Position 39, page 69
From Better Backgammon, by Tim Holland

White to play 6-1.

The correct play is to enter on Black’s 6 point and move one man from White’s 2 point to White’s 1 point, hitting Black’s blot. If Black fails to enter on his next roll ( he will fail to do so 16 out of 36 times), you will have 29 chances to cover your blot on your 1 point. Of the remaining seven numbers, 6 and 1, 5 and 1, and double 5’s will hit two additional blots of Black, putting three of his men on the bar, and a 6 and 5 will put a second man on the bar.

In short, in the event of entry failure by Black, you will have become a big favorite to win not only the game — but a gammon as well. Let’s see what happens when Black is able to enter.

In the even Black rolls a 1 and hits your blot, the tide will unfortunately be turned in Black’s favor. You will however still have some numbers that will keep disaster away from your door, depending on what Black’s other number was. If his roll was 1 and 6 or 1 and 5 then his correct play would be to hit you on his 6 point, putting two of your men on the bar; with 1 and 1, 1 and 2, or 1 and 4, he should make some point in his outer board. Let’s assume 3 and 1, however, in which case with 6 and 2, 6 and 3, 6 and 4, you would enter and once again hit Black’s blot on your 1 point; 6 and 5, which enables you to enter and hit Black’s blot on his 11 point; and double 6s, which enables you to hit the blot on Black’s 12 point. With all of these numbers, Black will once again be in jeopardy of losing a double game if he fails to enter on his next roll. If you are unable to roll one of these combinations, Black should double and you should decline.

In the event Black is able to enter on your 6 point and not your 1 point, but does not roll double 6s or 6 and 5 (in this case he would hit your blot on his 6 point, creating a condition similar to the condition just discussed), you man on Black’s 6 point will have several combinations that will hit one of Black’s blots, which by necessity must still be exposed. This will enable you to move into your home board, or move to a position in your outer board where Black will have only one man left with which to hit.

Having covered all of the possibilities of what might happen when you hit on the 1 point, let’s investigate the alternative. Your blot, whether left on Black’s 6 point or bar point, will almost surely be hit. The burden will then be on you to enter before Black can make his 6 point. The least Black can be said to be favored to win is 25 to 11 (the chance of your entering on the 6 point). Contrast this with all of the possibilities above and it becomes obvious which play is more advantageous.

bar/19, 2/1*
Rollout

Tom Keith 2013
Money play
Black owns 2-cube
White rolls 6-1

1296 games with VR
Checker play: 3-ply
Cube play: XG Roller
XGID=-aCCCC---a--aaa-----bbbbbA:1:-1:1:61:0:0:0:0

 6-1: Game G BG Equity 1 bar/19, 2/1* W L .6199 .3801 .4333 .0000 .0254 .0000 +0.5403

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List of Positions from Better Backgammon

Better Backgammon (1974), by Tim Holland