Position 10, page 17
From Better Backgammon, by Tim Holland

Should Black
double to 2?

Should White accept? Yes. In order to show you why you must accept the double, we must assume that you will play this exact position 36 times.

 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
11 rolls fail
to bear off

According to the laws of probability, if you were to accept the double and play this game 36 times, 25 times Black would win, giving you a minus score of 50 (25 × 2). Eleven times he would fail to bear off both of his men (any roll with an ace) and thus you would win 22 points (11 × 2). Your net score at the end of 36 games would be minus 28 (50 − 22).

This theory holds true regardless of the number showing on the doubling block (whether you are doubled from 1 to 2, 2 to 4, 4 to 8, etc.).

Rollout

Tom Keith 2013
Money play
Centered cube
Black on roll

1296 games with VR
Checker play: 3-ply
Cube play: XG Roller
XGID=--AA-------------------aa-:0:0:1:00:0:0:0:0

 Cube Action Game G BG Equity No double W L .6944 .3056 .0000 .0000 .0000 .0000 +0.3889 (0.3889) Double Take W L .6944 .3056 .0000 .0000 .0000 .0000 +0.7778 +0.7778 Drop +1.0000

Black should double and White should take

 Previous Position No. 9, page 15
 Next Position No. 11, page 18

List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland