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Old 2020-06-22, 09:50   #7
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

58816 Posts
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Quote:
Originally Posted by Batalov View Post
if the rules are >=5 and that hole in the middle, and players have no interest in outcome and play randomly, then you can sample quite accurately by:
- enum all lines of 5
- repeat 10^8 times {
. . . throw 40 random black darts (don't count if you hit a past dart, go on until 40), the rest assumed white,
. . . sum up all pre-enum'd lines of 5 (is it or is it not) and
. . . record both of the wanted outcomes (A) and (B)
. . . clean up
}
and you will have a fairly accurate estimate. You can estimate a CI of that random process.
I've also that in my mind. Generated 1e8 random boards, and counted 8499941 configurations that has no 5 or more same piece in a line. So roughly we are expecting 0.085*binomial(80,40) for the whole board, that is approx 2^72.952 .
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