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Average number of roll to Jump over Primes

Posted By: maxim
Date: Tuesday, 22 May 2012, at 8:58 p.m.

Some time ago I ran ~10M times simulation for the subject. In case some people are interested, here are the results:

https://docs.google.com/document/d/1o11cHTv4aT04KZblVYPP-pBgeF9NirZcvE6pVKg24AQ/edit

Bob Koca confirmed one of the values analytically:

"To jump 5 prime 1 from edge:

If at the edge already you have a geometric distribution with expected value of 36/11. You enter that state with 9 rolls. 25 rolls repeat and 2 rolls escape. So solve

X = 1 + 25/36(X) + 9/36(36/11) + 2/36(0)

(11X/36) = 1 +9/11 (11X/36) = 20/11

X = (36)(20)/(11)(11) which is approximately 5.95041322 "

In the tables you will find the average number of rolls to jump over 4 and 5-primes with 1-4 checkers.

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