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Close encounters of the cube kind

Posted By: Bob Koca
Date: Saturday, 26 April 2008, at 2:05 a.m.

In Response To: Close encounters of the cube kind (Daniel Murphy)

First position looks like optional take/pass.

For the 6 bad rolls (21, 31, 32) White has a cash for 6 wins. For the 3 big doubles (44, 55, 66) white has no wins. For the other 27 rolls white needs 33 or better. (27/36)(4) = 3 wins.

Third position is definitely a pass. Even if still a casher on the six bad rolls a winning double has been lost.

2nd position is still optional take/pass if it is still a cash after the 6 bad rolls. In 1296 games white will take more than two rolls in 2x19 + 3x13 + 2x11 + 2x5 + 6x2 = 121 games. So 121/1296 wins for blue (and not yet accounting for a cube after 21 or 11).

White will take exactly 2 in 1296 - 121 - 4(36) = 1031 games. Blue wins 1/6 of those for about 172 games. 121 + 172 = 293 so still a cash.

Bob Koca

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