Arimaa/Introduction to Strategy/Rabbit Advancement
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 help stronger pieces gain control of enemy territory. The pros and cons of rabbit advancement must be weighed on a case-by-case basis.
Exposed to capture
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. Once a rabbit is near an enemy trap, friendly pieces must contest control of that trap just to preserve the rabbit.
Advancing rabbits while doing little else will normally result in a large disadvantage. 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
Rabbits' inability to retreat homeward is a double-whammy. Not only are advanced rabbits more vulnerable to capture, but they also leave their home row more vulnerable to enemy goal, if an enemy rabbit can get close. 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 step the c7 horse to b7 to b8, pull the a7 rabbit to b7, and advance the a6 rabbit to a7, 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
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 has the advantage of a horse hostage at the f3 trap, but the e5 gold rabbit restricts the gold elephant, leaving the silver camel as the strongest piece on the western wing. Currently, the gold elephant can only reach the centre by maneuvering through the southeast. Silver should keep her elephant, g6 horse, dogs, and the advanced gold rabbit in place, and use her camel to drag a gold piece up to c6.
If multiple rabbits are advanced in the centre, they may accumulate into a complete elephant blockade. Rabbits may also block other pieces from getting to where they want to be, since they cannot retreat out of the way. In particular, advanced rabbits on a wing may block an attack.
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 step his elephant onto f7, pushing the f7 rabbit to f8, creating capture threats in f6 and a goal threat. Since the silver camel can't then move through f6, Silver's only chance to stop the goal is to unfreeze the now f8 rabbit and step it to g8, using all four steps of her turn; Gold could then make a capture in f6 and keep the pressure on. Suddenly, Silver is the one who must play perfectly just to have a chance.
When the board is empty and ragged, a latent goal threat can be a strategic asset, if only because it commits enemy pieces to goal defense. The western goal threat forced the silver horse to b7, and other silver pieces must stay nearby to back up that horse. Although the eastern goal threat is currently more promising, the western goal threat helped Gold get into this position.
To have a long-term impact, an advanced rabbit must be fairly safe from capture. Ideally it should be on the edge of the board. How far to advance a rabbit depends on how easily the opponent can threaten it. It might not be possible to safely frame the rabbit, or the position might be so sharp that there is not time to drag it into the trap. In that case, enemy pieces may have to decentralize in order to prevent the rabbit from becoming a greater threat.
Advanced rabbits also place great psychological pressure on a human opponent. Even when a correct defense exists, a blunder by the defender loses the game, whereas a blunder by the attacker only loses a rabbit.
The two diagrams at right illustrate the impact advanced rabbits have on a deadlocked trap. As long as both sides commit an elephant to the trap at c6, neither will ever capture anything in c6. This makes it tactically safe for gold rabbits to advance in the west; the question is how that would impact 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 several silver pieces would then be vulnerable. This is the essence of an elephant deadlock: either side will suffer for leaving.
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, Gold would clean house and then have an unstoppable goal; the advanced gold rabbits give the silver elephant little choice but to stay by c6. With so much now at stake in the northwest, the deadlock has been considerably tightened.
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 elsewhere, Gold should think twice about advancing rabbits in the west, since they would likely then be lost if the gold elephant had to leave.
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.
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.
In the position at right, from this game, Gold has overwhelmed both of Silver's home traps, to the point where the silver elephant and camel can't even move through them. Note that the c6 rabbit, despite not holding a key square, aids Gold's trap control by preventing the free movement of the silver pieces. Silver to move cannot prevent capture in the next two turns; if nothing else, the gold elephant could drag the silver camel into c3, and any Silver counterplay would open a capture opportunity in c6 or f6. Gold's home ranks are sparsely defended, but this is irrelevant since no silver rabbit can advance.