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doubles to play

Posted By: Daniel Murphy
Date: Friday, 7 October 2011, at 3:58 a.m.

In Response To: doubles to play (steve)

In the second position, taking 2 off leaves 12 checkers to go, a 6 roll position. Opponent need 15 crossovers to get off the gammon. So gammon is nearly assured. Taking 4 off appears to gain a whole roll, except it won't when, as I imagine you're favored to, with 7 checkers above the gap on the 2 point, you miss by rolling a deuce. Backgammons, of course, are irrelevant at the score.

The first position is quite different. First, you have a choice of bearing off the 7th or 9th checker, leaving 4 or 3 rolls. Second, you're unlikely to miss. Third, Opponent has 2 checkers on the bar, not 1. And fourth, winning a backgammon doubles your match winning chance from 50% to 100%. Either play leaves you with a 3 point board. But 3/off(4) leaves you with a 3 point board and needing only 3 rolls or even 2 rolls (with one doublet) to bear off. This should give you a much better chance of winning a backgammon. 3/off(4) gives you fewer than 8/36 sequences that leave a blot (since Opponent can 66, 65, or 55). Your chance of getting hit after playing 3/off(4) are about 6%. Even if you lose all such games, you've cost yourself 50% match equity about 6% of the time. Without trying to calculate exactly how many more backgammons 3/off(4) wins, just note that with only 6 checkers left your main routes to backgammon are by rolling a usable doublet next roll (an 8.3% chance) or on the following roll (often about a 14% chance). But with 8 checkers left, you'd need to roll two usable doublets to bear off in two rolls, about a 8.8% chance. So right there, 3/off(4) promises to win a lot more backgammons by enabling you to bear off in 2 rolls much more frequently, and obviously you'd be much more likely to bear off 6 checkers in 3 rolls than 8 checkers in 3 rolls, also.

If in the first position you trailed 3-6/7 instead of 1-6/7, and thus could not use a backgammon, the safer play 4/1(2) 3/off(2) would be better, since the gammon count with 8 checkers left and Opponent needing 18 crossovers is even more favorable to you than in the second position.

Messages In This Thread

• doubles to play
  steve -- Friday, 7 October 2011, at 2:45 a.m.
  • doubles to play
    Daniel Murphy -- Friday, 7 October 2011, at 3:58 a.m.
  • doubles to play
    Dmitriy Obukhov -- Friday, 7 October 2011, at 4:42 a.m.
  • doubles to play
    Mick Dyett -- Friday, 7 October 2011, at 7:15 a.m.