The Gambling Machine Puzzle
An entrepreneur has devised a gambling machine that chooses two random variables x and y that are uniformly and independently distributed between 0 and 100. He plans to tell any customer the value of x and to ask him whether y > x or x > y. If the customer guesses correctly, he is given y dollars. If x = y, he’s given y/2 dollars. And if he’s wrong about which is larger, he’s given nothing. The entrepreneur plans to charge his customers $40 for the privilege of playing the game. Would you play?