Expected value in roulette describes how much you can expect to win or lose in a single seating at a land-based, or online casino. The expected value is determined by calculating the probability of you either losing or winning in the game. Roulette in itself is a relatively simple game to play, but trying to establish expected value, and probabilities for any given bet within a game can become slightly confusing. Fortunately, we are here to help you make sense of it all.
In this guide, we explain how expected value and probability works in roulette. These two concepts, when applied responsibly, can help you accrue more frequent short-term wins. But, if you ignore the probabilities, you will be shocked at the end of several rounds when you realize how much money you’ve actually lost while playing the game.
You probably know how to play roulette, but before we get into expected value, we’ll have a quick recap of the game and how it works. There are three main variations of roulette which are American, European, and French roulette. The European roulette is the most popular among the three. There are also smaller versions of the game like mini roulette, multi-wheel roulette, and roulette royale.
We’ll focus on American roulette because the odds of winning in this version of the game are very slim. The American roulette wheel has 38 numbered pockets. Eighteen of them are red numbers, while the other 18 is black numbers. The remaining two pockets are 0 and 00 pockets both colored in green. These pockets are equal in size which means that there’s a uniform probability distribution between all numbers on this wheel. In other words, the chances that the ball will land in any of them is equal.
How to Play.
First, you place your bets. The roulette table has all the different bets printed on it and the dealer will assist you in placing your wagers in the right spots on the table.
The dealer will launch the roulette ball onto the spinning wheel and wait for it to rest in one of the pockets.
If your bet wins, meaning the ball rested on the number/color or area which you predicted, then you will receive the equivalent payout.
If you lose, the casino will collect your bet and you will receive nothing.
If the ball rests on either of the zero pockets, you lose as well.
Calculating Probability in Roulette
So, when you place your bet in roulette, you might want to know what the probability is that your specific bet will win or lose, right? If you’ve nodded yes, have a look at the case study below. One of the simplest bets you can make in American roulette is to make a color bet. This is what we call an even-money wager, which means that when you bet $1 you’ll either win or lose that exact amount. The number it falls on doesn’t matter, just as long as the pocket itself is the color that you predicted.
So, what are your chances of actually winning? In this case, there are 38 numbers on the wheel 18 of which are red. So, the probability of red coming up is 18/38. This amounts to about 47%. Based on this finding, you can already tell that you are at a disadvantage when playing American roulette because the chances of losing are higher than the chances of winning.
Calculating Expected Value
Now, we can quantify this probability figure by calculating the expected value of your bet. We’ve mentioned previously that the expected value is exactly how much you could win or lose presented as dollars.
Using the same example as above, when you bet $1, the probability of winning is 18/38. But, the probability of losing is 20/38 (the 18 black numbers plus the 2 zero numbers). The expected value of this particular bet can be calculated using the formula below.
Expected Value = 1(18/38) + (-1) (20/38)
Expected Value = -2/38
Expected Value = – .0526
Expected Value = -5.26 cents
This equation tells you that you should expect to lose about 5.26 cents for every $1 that you bet.
Remember, there are other types of bets that you can make when you play roulette, we used a color bet in our example because it’s simple. You can use the formula that we’ve given above to calculate the expected value of all your other bets as well because the denominator in American roulette remains the same (38). The numerator is the only dependent variable in this case and will change according to the dollar bet you’ve made.
