Alice and Bob play the following game: Alice generates a uniformly random integer between and , inclusive of both. Bob can pick any number that he wants between and , inclusive of both. Whoever has the larger number must pays out the amount of the smaller number to the person with the smaller number. For example, if Alice selects and Bob selects , Bob will receive from Alice. If they select the same number, nobody pays out anything. Assuming optimal play by Bob, what is his expected payout?