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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.

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  

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List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland