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2 Cube Max $$ Strategy

Posted By: David Rockwell
Date: Saturday, 12 June 2010, at 5:54 p.m.

In Response To: 2 Cube Max $$ Strategy (Alejandro)

I agree with everything UBK wrote. Here is my own derivation which illustrates strategy.

Ignore gammons for the moment.

In normal doubling situations, there are three possible locations for the cube; centered and held by either player. Player 1 must decide if equity is higher when the cube is centered or held by Player 2. Player 2 must decide if equity is higher when the cube is centered or held by Player 1. The cube stays in the middle when that is the place of maximum equity for both players. There is an equilibrium for an indefinite period of time.

With a cube limit of 2, there is only two cube positions; centered and turned. There is no equilibrium. Putting aside the trivial condition where equity is equal with either cube position, one player must have higher equity with the cube turned and the other player must have higher equity with the cube centered. It must be right for one of the two players to turn the cube. (Or at least, it must not be wrong for one of the two to turn the cube.) Which player should turn the cube? I'll give my answer in a separate post.

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