the payout for a five number bet between 0,00,1,2, and 3 is 6 to 1. Find the expectyed value of betting one dollar on the five number bet

The expected value of a bet can be calculated by multiplying each possible outcome by its corresponding probability, and then summing up these values. In this case, for a five number bet with a payout of 6 to 1, there are 6 possible outcomes: 0, 00, 1, 2, 3, and any other number.

To calculate the expected value, we first need to determine the probability of each outcome. In European roulette, there are a total of 37 numbers (0-36). Out of these, there are 5 numbers that would result in a win (0, 00, 1, 2, and 3). Therefore, the probability of winning on any given spin is 5/37.

Next, we calculate the expected value by multiplying the probability of winning by the amount won, and subtracting the probability of losing multiplied by the bet amount. The amount won is 6 times the bet amount because the payout is 6 to 1. The bet amount in this case is $1.

Expected value = (probability of winning * amount won) - (probability of losing * bet amount)
Expected value = (5/37 * 6 * 1) - (32/37 * 1)

Now we can calculate the expected value:

Expected value = (30/37) - (32/37)
Expected value = -2/37

Therefore, the expected value of betting one dollar on the five number bet is approximately -$0.0541.