What is the expected number of times you must toss a (fair) coin until you get n consecutive heads?

(In reply to solution by Charlie)

Really nice analysis and writeup.  Interesting that it is essentially 2^(n+1) tries on average to get n+1 heads in a row -- the same as the number of strings of n+1 heads or tails.  I conjecture that the problem can also be solved in closed form when the probability of a head is p. In fact,  the expected value should be 1/p + 1/p^2 + ... + 1/p^n and with r=1/p, this sums to

r(r^n - 1)/(r - 1).

Edited on December 13, 2004, 11:00 pm

Posted by Richard on 2004-12-13 22:10:02