How to calculate house edge of roulette?
Every casino game has a house edge but calculating it can be easy or quite difficult. For example, calculating the house edge percentage of slot machines is not something casual players can do and even professional gamblers who know what they are doing will have a hard time: they must make at least 1,000 spins and risk a huge bankroll.
Fortunately, this is not the case for roulette. Regardless of the variant, the calculation of roulette house edge is easy, as there are a maximum of 37 or 38 numbers on the wheel, i.e., it is possible to limit the possibilities to a certain limit. You can use this formula for calculation:
Expectation = (loss*odds) + (win*odds).
Let's explain the values in this formula one by one.
- “Loss” and “Win” represent the wager amount. For example, if the wager amount is 100 USD, you must enter this figure in both the loss and win sections in the formula. However, remember that the “loss” value will be a minus figure.
- Loss and win probability means your odds of losing and winning the bet. Contrary to popular belief, these are fairly easy values to determine. In this example, let's say you place a red/black bet on European roulette.
- In this variant of the game, there are 37 numbers on the wheel and your bet covers 18 of these numbers. We can express this as 18/37: this is your probability of winning.
- Likewise, your probability of losing will be 19/37.
If we apply all these values to the formula:
- (-100 x 19/37) + (100 x 18/37)
- -51.3 + 48.6
It is also possible to express this result as 2.70% because $2.7 is 2.7% of our $100 bet. Using this formula, the house edge value of each variant of roulette can be easily calculated. The only thing you need to pay attention to is the total numbers on the wheel. For example, American roulette has 38 numbers due to the additional 00 pocket. Therefore, the win and loss probabilities in the formula need to be changed. Let's explain with an example again:
- Let's say you are playing American roulette, and this time you place an odd/even bet for 100 USD.
- This bet covers 18 numbers, but this time there are 38 numbers on the wheel. Therefore, we must specify the win probability as 18/38.
- For the same reason, the probability of loss will be 20/38.
We can reflect all these values into the formula as follows:
- (-100 x 20/38) + (100 x 18/38)
- -52,63 + 47,36
In this case, 5.26 USD is also 5.26% of our 100 USD bet.
You can calculate the house edge percentage of any roulette variant, as long as you know the wager amount, how many numbers are on the wheel, and how many numbers your bet covers.The only exception is a five-number bet in American roulette. The house edge of this bet is 7.89%.
Let's check the possibility of calculating the house edge on the example of another bet. Let's put 100 USD on the corner bet in European roulette and calculate the expectation:
- -100 x 33/37 + 800 x 4/37
- -89.18 + 86.4
As you can see, we get the same value. The reason you can do this is that the roulette probabilities are limited (37 or 38) and can easily be expressed mathematically. You can calculate the house edge values of other casino games with the same principle too, as long as you know how many outcomes are possible. Currently, the house edge percentages of the main variants of roulette, calculated using this formula, are as follows:
What roulette has lowest house edge?
As you can see, French roulette has a much lower house edge than other games. This is due to the specific betting rules of this variant. These rules are:
- La Partage: If the player places a bet that pays 1:1 and loses, he gets half of his wager back.
- En Prison: If the player places a bet that pays 1:1 and loses, he can try his luck on the same bet on the next spin (without the need to place a new wager)
These special rules reduce the profit rate of the casino in the long run, which causes the percentage of the house edge to decrease. We can add these rules to the above formula like this:
(-Loss x Probability) + (Win x Probability) + (50 x 1/Total Numbers on the Wheel) = House Edge
So, for example, on a red/black bet, the percentage of the house edge of French roulette would be:
- (-10 x 19/37) + (10 x 18/37) + (50 x 1/37)
- -2.7 + 1.35
Special betting rules give the French variant the lowest house edge.
The roulette house edge of exotic variants
While European, American, and French are the most common roulette options, there are also many exotic variants of this popular casino game with side bets and/or jackpots. Each of these variants has different house edge values as they offer different chances of winning and odds. These values are almost always higher than the European/French variants. We share the house edge values of some popular exotic games below so you can get an idea.
||House edge rate
|100 to 1 Roulette
|Age of Gods Roulette
|Roulette Max by Netent
How do casinos make money from house edge?
The house edge value also shows how much the casino will win from player bets. As a player, you need to see these values as "money to lose in the long run". For example, if you started playing with 100 EUR/USD:
- In European roulette, the casino will make a profit of 2.70 USD in the long run (2.70%)
- In American roulette, the casino wins 5.26 USD (5.26%) on your bets in the long run
- In French roulette, the profit the casino will make from your bets will be 1.35 USD (1.35%)
We can also express this as “if you play European roulette with 100 USD, you will lose 2.70 USD in the long run, no matter how lucky you are”. Because even if you win more than your bet, the casino will always turn the profit/loss ratio in its favor as long as you keep playing.