The payoff for getting x heads followed by a tails is $2^{x}.

The expected return is the sum of the products of the probabilities and
the payoffs is the sum for x=0 to infinity of (1/2) * (1/2)^{x} * 2^{x}.

(1/2)^{x} * 2^{x} = 1. So the answer is an infinite sum of 1/2's, or
infinity.

This problem is a well known paradox in mathematics. The final result must be finite yet the expected value is infinite.

Michael Shackleford, A.S.A.