From Better Backgammon, by Tim Holland
||White to play 5-4.|
The correct play is to move one man from Black’s 3 point to Black’s 12 point.
When your opponent has no builders left on his high points — one man does the work of two, except when he rolls double 1s, 2s, 3s, or 6 and 3. Offsetting this, however, is the fact that your board is still intact versus that of having opened your 6 point.
It would be wrong to move both men from Black’s 3 point. For example, if Black rolls 6 and 3, and both of your men have moved to Black’s outer board, Black would bear a 6 off and move one man to his 3 point. You would then have 11 chances to roll a 2 which would hit his blot. On the other hand, if you still had a man on his 3 point, he would be forced to hit this blot. You would then be able to hit his man on his 3 point with 15 combinations. Any 3 (11), 1 and 2 (2), and 6 and 2(2). Basically similar statistics would hold true if Black rolled 4 and 3 or 3 and 2.
Now take the roll of 6 and 5. By leaving one man on Black’s 3 point you would be able to hit one of his blots with 2s, 3s, 4s, or 5s (33 chances). If on the other hand you did not have that man on his 3 point, then only 4s and 5s, double 2s, and 2 and 3 would hit (23 chances). Your gain is almost the same when Black rolls 5 and 4.
Tom Keith 2013
White owns 2-cube
White rolls 5-4
1296 games with VR
Checker play: 3-ply
Cube play: XG Roller