How to Calculate Expected Value for Roulette

The idea of predictable value can be used to analyze the roulettegame. This idea can be used of the chance of how much money to make in the long run, you will lose the game of roulette.


The roulette wheel in the USA contains 38 equal sized spaces. The wheel spins, the ball randomly lands in one of these spaces. Two squares use to be green and have numbers from 0 and 00 over them. The extra spaces happens to be numbered from 1 to 36.

Probabilities Roulette

Since the space is the same size, the ball is just as likely to land in any spaces. This means that the roulette wheel involves a uniform probability distribution. The probabilities that we should calculate the expected value are as follows:

There are a total of 38 squares, so the probability of a ball in a given square is 1 ⁄ 38.

There are 18 red squares, and thus the probability that red occurs in 18 ⁄ 38.

There are 20 squares that are black or green, and so the probability that red does not occur is 20 ⁄ 38.

Random variable

The net payout of a roulette bet can be like a discrete random variable. If you bet $ 1 red and red occurs, then we win the dollar back and additional dollar. This consequences in a total win of 1. If our bet of $ 1 in red and green or black occurs, we will lose the dollar that we bet. This results in a net payout of -1.

Clarification of results

It happens to help to recall the sense of probable value to understand the consequences of the calculation. The expected value is very much the measurement of the center or average. This indicates that what will happen in the long run every time that we bet $ 1 on the red.Click web page of roulette calculator.

As long as you can win several times in a row in the short run, in the long run we will lose more than 5 cents on average every time we play. The presence of 0 and 00 squares is just sufficient to offer the house a slight benefit. This benefit happens to be so minor that it can be problematic to recognize, but in the end, the house always wins.