(from Hamming) A game is played as follows: A random number [math]X[/math] is chosen uniformly from [math][0, 1][/math]. Then a sequence [math]Y_1,Y_2,\ldots[/math] of random numbers is chosen independently and uniformly from [math][0, 1][/math]. The game ends the first time that [math]Y_i~ \gt ~X[/math]. You are then paid [math](i-1)[/math] dollars. What is a fair entrance fee for this game?

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