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Memorizing two-roll positions

Posted By: Mochy
Date: Wednesday, 20 February 2013, at 3:31 a.m.

In Response To: Memorizing two-roll positions (Timothy Chow)

I remember probabillity of bears off within 2 rolls for positions where you have 2, 3 or 4 checkers. Not all positions, but at least for ideal positions.

It is not too much work comparing remembering 3rd roll positions.

3 checkers remained: http://www39.atwiki.jp/backgammon/pages/24.html
4 checkers remained: http://www39.atwiki.jp/backgammon/pages/26.html

Here is how I calculate the problem.
I remember white's position (245) bears off in 2 rolls is 84%.
Blue's position bears off in 2 rolls should be tad more than 60%, as I remember (1245) is 60%. I guesstimate 63%

White's winning senarios are
1, Blue bears off at one roll = 0%
2, Blue bears off at two rolls and White bears off in one roll
3, Blue takes more than two rolls and white bears off in two rolls

1, 0%
2, (63%-8.3%) * 1/12 = around 4.5%
3, (100%-63%) * 84% = around 31%

0+31+4.5 = 35.5%

True number is 36.3% so I am off by 0.8% but I can live with that...

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