freeze the gold horse in place. One way or another, this horse can soon accomplish something.
Cat and dog hostages
Silver does not have an ideal alignment, but may eventually overload Gold. (Game)
A smaller piece may also make a valuable hostage, if its elephant is the only piece which can defend it. In this example, the silver camel holds a gold dog hostage next to c6. The silver elephant is free to pull gold pieces toward f6. The gold elephant can't defend both traps.
However, Silver's situation is less than ideal, for two reasons. First, the gold elephant could currently leave the c6 trap without losing the c8 dog on the next turn, since the silver cat would have to leave the trap square to allow for the capture. Second, the h5 gold rabbit will make it harder for the silver elephant to threaten the gold camel. Silver might have to capture the h5 rabbit before making any other threat in f6.
Silver would have a greater advantage if her horse held the dog hostage and her camel were free; with the gold elephant stuck defending against a silver horse, the silver elephant and camel together could make a strong threat elsewhere. Like a horse-by-elephant hostage, a dog-by-camel hostage is at best non-ideal in most situations.
Gold's dog-by-horse hostage allowed the gold camel to safely advance to g6.
In this game, Gold's early dog-by-horse hostage allowed the gold camel to lead an attack on f6. An early camel advance would often result in a camel hostage, but the southeastern hostage gave Gold time to advance his camel and support it with rabbits.
In this game, the gold elephant is pinned to the horse framed on c6.
A piece held on a trap square, securely surrounded on three sides, has been framed. In the position at right, Silver has framed a gold horse on c6; a phalanx stops the framed horse from pushing onto c7. The gold elephant is pinned: if it takes one step, the framed horse will disappear.
Unlike a hostage defender, which must merely end each turn adjacent to the trap, a pinned piece is completely stuck. Here, it would be pointless for the pinned gold elephant to break the phalanx; even flipping the d7 rabbit would instantly lose the framed horse. If a pinned piece abandons a framed piece, the framer won't even use up a turn making the capture, since the piece is already gone. This strength of frames is balanced by the high material cost of maintaining them.
When possible, one holding a frame should rotate out strong pieces, replacing them with the weakest ones which can reliably hold the frame. At right Silver can replace the elephant with the a5 horse, making the silver elephant the strongest free piece, although it may not be totally free if Silver wants to avoid an even horse trade.
Even if rotation is not feasible, a frame involving both elephants will usually give the framer an elephant mobility advantage. Gold would instantly lose the framed horse if he moved his elephant, whereas Silver could move his elephant at no cost other than giving up the frame. The gold camel would thus have trouble advancing, whereas the silver camel is already in Gold's home territory.
A frame may be broken by the arrival of a piece strong enough to dislodge a framing piece. If a piece on a trap gains a second supporter, or gets off the trap square, it is no longer framed. A frame might be broken from the side or from behind, but here Silver can likely prevent either maneuver. With the gold elephant stuck, the gold camel is the only piece that could dislodge a silver horse, but Silver can easily stop such an intrusion in the west. Gold might instead aim to break the c7 phalanx. Since the gold elephant is immobile, breaking the phalanx would require a gold piece to be safely on e7 or d8; on Gold's next turn, this piece could pull away a rabbit, allowing the c6 horse to push its way out. Silver can strengthen the phalanx by sliding the d7, c7, b7, and a7 pieces east.
Frames vary widely in value, depending on each side's free pieces. A breakable frame might have negative value, since the formerly framed piece could become an attacker.
Frames are most effective when there is enough material to hold a frame and still accomplish something else. Even a solid frame may not be worthwhile on a depleted board.
Gold might prefer to have his elephant pinned on d6 rather than on c5:
- With the pinned gold elephant on d6, the frame requires a silver piece on c5 (except in the case of rabbit frames). If the silver elephant is not in the west, the c5 piece may be vulnerable to capture in c3.
- The pinned gold elephant on d6 stops Silver from moving the framed piece onto d6 or e6 for a fork.
- d6 is a better attacking square than c5 for the gold elephant. If the frame can be broken, Gold may then have a solid attack.
On the other hand, the pinned gold elephant may be better placed on c5 if the framed gold piece is not at imminent risk of capture in f6. With the gold elephant on c5, a gold piece might have an easier time attacking the frame along the b-file.
In this game, Gold has both a camel frame and a horse hostage.
When an elephant is pinned to a camel framed by the enemy camel and elephant, the four strongest pieces are all tied up. The framer would have greater elephant mobility, but the framed side might gain a space advantage; this could result in a long game with an unclear outcome. A camel frame can be strong, however, if it gives the framer an advantage in free pieces. If the framing elephant or camel can be replaced by a phalanx of weak pieces, the framer will have the strongest free piece while still rendering the two strongest enemy pieces completely immobile. The diagram shows another possibility: the gold camel is both participating in the frame and holding a horse hostage. There is no single strongest free piece, but Gold has two free horses against Silver's one. Gold's progress may be slow, but Silver has little counterplay, having so much to lose if she abandons f3. This frame-hostage gives Gold a strong advantage.
An away horse frame, from this game
In the course of a trap attack, it is sometimes possible to frame an opponent's piece in his own home trap. Gold's frame at right is strong; the pinned silver elephant can't think of leaving, as there would be catastrophic losses in f6. From here, Gold can advance rabbits on the h-file to solidify the space advantage.
Gold would not benefit by rotating anything out of this frame, even if other gold pieces were closer. A phalanx would not be viable, and replacing the gold elephant with the camel might let Silver get a horse-for-camel trade if the gold elephant didn't stand guard.
The one potential threat to the frame is the silver camel. If it went east, however, the gold camel would be a strong threat in the west.
If Gold can advance enough pieces to support his horses, he might eventually want to move his elephant elsewhere; at that point, Gold should flip the silver horse out of f6 and then push it away, so that it couldn't simply step to e6 and help the silver elephant retake control of the trap. If both gold horses were securely beside f6 even with the gold elephant elsewhere, Gold could quickly overload Silver.
The silver camel is pinned to the c3 cat, and both pieces will be at risk if the gold elephant can step to d4. (Game)
In this position, the silver camel is pinned to the c3 cat, and the silver elephant must stay on d4, to defend both the cat and camel. This leaves the gold camel as the strongest free piece; if this will remain so, the silver camel should abandon the cat.
However, Silver might hope to replace the elephant with a phalanx on d4; this might also require a piece on c5 or b4 to prevent a flip. Such a phalanx would divide up the board; the gold elephant might be forced to give up the frame and make its way east, but then the position would be unclear. A similar position with the camel instead on b3 might be good for Silver, since Silver's trap control could be fairly solid. See, for instance, the blockade on 29s of this game.
Even if Gold defends the trap, this horse basket could lead to a strong frame.
In this position, the gold horse is in a basket: it is blocked on three sides, so that no escape is possible even if it is unfrozen from the fourth side. To prevent an immediate capture, the gold elephant must go to e6; Silver could still flip the gold horse into the trap, creating a frame which the silver elephant might soon rotate out of. Gold to move might possibly prevent a frame via congestion, if he can occupy both f4 and e5 while defending the trap.
Were the gold elephant already on e6, Gold could delay the frame by flipping the e7 dog. With e7 empty, Silver should not flip the gold horse into the defended trap, since the horse could then push onto f7, where it would be well placed. However, the dog flip would usually lose time, since Silver could restore the phalanx in fewer steps than it took to flip the dog. Silver might also answer a flip by forcing the frame via a fence, pulling the gold horse to f5 and moving the h5 horse to g5. On the next move, the horse could be pushed into the trap in two steps, leaving another two steps to reestablish the phalanx.
Silver shouldn't allow a rabbit to be moved into the trap, since it couldn't retreat and would block the intended frame. A silver rabbit on e7 could be flipped into the trap. A rabbit on f7 would make a fence less effective, since with the gold horse on f5, the gold elephant could pull the rabbit into the trap.
This basket is of only temporary value to Silver.
In the second position, the silver elephant is on g4 instead of f5. Now the gold elephant can go to f5 to block the horse frame. For the moment, the silver elephant is more mobile than the gold elephant: the gold elephant must stay on f5 to prevent a frame, while the silver elephant can safely leave the east, since the gold horse is not a direct threat to the f6 trap. However, the silver elephant is decentralised, and Gold can exploit this by beginning to blockade f4. Depending on the rest of the board, it might be urgent for the silver elephant to leave g4 if it is about to become marginalized thereon. In this game, for example, the gold elephant took a long time returning to the centre round the back of an away trap.
The above frames would all be hard for the defender to break. However, a frame is sometimes vulnerable enough that the defender could break it and come out ahead. A camel with friendly support can sometimes break a frame from the side. In the diagram at left, Silver to move can play a pull-and-replace, getting the silver horse onto b3 (mb5sn Hb3n hc3w). Although Gold could do a pull-and-replace to restore the frame, Silver would win the repetition fight; by undoing Silver's move, Gold would restore a position he created previously, namely the position in the diagram. Once the frame is broken, Silver will have a good position: the formerly framed horse will be a strong attacker, and the camel might pull the gold horse to c6.
Gold to move could delay the frame-break with Ec4ns mb5e. However, if there is a silver piece on d5 or c6, the camel could return to b5 in a single step, thus undoing in one step what Gold did in three. Instead of wasting steps and letting Silver strengthen her position, Gold to move might flip the silver horse to b4; the horse might escape, but at least Gold would retain control of the c3 trap, and might soon capture a silver rabbit.
The second diagram shows a similar position, but with the silver camel on b4 rather than b5. Now, the frame can be broken in three steps (mb4n Hb3n hc3w), but there is a complication: Gold could restore the frame with a pull-and-replace (Ec4sn hb3e Hb4s), and this time Gold would create a new position, since the silver camel would not be where it was after Gold's last turn. For this same reason, Silver would then need four steps for her own pull-and-replace, and thus would create the exact position she created the first time she broke the frame: the silver camel on b5, the gold horse on b4, the silver horse on b3, and nothing else different since she had no extra step. Thus, Gold would win the repetition fight. However, Silver has other ways to break this frame:
- mb4n Hb3n hc3w Cc2n pulls the cat into the trap to prevent Gold's pull-and-replace. This is the simplest, and thus most common, maneuver to break such a frame.
- mb4n Hb3n hc3w ed3w: the silver elephant can occupy the trap to prevent a horse frame, but must be careful not to get framed itself.
- mb4n Hb3n ra3e ra4s: silver rabbits block the gold horse out of b3.
- mb4n Hb3n mb5e Hb4n: the camel moves to c5, pulling the horse twice. The silver pieces on c6 and d5 contribute to a phalanx on c5, stopping the gold elephant from stepping forward and unfreezing its horse which is now on b5; the gold elephant could step to b4 and unfreeze the horse from below, but then the horse couldn't return to b3.
In this second diagram, note how the silver cat on d4 prevents a camel flip, which would buy Gold some time. A silver piece on c5 would do the same job.
In both diagrams, Silver's a4 rabbit keeps the camel unfrozen on b4. If instead a gold piece were on a4, the frame would be stronger.
Silver must break this frame and move his elephant, before the gold camel can dislodge the pinned silver horse.
An elephant frame is occasionally possible, if an elephant has chosen to occupy a trap square. If the pinned piece can be dislodged, the framed elephant will be captured. On 12s of this game, Silver likely did not see the danger he was putting his elephant in. Even on 13s, Silver did not quite see the two-turn forced elephant capture he faced if he didn't get his camel to e5 or d4. It is not always bad to place one's elephant on a trap square, but extreme caution is needed; an elephant should never be left in a trap that is not adequately defended.
At the outset, each player essentially has full control of his two home traps. Each elephant can quickly share control of one away trap, but as long as a home player can occupy two key squares of each home trap, having the enemy elephant next to one is not a problem. However, if one can get a non-elephant safely onto a decentralized key square of an away trap (e.g. b6 or c7 when attacking the c6 trap), there is at least the potential to take full control of that trap.
The b2 horse effectively gives Silver shared control of the c3 trap. (Game)
Sharing control of an away trap will limit the opponent's capture threats, allowing one to play more aggressively. As long as one adequately defends an away trap, no friendly piece can be captured therein. This allows more pieces to advance toward it, and perhaps soon take full control of the trap if the opponent doesn't prioritize its defense. If one does get full control of an away trap, several quick captures may be possible, since an enemy trap usually has plenty of enemy pieces nearby. Once space has been cleared, by captures or by enemy pieces scattering, a strong goal threat may be possible. If the enemy elephant defends its own home trap in order to prevent this, that elephant will be less of a problem elsewhere.
On the other hand, one attacking for trap control might soon find the tables turned on him. If too many pieces advance too quickly, the home traps may be vulnerable to a counterattack. Moreover, advanced pieces may end up hostaged, framed, or blockaded. Even if the trap defense appears too weak for that, stronger defenders may arrive later, if the whole-board fight allows. Attackers may even end up blocking each other. Rabbits often advance to support an attack, but since they can't retreat, the defender might use them against other attackers. The attacking side might then be weak on the entire wing, with any attack blocked and fewer pieces defending home territory.
In the position shown, a silver horse has penetrated enemy lines in the opening, giving Silver a long-term trap control advantage. Although Silver has no immediate way to take complete control of the c3 trap, Gold has no direct way to deal with the intruding horse: the silver elephant would stop the gold camel, and Gold cannot afford to decentralize his elephant just to deal with a horse. Silver might soon advance more pieces in the west.
There is an elephant deadlock at f6 and a camel deadlock at c3. (Game)
A trap is deadlocked when its strongest gold defender and strongest silver defender are equal. If both elephants stay beside the same trap, it is usually because both sides have a large stake there. Remember that a hostage position can tie down both sides, as a hostage could become an attacker if the hostage-holder simply left. Here, the silver elephant is not holding a hostage, but is defending against an attack which more gold pieces might soon join.
A camel deadlock will hold only so long as neither elephant can be bothered to break it. Here, Silver is well up in material, but has more to lose than does Gold; the silver camel and hostaged horse would both be at risk if the gold elephant went west. What happens in the northeast will help decide what happens in the southwest.
Gold will lose a horse for abandoning c6; Silver will lose a dog and some rabbits for abandoning c6.
When both sides commit an elephant to the same trap, neither can capture anything in that trap. This can create a space disadvantage for the player whose home trap is deadlocked, especially if the home elephant is decentralized. Enemy pieces can safely advance toward such a deadlock, whereas the home elephant would have to leave if it wanted to ensure safe advances of its own pieces. If the deadlock is the result of a hostage position, the defender's space advantage might allow him to rotate his elephant out of hostage defense.
Before and after diagrams illustrate the effect of gold rabbit advances on a northwestern elephant deadlock. In the before diagram, the gold elephant does not want to abandon c6, because Silver would capture the b7 horse. Likewise the silver elephant does not want to abandon c6, because the gold horse and elephant together could force the capture of any silver piece near the trap. This is the essence of an elephant deadlock: either side would suffer for leaving.
Gold will lose a horse and some rabbits for abandoning c6; Silver will lose a dog, some rabbits, and the game for abandoning c6.
In the after diagram, the advanced gold rabbits have further raised the stakes for both sides. If the gold elephant abandoned c6, Silver would then clean house. If the silver elephant abandoned c6, a gold rabbit would soon reach goal. With so much now at stake in the northwest, the deadlock has tightened considerably.
In advancing three rabbits in the west, Gold may have figured that the threat of an eventual goal outweighed the risk of eventually losing a few rabbits. That is often correct, but the whole board must be considered. If the silver camel advances in the east, it can soon cause trouble unless the gold elephant leaves the deadlock. The result could be a three-for-one trade, which would strongly favor Silver on this already depleted board. Gold should have kept his western rabbits at home, and taken advantage of the effect the original deadlock had on the respective camels.
One whose elephant is stuck in a home deadlock must force the opponent to do something other than work that deadlock to his advantage. One unprepared to make a strong second threat should avoid getting into a home elephant deadlock; for example, taking a hostage could backfire if one is not already poised for an attack on the other wing.