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Escaping a checker from behind a 5prime
Posted By: Timothy Chow
Date: Sunday, 9 August 2009, at 6:12 p.m.
A little while back I posted the following position on rec.games.backgammon. I was playing White.
Money Game
Blue on roll. Cube action?White 142 Blue 93 Position Id: 2G6DAWBt2woCIA
Match Id: cAkAAAAAAAAA
In the actual game, my opponent doubled, I took, and then he rolled 66. I held the cube. He rolled 65. I doubled and he dropped.
I won't tell you what gnubg said, so that you can have fun figuring out where we erred. The main reason I'm posting, though, is that in the course of trying to understand this position, I did a little handcalculation to answer the question, "How many spare pips do I need if I want a
25%/50%/75% chance of leaping a 5prime, if I am x pips away from the edge?" The resulting table seems like one that is worth studying and learning, at least approximately:
value of x 25% 50% 75%

1 13 30 54
2 12 28 51
3 11 25 46
4 10 23 43
5 9 23 41
(Math weenies who want to know the exact assumptions behind the above table can look here for details.)
What's slightly surprising to me is how spread apart the 25%/50%/75% columns are. The table tells me that if I'm trying to roll a 1 then a 6, then I have a 50% chance of success if I have 30 pips to spare, but if I want a 75% chance of success then I need 54 pips to spare. And even if I have only 13 pips to spare then I still have a 25% chance of success.

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