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Ace2
Ace2
Joined: Oct 2, 2017
  • Threads: 4
  • Posts: 271
September 6th, 2018 at 7:26:19 PM permalink
I also calculated the Fire Bet with the Poisson process. This method is much less tedious than any other method I've seen.

The probability of winning with all 6 points is the integral from zero to infinity of:

((1 - e^(-x/a)) * (1 - e^(-x/b)) * (1 - e^(-x/c)))^2 * e^(-x/s) / s dx

Where:

a = 6,684 / 55 = average rolls to hit a point-8 winner
b = 1,671 / 22 = average rolls to hit a point-9 winner
c = 6,684 / 125 = average rolls to hit a point-10 winner
s = 1,671 / 196 = average rolls to seven out

The exact answer is 3700403899126040038831518494284887738125 / 22780863797678919004236184338193605974839452

=~ 0.000162.

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