Position 46, page 82
From Better Backgammon, by Tim Holland

Should White
double to 2?

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.

 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 61 62 63 64 65 66
10 rolls win for Black

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.

* TK: This is one of the perils of using odds instead of probabilities. Probabilities you can multiply; odds you cannot. The chance of rolling 2-1 twice in a row is 1/18 × 1/18 = 1/324, so the true odds are 323 to 1 against.

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