Re:Nontransitive dice
by tgb on Sunday April 30, 2017 @07:41AM
(#14231085)
I see an immediate solution to that riddle and it matches the idea of the Wikipedia page you link. But I don't see any connection to Penney's game. Can you explain?
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Re:Nontransitive dice
by frumiousirc on Sunday April 30, 2017 @09:07AM
(#14231337)
The operative words in the rules of both riddles are "appears first".
Yup, Penney's game is surprising because at first glance the probabilities of two sequences of the same length are unrelated. But if more than half of the sequences overlap, then one sequence will tend to arrive before the other. As the proportion of overlap tends to 100%, Player B has a 2:1 advantage over Player A: https://i.imgur.com/eKujwrK.png