From Better Backgammon, by Tim Holland
||White to play 4-2.|
The correct play is to move one man from Black’s 12 point to White’s bar point. It seems you have unnecessarily exposed a blot to being hit by a 6 (11 chances), for you could have played safe by bringing one man into your board form your 11 point to your 5 point. When analyzing this position, one must assume that if Black rolls a 6 (assuming that you have moved one man from your 11 point to your 5 point), White’s chances of winning the game would then in all probability be restricted, hopefully, to hitting a blot as Black is bearing off.
In explanation of this, let’s assume that Black rolls 6 and something. In order for White to have any chance to win other than the chance of hitting a blot of Black’s later in the game, the following would have to happen: White hits Black’s blot with his men on Black’s 12 point (the chances of hitting, of course, will vary according to where Black’s blot will land). Black then must enter on White’s 1 point and not be able to escape (the odds are 25 to 11 that he will not enter). White will have to roll very small numbers so that he is not forced to advance his men or break his board. Black would then have to roll large numbers (without a 6), thus forcing him to break his prime. White would then have to escape with his two men from Black’s 1 point, and at the same time contain Black’s blot on White’s 1 point. There is more, but as you can see, White’s chances of winning in this fashion are extremely remote.
Instead of moving from White’s 11 point to White’s 5 point, you move from Black’s 12 point to White’s bar. If Black rolls a 6, he will hit one, perhaps two or even three of your blots.
Unquestionably, if this happens, you will have exposed yourself to an increased probability of being gammoned. Commensurate with this are your increased chances of winning. Since you will be unable to move until you enter (this should take several rolls depending on how many of your blots Black picks up), you will not be forced to break your board. There is also the possibility of your still having a man on the bar if Black is forced to leave a blot while bearing off. This increases your chances of hitting.
Now that we have covered what might occur with both plays of the 4 and 2 when Black rolls a 6 and something, let’s investigate the more likely occurrence when Black does not roll a 6.
First, let’s assume you moved one man to your bar point. Without a 6, Black will be forced to advance his men on his side of the table. If on your next roll you are able to cover your blot on your bar point (29 chances out of 36), giving you a prime, there will be a good likelihood of Black’s being forced to break his prime on his next roll. The following diagrams illustrate a possible, and probable, progression of positions, assuming you had moved one man to White’s bar point (excluding any roll of Black’s that contains a 6).
Tom Keith 2013
White owns 2-cube
White rolls 4-2
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