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White should double. White will automatically bear his men off in two rolls unless he rolls 2 and 1 followed by 2 and 1. Since the odds are 17 to 1 against rolling 2 and 1, to roll it twice consecutively the odds are 17 to 1 × 17 to 1, or 289 to 1 against.* We will therefore discard this possibility as totally irrelevant to any calculation.

White can win the game outright with the rolls of double 6s, 5s, 4s, and 3s.

This will occur 4 times out of 36. For the remaining 32 games lets assume White bears off two men. Now, unless Black bears off both men on his roll, White will win. Black will accomplish this only with the rolls of double 6s, 5s, 4s, 3s, 6 and 5, 6 and 4, and 5 and 4 (a total of 10 times out of a possible 36).

If you were to play this same position 36 times, 4 of these times White would end the game in 1 roll. Of the remaining 32 games White will win approximately 23 times, giving White an expected winning total based on probabilities of 27 out of 36 games, or in other words 3 out of every 4 games.

Rollout  Tom Keith 2013

Money play Centered cube White on roll 1296 games with VR Checker play: 3-ply Cube play: XG Roller

XGID=-BAA----------------aa----:0:0:1:00:0:0:0:0

Cube Action			Game	G	BG		Equity
No double		W L	.7510 .2490	.0000 .0000	.0000 .0000		+0.5062	(0.4938)
Double	Take	W L	.7510 .2490	.0000 .0000	.0000 .0000	+1.0036	+1.0000
	Drop					+1.0000

  White should double and Black should pass  

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List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland