Here is a brief lesson in how mathematical expectation works.

On the roulette wheel there are 36 numbers, double zero, and the blank. That makes 38 spaces to bet on. Each bet costs $1 to play. The winner pays $35. To calculate the mathematical expectation of the roulette wheel you do the following:

Multiply the probability of winning by what you win when you win. And from that, you subtract the probability of losing by the cost of each bet. The difference is the mathematical expectation. If it’s positive, it’s a fair bet. If it’s negative, you don’t play.

[(1/38) x (35)] – [(37/38) x (1)] = mathematical expectation of playing roulette.

(35/38) – (37/38) = (-2/38) or (-1/19).

So in the case of the Roulette wheel, the best bet is not to play. The problem is playing Roulette is fun! Most professional money handlers don’t find losing money fun. And that’s the difference between the professional and an amateur.