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Penny Ante game

I've been studying the Penny Ante game and took a look at some of the math involved. The game is logically flawed and it can be shown. No triplet combination has better odds of coming out than any other. Also, at least, some of the math here is one-sided. For example, the probability of TTH coming out is also 1/8(i.e. 1/2 X 1/2 X 1/2) and the probability of HHH coming out would be 1-1/8 giving 7/8. This gives the same probability for both triplets. Aside from this, I've manually worked through all combinations and ,undoubtably, all triplets have an equal chance of coming out.

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