The game of roulette uses a wheel containing 38 pockets. Thirty-six pockets are numbered 1, 2, 3, ..., 35, 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

175(1/38) - 5(37/38) = ?

Of course, strictly speaking, you won't "win" exactly $175 on 18, because $5 of that was your original bet.