When playing roulette at a casino, a gambler is trying to decide whether to bet

Question

When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 25 or to bet $5 that the outcome is any one of the three possibilities, 00, 0, or 1. The gambler knows that the expected value of the $5 bet for a single number is -53 cents. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $20 and a 35/38 probability of losing $5.

a. Find the expected value for the $5 bet that the outcome is 00, 0, or 1.
b. Which bet is better: a $5 bet on the number 25 or a $5 bet hat the outcome is any one of the numbers 00, 0, or 1? Why?

Explanation / Answer

a) The expected value for the $5 bet that the outcome is 00, 0, or 1 can be computed by using the probability distribution of payoffs as:

Therefore the expected payoff here is computed as:

E(X) = 20*(3/38) - 5*(35/38 ) = -3.0263

Therefore the expected value of the bet here is - $3.0263

b) Clearly the $5 bet on the number 25 has an expected value of - 0.53 which is > - 3.0263 therefore clearly the $5 bet on the number 25 is a better bet than the $5 bet on the outcome is any one of the numbers 00, 0, or 1

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