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CUBE Problem Here!!!

Posted By: Daniel Murphy
Date: Wednesday, 6 June 2007, at 8:49 a.m.

In Response To: CUBE Problem Here!!! (pekfrench)

If the Jacoby rule is active, double/pass.

If it isn't, compare double/pass now to never doubling. Double/pass nets 1 point per game, or 1*(Single Wins). Never doubling nets 1*(Single Wins) + 2*(Gammon Wins) - 1*(Losses). Since the (Single Wins) cancel out, what's left is (Gammon Wins) and (Losses). So, if you never double, in order to play on for Gammon, your gammon wins must be twice your losses.

Never doubling is a simplification. It's often the case that after playing on for gammon, you end up doubling anyway, so you don't win as many gammons cubeful as you would cubeless (but you don't lose as many games, either).

How often does White lose? I will make a simplified estimate. If White leaves a direct shot next roll, Blue wins 1/3 of the time, If White leaves two direct shots, Blue wins 1/2 the time. If White leaves no direct shots but does not close his board, Blue wins 1/6 of the time.

4/36 numbers leave 2 direct shots. 12/36 numbers leave 1 direct shot. 20/36 other numbers fail to close the board. So I estimate that Blue wins 9.3 games in 36, about 26%. Then, for playing to be right, in the other 74% of games, White needs to wins 2*26% = 52% gammons. Again I will make a simplified estimate that White can hit the second blot 1/2 the time, when he does he wins 60% gammons, when he doesn't he wins 30% gammons, for an average of 45%. 45% of 76% is only 33%, well short of 52%.

Double/pass.

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