Consider a simplified game of roulette with two outcomes: red and black. A bet of any fraction may be placed on red or black for any individual draw. If red or black is chosen correctly, $1 is paid for each unit bet, while if chosen incorrectly the payoff is $0. Assuming the events red and black are equally likely, what is the expected payoff of the game? How much should an investor be willing to pay for a chance to play this game once? Are risk preferences involved in the calculation? Does the answer change if the investor is allowed to play the game infinitely many times?