Arimaa/Rabbit Advancement

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An elephant, camel, horse, dog, and cat differ only in their power over enemy pieces. Rabbits, however, differ from all other pieces in two ways: a rabbit can score a goal, and it can't step backward. Since rabbits can't backtrack, they can easily get stuck in non-ideal places, from where they might get captured or block friendly pieces. Even in the opening, however, advanced rabbits can aid stronger friendly pieces or impede attacking enemy pieces. The timing of rabbit advances is thus a difficult strategic issue.

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.

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.

Advancing a rabbit often entails a willingness to let the opponent use up steps capturing it; if something else is going on, the opponent may not have time for the capture. Furthermore, no piece can be captured in a trap defended by its friendly elephant, so one attacking an enemy trap can safely advance rabbits on that flank. The problem here is that the silver elephant is only protecting rabbits, which is very wasteful.

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's southeastern horse-by-camel hostage is useless, since the e5 gold rabbit restricts the gold elephant, leaving the silver camel as the strongest western piece. If Silver keeps her elephant and g6 horse in place, and also keeps the e5 gold rabbit blocked from the north and west, the gold elephant will have to maneuver through the southeast in order to go west. This will leave Silver time to pull a gold piece to c6.

Multiple misplaced rabbits could prove even more disastrous, perhaps allowing a complete blockade of the friendly elephant. Misplaced rabbits may also block a friendly attack or capture.

Advantages[edit]

Nevertheless, rabbit advances are sometimes necessary. Since rabbits constitute half of one's army, various jobs could fall to them. Rabbits might advance to block enemy pieces, unfreeze friendly pieces, help control a trap, or threaten goal.

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.

If an advanced rabbit can't be captured quickly, it is a perpetual goal threat that must be 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.

Unfreeze friends[edit]

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


In the diagram at right, Silver could play ec4we Mb3n, freezing the gold camel on b4. Gold could respond with Ra1nnn Mb4s, unfreezing the camel and stepping it back to b3. Silver might then pull the gold rabbit further along the a-file, with the aim of eventually capturing it in c6.

Neither side misjudged the position. Silver pulled the camel knowing that it could be freed, and Gold advanced a rabbit knowing that it would be exposed. There is a downside to almost any move, especially a rabbit advance, but the upside may be worth it. In this case, Gold's rabbit advance prevented a camel hostage.

Trap control[edit]

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The silver rabbit on b3 currently gives Silver control of c3. (Game)

Here, Gold is well ahead in material and appears to have a strong alignment. Silver is closer to goal, however. Gold rabbits commonly advance into a northern elephant deadlock, but here a silver rabbit advanced away from it and now gives Silver control of c3, which could quickly lead to a silver goal. Had a gold rabbit been on b3, Gold would retain shared control of the trap, and the silver dog would be at greater risk of capture.

Gold must now do something about Silver's southwestern threat, but must also watch the east, where there is likewise strong potential for a silver goal. Without the gold camel freezing it, the f4 rabbit could goal in one turn; even if that rabbit were captured, the g7 rabbit could quickly advance. Despite Gold's apparent overall strength, his weak home defense may cost him the game.