Position 48a, page 88
From Better Backgammon, by Tim Holland

White to play 4-1.

To illustrate a followup from Position 48, let’s assume that you have made Black’s five point and that Black’s next roll was 5 and 4, with which he made his 2 point.

Now let’s further assume that you do not roll any of the good numbers that are available, such as 2 and 1, 6 and 1, 6 and 2, double 2s, 1s, 3s, 6s, etc., that would enable you either to make your bar or 4 point. Instead, your roll is 4 and 1 as shown above.

Your play should be to move one man from Black’s 12 point to White’s 9 point and one man from Black’s 12 point to White’s 12 point. You have left 2 blots (you could have left none by moving one man from Black’s 12 point to White’s 8 point) which increase your chances of making your bar point on your next roll. Black can hit only with the rolls of double 6s, double 3s, or 6 and 5 (the odds are 8 to 1 against this, but these numbers would be good for Black no matter how you elected to play your 4 and 1).

Let’s continue this hypothetical game by having Black roll double 4s. (Admittedly I choose a poor roll for Black. However, one’s opponent doesn’t always roll good numbers. Also, White’s previous roll could have been much better.) Regardless of how Black may decide to play his double 4s, White, on his next turn, should double, for nearly every number will either make White’s bar point, 4 point, 3 point, 10 point, or escape with both men from Black’s 5 point (depending on how Black’s double 4s were played).

13/12, 13/9  13/9, 6/5
Rollout

Tom Keith 2013
Money play
Black owns 2-cube
White rolls 4-1

1296 games with VR
Checker play: 3-ply
Cube play: XG Roller
XGID=-b---BC-CB---C-bbcbbB--b--:1:-1:1:41:0:0:0:0

 4-1: Game G BG Equity 1 13/9, 6/5 W L .6315 .3685 .1710 .0692 .0066 .0027 +0.2370 2 13/12, 13/9 W L .6297 .3703 .1673 .0694 .0065 .0030 +0.2181 (0.0189) 3 13/8 W L .6205 .3795 .1657 .0698 .0064 .0027 +0.2008 (0.0362) 4 13/12, 8/4 W L .6035 .3965 .1672 .0935 .0071 .0040 +0.1561 (0.0809) 5 13/9, 8/7 W L .6071 .3929 .1592 .0864 .0073 .0032 +0.1415 (0.0955)

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 Next Position No. 49, page 89

List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland