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Probability of hitting a checker from a long running start

Posted By: ah_clem
Date: Sunday, 6 July 2025, at 9:03 p.m.

In Response To: Probability of hitting a checker from a long running start (ah_clem)


Here's the probabilities for (almost) real world backgammon, where you can't be more than 24 pips away. "Almost" since the white checker doesn't move in this problem. Note the "spikes" at multiples of six. 

 

1 0.3055555555555556 

2 0.3333333333333333 

3 0.3888888888888889 

4 0.433641975308642 

5 0.46064814814814814 

6 0.5555555555555556 

7 0.30264060356652944 

8 0.3688271604938272 

9 0.40832904663923186 

10 0.4029159045877153 

11 0.40727166209419297 

12 0.45475989750038104 

13 0.38353164585767757 

14 0.3757350886551846 

15 0.4021349721206117 

16 0.39680785796306645 

17 0.378304244012388 

18 0.41000307712897577 

19 0.3798393132291366 

20 0.4070820387865061 

21 0.38710904191918044 

22 0.38669867315866513 

23 0.38056395146127253 

24 0.4116520093778419



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