Arimaa/Introduction to Strategy/Early Ideas

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Direct Goal Is Impossible[edit]

37px-Arimaa board.jpg
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a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
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Gold has no way to make progress with the h6 rabbit

The most straightforward strategy in Arimaa is to advance a rabbit and some strong pieces, attempting to rip a hole in the opponent's defenses through which the rabbit can score a goal. If both players try to do this, the game turns into a race. Each player in a race must judge how many steps to spend delaying the opposing rabbit, and how many steps to use furthering their own rabbit.

Before long, however, the Arimaa community discovered that if one player tries to force goal in the opening while the other player defends, advantage accrues to the defender. The board is too crowded for rabbits to make headway until some defenders have been captured, but the defender can easily protect his troops from capture while they are all still at home. Meanwhile the attacking rabbit is vulnerable to capture in the defender's home traps. In the diagram at right, the h6-rabbit is no threat to reach the goal, but the rabbit itself is in danger of capture in f6. Furthermore, rabbits can't retreat, so the h6-rabbit can't save itself. Finally, if the gold elephant advances to g6 to protect the h6-rabbit, the elephant will be blockaded.

Capturing Is Impossible Too?[edit]

In light of the futility of forcing an early goal, top Arimaa players next turned to capturing pieces as the most plausible strategy. Each player can easily defend his home traps, so the main offensive strategy was to drag an opposing piece to one's own home traps for capture. (An elephant can safely go hunting for a piece to pull home, because elephants aren't vulnerable to capture.) Unfortunately, this strategy also initially appears futile, because the opposing elephant can camp out by the trap in which the dragged piece has been threatened, and permanently make that trap safe.

37px-Arimaa board.jpg
Arimaa-border.png
Arimaa-border.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Arimaa-border.png
Arimaa-border.png
Silver has defended against an elephant with an elephant, and against a camel with a camel

Since a defensive elephant can make any one trap safe forever, attackers resort to overloading the defending elephant by simultaneously threatening to capture two different pieces in two different traps. Yet even this may lead to one more round of frustration. If you make a capture threat with your elephant, the opposing elephant will block it, and if you make a second capture threat with your camel, the opposing camel will block it. In the diagram at left, Gold is apparently stymied despite having generated a capture threat in each home trap.

Indeed, one might wonder why pieces of equal strength don't stalemate each other on down the line, resulting in a quagmire where neither side can ever make progress. Some Arimaa players feared that the game was by nature too defensive for attacking play to ever pay off.

The strategic answer to this conundrum, namely taking a camel hostage, was the first deep strategy ever discovered in Arimaa. It gave humans their first advantage over computer programs in what had been, before then, a nearly equal contest. Indeed, to this day the fact that neither player can afford to give up a camel hostage informs every opening strategy. It makes the lone elephant attack ultimately effective, and discourages counter-attack when one launches an elephant-horse attack.

Throughout the opening and midgame, a player who can't punish an opposing camel advance will likely be unable to make any progress whatsoever, because most trouble apart from a camel hostage can be relieved by the opposing elephant and/or camel. Applying secondary strategies first, even successfully, will only lead to frustration when the opposing heavy pieces sail to the rescue. Gaining a camel hostage, in contrast to subtler plans, not only gives one an advantage, it also makes the resulting position simpler and easier to play. Therefore the camel hostage should be every beginner's first study after the basic tactics.

Camel Hostage