Position 16, page 28
From Better Backgammon, by Tim Holland

White to play 4-1.

The correct play is to bear one man off your 4 point and move one man from your 4 point to your 3 point. If Black fails to enter on his next roll, only 6 and 2 will cause you to leave a blot. If you were to break your 6 point by moving one man 4 to your 2 point and one man 1 to your 5 point, and Black did not enter, on your next roll you would be forced to expose with 6 and 5, 6 and 4, 6 and 3, 5 and 4, 5 and 3, doubles 6s, 5s, and 4s. This adds up to 13 possible combinations that will cause exposure, while there are only 2 with the correct move. If you were to break your 5 point by moving one man to the 1 point and one man to the 4 point, then you would expose with 6 and 1, 5 and 1, double 6s, 5s, and 4s — seven combinations in all. This is better than moving from the 6 point, but hardly correct when you can make a move that will leave only 2 possibilities.

It is true that by breaking your 6 point, if Black enters, he is out of your hair for good; whereas, by breaking your 4 point, if he enters, you still must get your men past him. If this occurs, only the roll of 6 and 2 will cause a blot. This slight possibility should not in any way influence the decision to choose the move that you did.

4/off, 4/3
Rollout 
XG logo
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=aDCBBBB------------bbbbcc-:1:-1:1:41:0:0:0:0

4-1: Game BG   Equity
1 4/3, 4/off W
L
.9370
.0630
.0089
.0000
.0001
.0000
+0.8631 x  *
2 5/4, 5/1 W
L
.9091
.0909
.0053
.0003
.0001
.0000
+0.8023 (0.0608) 
3 6/5, 6/2 W
L
.8898
.1102
.0082
.0000
.0001
.0000
+0.7589 (0.1042) 

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No. 15, page 26
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No. 17, page 29

List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland

Backgammon Galore : Books