St. Petersburg with a Finite Bank

A fair coin is flipped until it first lands heads. If the first heads occurs on flip k, the casino owes you 2^k dollars. However, the casino has only 2^20 = 1,048,576 dollars, so whenever it owes more than that, it pays you 2^20 dollars instead. What is the expected payout, in dollars? Give an exact number.

• expected value

Source: Variant of the St. Petersburg paradox (Nicolaus and Daniel Bernoulli, 18th century). Statement written for AxiomIQ.