Arimaa/Rabbit Advancement

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The timing of rabbit advances is a difficult strategic issue. While other pieces can retreat homeward, rabbits can only move forward, left, or right. Since rabbits can't backtrack, quick rabbit advances may create a mess. Even in the opening, however, advanced rabbits can aid stronger friendly pieces or impede attacking enemy pieces. Such benefits must be weighed against the risks of having friendly rabbits stuck in non-ideal places.

Disadvantages[edit]

Exposed to capture[edit]

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Silver's advanced rabbits are no threat to goal, and the silver elephant can't defend them all.

Since rabbits can't retreat homeward, they are especially vulnerable to capture in enemy traps. Going fishing for rabbits would be slow, but when rabbits advance on their own, they have done part of the job for the enemy.

Advancing rabbits while doing little else will make things easy for the opponent. In this game, diagrammed at right, Silver's three advanced rabbits are doing nothing useful, and can't all be saved. Although material is even at the moment, at least one silver rabbit is about to be lost. As long as the silver elephant protects the other two, its mobility is severely limited. Silver is clearly losing.

It is rare for the board to empty out enough that rabbits may advance unaided. Advancing a rabbit usually entails a willingness to contest an away trap for a while, or to let the opponent use up steps capturing the rabbit.

Weaken goal defense[edit]

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With no rabbits on his back row, Silver can't stop the a6 rabbit from reaching goal.

Rabbit advances also affect the area they leave behind. If one's home rank is left sparse, an enemy rabbit may have an easy path to goal. In the diagram at left (from this game), it is Silver's turn to move, but he is helpless to stop Gold's a6-rabbit from reaching goal in two turns. If even one silver rabbit remained on the home rank, it could slide over to unfreeze the dog on c8, which could then block the a6 rabbit. Instead, Silver is lost; no matter what Silver does, Gold can play Hc7wn ra7e Ra6n, forcing goal on the next turn.

By contrast, Gold has four rabbits still at home. The three advanced gold rabbits threaten goal right, left, and center, yet the four gold rabbits at home ensure that Silver would have to fight through more than one line of defense to score a goal.

Impede friendly pieces[edit]

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The e5 gold rabbit blocks the gold elephant from moving west. (game)

An enemy rabbit can be pushed in any cardinal direction that there is an empty square, but there is no way to move one's own rabbit backward. Advanced rabbits can thus be used against their own friendly pieces, sometimes with devastating effect.

In the diagram, Gold holds a horse-by-camel hostage at the f3 trap, but the e5 gold rabbit restricts the gold elephant, leaving the silver camel as the strongest western piece. Currently, the gold elephant would have to maneuver through the southeast in order to go west. Silver should keep her elephant, g6 horse, dogs, and the advanced gold rabbit in place, and use her camel and/or a6 cat to drag a gold piece up to c6.

Multiple misplaced rabbits could prove even more disastrous, perhaps allowing a complete blockade of the friendly elephant. Advanced rabbits may also block the movement of other friendly pieces. In particular, advanced rabbits on a wing may block an attack.

Advantages[edit]

There are examples elsewhere in which advanced rabbits assist in an attack or slow an enemy attack, by giving friendly pieces greater mobility and/or blocking enemy pieces. This section will focus on rabbit advancement advantages that do not fit in other chapters.

Endgame goal threat[edit]

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Gold to move has strong goal threats, despite being way behind in material.

Once substantial material has been traded, or multiple traps have been contested, holes start to appear in each side's defenses. The emptier and more ragged the board becomes, the more an advanced rabbit is a direct threat to win the game. In the diagram at left, from this game, Gold is way behind in material, but the a7 and h7 gold rabbits generate significant winning chances. Gold to move could threaten goal on either wing: Ed7e rf7n Ee7e would require Silver to use her entire turn on goal defense, leaving the silver camel or g7 rabbit to be captured. Alternatively, cc7s Ed7w hb7s Ec7w would require Silver to occupy c8, leaving at least one trap vulnerable. With the latter move, Gold can force a goal in five turns.

Gold's goal threats have diminished the silver elephant, which is far away and won't have much time to move. Other silver pieces have also lost power; the northwestern goal threat effectively ties up both silver horses, and the silver camel could be captured or forced to the goal line if Gold pursues the eastern goal. Goal threats often outweigh a raw material lead.

Goal threats also place great psychological pressure on a human opponent. Whether or not the goal could be forced with perfect play, a blunder by the defender could lose the game, whereas a blunder by the attacker would only give the defender a reprieve.

Strategic goal threat[edit]

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The a7 gold rabbit will force Silver to keep the western goal line blocked.

Whenever a rabbit is in enemy territory, the enemy must keep any goal path blocked. In this game, a gold rabbit on a7 tied up several silver pieces in the northwest. Gold eventually lost shared control of the c6 trap, as the gold horse and dog were captured in a material exchange, but Silver never had time to capture the rabbit. With material depleted, blocking this western goal was costly for Silver, especially when Gold made another goal threat in the east.

Cement deadlock[edit]

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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. When there is a northwestern elephant deadlock, it is tactically safe for gold rabbits to advance in the west; before and after diagrams illustrate the effect on the deadlock.

In the first 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 will suffer for leaving.

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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 second 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.

Generally the side advancing rabbits gains from cementing an elephant deadlock, because the threat of an eventual goal outweighs the risk of eventually losing a few rabbits. Nevertheless, one must remember that rabbits can never retreat homeward, and thus any rabbit advance is a commitment. If for instance the silver camel is poised to cause trouble in the east, Gold should think twice about advancing rabbits in the west, if they would depend on the gold elephant to defend them.

Unfreeze friends[edit]

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If Silver pulls the gold camel to b4, the a1 rabbit may be enticed forward three steps.

An advanced rabbit can often give a stronger piece more freedom to move along the next file.

In the diagram at right, the silver elephant could step left to b4, then return to c4 while pulling the gold camel onto b4. In reply, Gold could advance the a1 rabbit to a4, unfreezing the camel and stepping it back to b3. In the following move, Silver might pull the gold rabbit further along the a-file, with the aim of eventually capturing it in the c6 trap.

Neither side is making a mistake here. Gold knows that the advanced rabbit will be vulnerable to capture, but prefers to expose it rather than give up a camel hostage. Likewise, Silver was correct to attack the exposed camel even though it could be freed, because this brought up an enemy rabbit. Even if Silver had already planned to pull the a1 rabbit to c6, directly attacking a piece on a1 would have been quite slow.

Trap control[edit]

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The silver rabbit on b3 helps Silver contest control of c3.

Rabbits can strengthen control of traps held by stronger pieces. Especially later in the game, they may be strong enough to hold key squares on their own. In the position at left, from this game, two gold rabbits are adequate to defend f3, since no stronger silver pieces are in the area. Meanwhile, a silver rabbit gives Silver control of c3. Because of this rabbit, the silver dog on c4 is currently safe, and the gold cat on c2 isn't. If instead a gold rabbit occupied b3, Gold would be in good shape.