Why would anyone play a game that they are doomed to inevitably lose? But to make money, casinos do need players to actually play the game. This negative expected value is why casinos make money: on average, players will lose more than they win. This makes Roulette simply a game in which the player accepts a certain negative expected value, but chooses the variance that player wants to accept.
If you do this for every possible bet, you will find that the expected value is almost always the same (a rare exception is the top line bet in American roulette, which is even worse), but the variance/standard deviation is different. For example, if we bet €10 on a single number, we expect to win: > (36/37) * -10 + (1/37) * 350 Due to the number zero, however, the expected value of any bet is negative. All payouts are based such that the game is completely fair if the number zero was not included. You can bet on a lot of different things, such as a single number, three numbers, a column, a row, even/odd, red/black, etcetera. A french roulette game looks like this:Ī ball will roll in the left basin and land on one of the 37 values. In my class on Structural Equation Modeling, I introduce the concepts of expected values and variances through the game of roulette.