Jumping Checkers Probabilities

The table below gives the probabilities of m jumps in a game of Jumping Checkers.   To get the probability of m jumps with b checkers, divide the entry in the appropriate row & column by 28Cb -- found in the last column of the table.

Number of ways that m Jumps Can Occur When Playing b Checkers

m=0 m=1 m=2 m=3 m=4 m=5 m=6 m=7 m=8 m=9 28Cb
b=1 25 3 28
b=2 301 68 9 378
b=3 2326 742? 183? 25 3,276
b=4 12,972 ? ? ? ? 20,475
b=5 55,663 ? ? ? ? ? 98,280
b=6 191,344 ? ? ? ? ? 48 376,740
b=7 541,608 ? ? ? ? ? ? 25 1,184,040
b=8 1,288,110 ? ? ? ? ? ? ? 9 3,108,105
b=9 2,613,128 ? ? ? ? ? ? ? 131? 1 6,906,900

Probability of "No Jumps"

It is not too hard to show that the probability of no jumps when b checkers are placed on the board (b between 1 and 28), can be written as

(25Cb+24Cb-2+2*23Cb-3+3*22Cb-5+21Cb-7)/28Cb

where aCc=a!/(c!(a-c)!) for c and a-c non-negative and aCc=0 if either c or a-c is negative.