Question

A casino company offers a simple game which is described as follows:
The prize of the game depends on four unbiased coins you toss. If all four heads appear, you get $650. If all tails appear, you get $50. If exact three heads appear, you get $180. If exact three tails appear, you get $120. Otherwise, you get $150.
1. The company offers you a promotion as follows: A free cash of $150 or a chance to win the prize of the coin game. Your utility function is U(W)= -1/W. What is your choice? What is the lowest cash offer that you are willing to take it and not to play the game?
2. After the promotion period ends, the company charges the entry fee $150 for the game. One day, a group of tourists, who all exhibit utility function U(W)= -1/W, visit the casino, but no one plays the coin game. To induce them to play, the company decides to raise the payoff, instead of lowering the entry fee. What will be the smallest compensatory risk premium the company has to offer?
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3. Suppose now the utility function is U=E(r)-0.5Aσ . (Inputs should be in a
decimal format.) The company still charges the entry fee $150 for the game. For an investor with A=0.4, will the investor prefer this coin game to an instant risk-free rate of 1%?

Answer 1

Given facts, Available cash = $150.00 Prize coin game: 4 coins toss outcome will get 16 So, probability of getting Head and Tail are; Head (H) = P(H) = 1/16 Tail (T) = P(T) = 1/16 Others (0) = P(0) = 1- (1/16)+(1/16) = 7/8 Prize gain or cash expected from game; = (650/16) + (50/16) + (150 *7/8) = 175 So, Excpected cash prize is more than cash available that is $175 > $150 Decision: Play the game is the best option because of getting outcome is more.