Position 57, page 108
From Better Backgammon, by Tim Holland

White to play 4-1.

The four is easy — the one is difficult. It may seemingly be unimportant where the ace is taken; the only correct move, however, is to move from Black’s 4 point to Black’s 5 point.

The reason for this move is that the only number that you have to fear that Black can roll is double 5s. If you move any other 1 in Black’s outer board or you outer board, with the roll of double 5s, Black will enter and move to his 5 point. Thus, you will have just a 1 with which to hit his blot with your man on his 4 point. If you are on his 5 point, he will be forced to hit you. You will therefore be on the rim and will have a chance to hit Black’s blot on his 2 point, plus his newly arrived blot on his 5 point. You have increased your chances of hitting from 11 out of 36 to 22 out of 36, exactly double.

If Black rolls 5 and 6, 5 and 3, or 5 and 2, you will have three men directly bearing on his resulting blot. If Black’s roll is 5 and 4, hitting your blot on your 9 point, you will have the opportunity to hit his blot on his 2 point, plus re-hitting his blot now on your 9 point. If Black rolls 5 and 1 (his best roll), he will save his blot on his 2 point. You’re still okay, however, for you will be able to hit his blot on your 5 point with 4s, 7s, 8s, 12s, and 15s.

bar/21*/20
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=-BBBB-B--A--AA---A---a-agA:1:-1:1:41:0:0:0:0

 4-1: Game G BG Equity 1 bar/21*/20 W L .6235 .3765 .0000 .1130 .0000 .0025 +0.0300 2 bar/21*, 12/11 W L .6204 .3796 .0000 .1169 .0000 .0025 +0.0179 (0.0121) 3 bar/21*, 17/16 W L .6105 .3895 .0000 .1119 .0000 .0019 +0.0055 (0.0245) 4 bar/21*, 9/8 W L .6069 .3931 .0000 .1225 .0000 .0024 −0.0148 (0.0448) 5 bar/21*, 13/12 W L .5965 .4035 .0000 .1241 .0000 .0018 −0.0459 (0.0759)

 Previous Position No. 56a, page 107
 Next Position No. 58, page 110

List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland