Position 41, page 72
From Better Backgammon, by Tim Holland

Should White
double to 2?

White should double. Black’s position is definitely not good — but it is not hopeless. If you were to play this same game 36 times to its conclusion without doubling, Black would certainly win several games. White, on the other hand, would probably win several gammons. So it becomes a problem of simple arithmetic to determine whether you should double. Examine the following figures, realizing that they are only probable and could vary a little in either direction.

First, assume you do not double, and play the same game 36 times:

 18 times you win 1 point +18 9 times you win 2 points (a gammon) +18 9 times you lose 1 point(assume you do not accept a redouble) −9 Net result +27

Now, assume you double and your opponent declines all 36 times (it would be correct to decline):

 36 times you win 1 point +36

Since not all of your opponents will decline, what happens when one accepts?

 18 times you win 2 points +36 9 times you win 4 points (a gammon) +36 9 times you lose 2 points(assume you do not accept a redouble) −18 Net result +54

As you can see, not only should you double but you hope your opponent accepts. If you were now to say to yourself, “How can I possibly become so experienced as to be able to judge or predict that 9 out of 36 games I will win a gammon and 9 times I will lose the game?” You can’t — nor can I.

What you can do is realize that unless you are able to win more than twice as many gammons as games, you will lose (assuming you were to play the same game X number of times); then you must double.

For example, in those same 36 games, instead of predicting that you will win 18 at 1 point, 9 at 2 points (a gammon), and lose 9 at 1 point, for a new of +27 points, change that to 24 at 1 point, 6 at 2 points, and lose 6 at 1 point for a new of +30; you still don’t win as many points as when you double.

By the way, it doesn’t matter whether you use the number 36 or 50 or 100 as a determining number of games to play. I choose 36 out of habit, since that is the number you will always used in determining probabilities as applied to rolls of the dice.

Rollout

Tom Keith 2013
Money play
Centered cube
White on roll

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

 Cube Action Game G BG Equity No double W L .8655 .1345 .3539 .0040 .0266 .0001 +1.1961 Double Take W L .8646 .1354 .3513 .0041 .0286 .0001 +2.0989 +1.0000 (0.1961) Drop +1.0000

White is too good to double

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List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland