Arimaa/Introduction to Strategy/Rabbit Advancement
The timing of rabbit advances is the most difficult strategic issue in Arimaa. 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 a judgment that the opponent doesn't have time to capture 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.
Blockade friendly elephant
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.
At right, observe the position after move 48s of this game. Well-placed silver pieces combine with five advanced gold rabbits to blockade the gold elephant, camel, and dog. In the east, four more gold pieces can't move at all. The gold horses are stuck in their home half of the board. Silver must be careful not to loosen the blockade, but the g4 dog can be safely captured or moved, as long as no viable path is opened for it or a gold horse to dislodge the silver cat on f5. Short of a miscue by Silver, Gold has no way to free his elephant, although he could get limited freedom for other pieces by sacrificing the elephant, which he did on 57g.
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 stop the gold elephant from quickly forcing goal. 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 on either the fourth or the seventh rank. A rabbit on the edge of the fourth rank is a potential one-turn goal threat, and could become a stronger goal threat by advancing to the seventh rank. The opponent would like to capture or frame the rabbit, but may not have time to drag it into the trap, or may not be in a position to safely frame it. In that case, enemy pieces may have to decentralize in order to prevent the rabbit from becoming a greater threat. A rabbit on the edge of the seventh rank is in greater danger, but is also a greater threat to force a goal. The value of such a rabbit depends on the position being so sharp the opponent can't spare two turns to capture the intruder, or can't spare the material to frame it.
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.
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.
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.
Endgame trap control
As the board clears, important jobs increasingly fall to rabbits. In the position at left, from this game, the b3 rabbit is both a goal threat and a direct defender of the c3 trap. It will at least delay any capture of the c4 dog, and currently allows that dog to enter c3, from where it could capture the c2 cat. Finally, the silver rabbit on b3 prevents a gold rabbit from occupying b3, which would let Gold contest control of the trap.
Gold had correctly advanced rabbits to defend the f3 trap. Had there been a Gold rabbit on b3 as well, it would have forestalled the myriad of threats listed above, and at a minimum delayed Silver in gaining control of c3. Taking rabbits off the back rank to fight for trap control does weaken one's goal defense somewhat, but in an endgame the additional power in contesting traps is usually worth it.
Early trap control
In the position at right, from this game, the board is still full, but Gold is severely cramping Silver. Rabbits are a crucial part of the invading gold army, since advanced gold rabbits prevent the silver elephant and camel from moving through their own home traps. 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 has left his home rank vulnerable, but his advanced rabbits give Silver little hope of reaching goal first.
In the position at left, from this game, advanced silver rabbits on both flanks prevent gold rabbits from advancing there; this in turn makes it harder for other gold pieces to advance effectively on the wings. By contrast, Silver's rabbits are working very well with her other pieces, leaving Gold few good options.