The game of roulette uses a wheel containing 38 pockets. Thirty-six pockets are numbered 1,2.....,36, and the remaining two are marked 0 and 00. The wheel is spun, and a pocket is identified as the "winner." Assume that the observance of any one pocket is just as likely as any other.

Question

Suppose you bet $5 on a single number--say, the number 18. The payoff on this type of bet is usually 35 to 1. What is your expected gain?

Answer 1

prob of your number coming up is 1/36

expected gain = 35(5)(1/36) = 4.86

So, just like in every gambling game, in the long-run you would lose.

Answer 2

thank you

Answer 3

the Prob of your number coming up is 1/38 , not 1/36

which changes the result to
5(35)(1/38) = 4.61

even worse than before