A bettor starts with a $1 bankroll, tosses a coin against
the house, with bottomless bankroll. He bets $1 each
play, with 1:1 payoff.

His chance of winning is p, on each toss.

i) p < 1/2
He eventually goes bust, for sure.

ii) p > 1/2
There's a finite chance he never busts, depending on p.

iii) p = 1/2
He eventually busts.


What is the expected number of plays until he busts,
in each case (as function of p)? How is this calculated?

--
Rich

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