Position 26, page 44
From Better Backgammon, by Tim Holland

White to play 4-3.

The correct move is to bear one man off White’s 4 point and move one man from White’s 4 point to White’s 1 point, hitting Black’s blot. Your blot will be hit 11 out of 36 times. However, of those 11 times, double 1s, 1 and 2, and 1 and 3 will cause Black to break his board. With the exception of double 1s, you will have a shot at hitting whichever blot he chooses to leave.

With the alternate move of bearing one man off your 4 point and one man off your 3 point, Black will have the same number of chances to hit your blot. If he does, none of these 11 combinations will cause him to break his board (versus 5 out of 11 with the move of hitting on your 1 point).

There are other things to be taken into consideration. I am going to explain all of them now in some depth, because positions that are similar but not quite identical constantly arise. Therefore you should be aware of all the facts that may influence your decision.

I will start by discussing what will happen when Black misses your blot. When you have hit him on your 1 point one of two things can occur: he can enter on your 5 or 6 point, thus ending your problems, or he can fail to enter, in which case the worst that can happen is that you leave a blot after your next roll. By this time, however, you should have enough men off to win even if you are hit. In the event you are not hit, you will have a good chance of winning a gammon.

Now let’s see what happens if you bear 2 men off instead of hitting on the 1 point, again assuming that Black misses your blot. If his roll contains a 6, he is forced to leave your board, again ending your worries (11 chance versus 20 when you hit on the 1 point). If on the other hand he is able to remain on your 1 point, there are several rolls that could force you to leave 2 blots, such as 6 and 5, 6 and 4, and 5 and 4.

All things taken into consideration, you can see that it’s quite obvious which is the correct play.

4/off, 4/1*
Rollout

Tom Keith 2013
Money play
Black owns 2-cube
White rolls 4-3

1296 games with VR
Checker play: 3-ply
Cube play: XG Roller
XGID=-aBBD--------------bbbbcc-:1:-1:1:43:0:0:0:0

 4-3: Game G BG Equity 1 4/1*, 4/off W L .8681 .1319 .1283 .0000 .0036 .0000 +0.8181 2 4/off, 3/off W L .8626 .1374 .1328 .0000 .0033 .0000 +0.8100 (0.0081)

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List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland