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BGonline.org Forums
Position of the Day 08-20-26 - A simple reminder
Posted By: Chuck Bower In Response To: Position of the Day 08-20-26 - A simple reminder (Stick)
Date: Friday, 4 September 2026, at 7:56 p.m.
Blue gets off with 27/36 rolls. If White gets another chance she misses with {11,21,31,32} = 7/36, so bears off 29/36. Note that if Blue redoubles and fails to bear off he won't get the 7/36 chance as White will cash.
With White owning the cube on 4, Blue's equity is 4*(3/4) - 4(1/4) = 2.
With Blue owning the cube on 2, Blue's equity is 2*(3/4) + 2*(1/4)*((7/36) - (29/36)) = 1.5 + 0.5*(-22/36) ~ 1.194.
Note that White's take on 2 -> 4 is optional with perfect actions; she only gains if (steaming?) Blue fails to bear off and then takes the subsequent recube to 8. The fact that White's take is optional is another way to know the cube is correct, without going into the second (more annoying and easier to screw up) calculation. Optional take/pass means perfect cube efficiency for the doubler, and he can't do better than that without later help from the opponent.
This problem has some semblance to the famous Jacoby Paradox (which IMO is a misnomer since it is from the classic 1970 Backgammon Book by Oswald Jacoby AND John R. Crawford, position 41 on page 116). White's position is identical there but Blue's has a checker on each of his 2- and 5-points. The paradox is that if White's position were gin instead of the above, Blue should redouble, but not as illustrated, even though he's less likely to win the game if White is gin.
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