This is a paradox only because we are allowing infinite winnings. That's not possible in the real world. The solution is to end the game when the 'casino' can no longer pay the amount on the table.
In this case, the expected value is simply .50 * log 2 C, where C is the total cash available.
In this case, the expected value is simply .50 * log 2 C, where C is the total cash available.