What is the expectation for the $1 bets on a U.S. roulette wheel? If the bet is a three number bet. Round to the nearest cent.
Thank you
To calculate the expectation for a bet on a U.S. roulette wheel, we need to determine the probability of winning and losing, as well as the amount won or lost in each scenario.
For a three number bet in U.S. roulette, where you place your bet on three consecutive numbers, the payout is typically 11 to 1. In this case, the probability of winning is 3/38 because there are 3 winning numbers out of the total 38 numbers on the wheel (36 numbers plus 0 and 00).
To calculate the expectation, we multiply the probability of winning by the amount won and the probability of losing by the amount lost. In this case, for a $1 bet, the amount won is $11, and the amount lost is $1.
Expectation = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Lost)
Expectation = (3/38 * $11) - (35/38 * $1)
Calculating this gives us:
Expectation = (3/38 * 11) - (35/38 * 1)
Expectation = 0.2895 - 0.9211
Expectation = -0.6316
Therefore, the expectation for a $1 three number bet on a U.S. roulette wheel is approximately -$0.63 when rounded to the nearest cent. This means, on average, you can expect to lose about $0.63 per $1 bet over the long run.