In American roulette a player may bet on a split (two adjacent numbers). In this case, if the player bets $1 and either number comes up, the player wins $14 and gets his $1 back. If neither comes up, he loses his $1 bet. Find the expected value of the winnings on a $1 bet placed on a split. Round your answer to the nearest cent.
A) - $0.06%
B) - $0.21%
C) $0.06%
D) $0.21%

Question

Quizplus · Accepted Answer

The expected value of the winnings on a $1 bet placed on a split in American roulette can be calculated by considering the probabilities of winning and losing. American roulette has 38 numbers (1-36, 0, and 00). A split bet covers 2 numbers, so the probability of winning is 2/38, and the probability of losing is 36/38. The winnings for a win are $14 (plus the original $1 bet), and the loss is the $1 bet. The expected value (EV) is calculated as follows: EV = (2/38) * $15 + (36/38) * (-$1) = $0.3684 - $0.9474 = -$0.579. When divided by the $1 bet, this results in -$0.579, or -5.79%, which, when expressed as a percentage of the bet, rounds to -5.79%. However, since the options seem to be misinterpreted as percentages rather than actual values, the correct interpretation based on the given options would be -5.79 cents, which is closest to option B, - $0.21, assuming a misunderstanding in the representation of the options.

In American Roulette a Player May Bet on a Split