Fair game problem

[Siegmund]

Yes, a nice tidy solution from Aaron. (The Markov chain approach isn't too messy either, pairs of iterations forming a geometric series.)

For those interested in the more general case or scratching their heads over "where did 34 come from?" ...

If it's a race between M heads in a row and N tails in a row, the odds are 2^N-1 : 2^M-1, or the probability of heads winning is (2^N-1)/(2^M+2^N-2).

[AaronBrown]

Great minds think alike. That was my first answer as well, but Siegmund proved us both wrong.