Roulette House Edge

You have probably heard the saying “The house always wins”. And indeed, this is the truth as after all, casinos are not charity organisations and need to turn a profit in order to cover the costs associated with paying their employees and maintaining the venue. Because of this, every casino game has a small built-in advantage in favour of the house, which allows gambling venues to profit from both winning and losing bets.

This built-in advantage is commonly referred to as vigorish, house edge or house advantage and ranges from one casino game to another. In some casino games, the house edge also depends on the type of bet one places. The house edge represents the mathematical advantage the gambling venue has over players and reflects the difference between the real probabilities or odds of winning and the casino’s payouts for winning bets in specific games.

It is important to mention players can never fully offset the house edge no matter how skilled or experienced they are. Of course, individual gamblers can win money over short periods of time but in the long run, they are always at a loss because the house does not pay their winnings off fairly, on the basis of the true odds. That is why experienced players typically engage in games which have lower house advantage.

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As far as its house edge is concerned, roulette is a mid-range game, but in this instance the house advantage differs depending on which variation of the game one plays. For example, in American roulette where there are two zero pockets on the wheel, the advantage of the casino is significantly higher at 5.26%. In comparison, European roulette, with its single-zero wheel, can be more profitable for players because the house has an advantage of 2.70% only. Please note the house edge in roulette remains the same despite the fact the payouts for different types of bets vary.

The ability to calculate the house edge in the game of roulette is crucial because it enables players to make more informed choices when placing their bets and thus, minimise their losses when playing for longer periods of time.

Calculating the House Edge

Let’s demonstrate how the house edge is estimated in a game of European roulette. There are 37 pockets – 36 numbered ones and a single-zero pocket. If you place a Straight Up bet on any given number, mathematically your chances of winning are 37 to 1. This is what the true odds dictate. Yet, the casino holds players at a slight disadvantage as it pays out 35 to 1 for winning Straight Up bets.

To make things as simple as possible, let’s assume you have wagered £1 on every single number on the wheel, including the zero. You are guaranteed to win on one of the 37 numbers and have left a total of £37 in casino chips at the table. Yet, you will collect £36 (your original wager plus £35 in profit), regardless of which the winning number is. It turns out you pay £37 to win only £36 which practically means you are £1 behind. And don’t forget the longer you play, the greater this discrepancy will become.

To calculate the house edge for Straight Up bets in roulette, all you have to do is divide the difference of £1 by the number of the pockets on the wheel, which in this case is 37. So, 1/37 = 0.027027027 which makes for 2.70% ( 0.027027027 x 100 = 2.70270). Using this formula, players can calculate the house edge for all inside bets in roulette.

Or you can calculate the house edge for Straight Up bets in the following way – the odds of winning with a single number in European roulette are 1 to 37 (1/37), while those of losing your stake are 36 to 37 (36/37). As we know, the house pays 35 to 1 for winning Straight Up bets. In this case, the formula will be: -1 x 36/37 + 35 x 1/37 = 0.0270 x 100 = 2.70%.

If you calculate the house edge for even-money bets, you will get the same result. Let’s assume, you want to place an Odds or Even bet and wager £1 on Even. As we know, there are 18 even numbers of the wheel, which means there are 18 ways to win with this bet. Yet, there are also 18 odd numbers plus the zero pocket, which makes for 19 ways to lose.

Thus, your chances of losing are 19 to 18. The house pays 1 to 1 for this type of bet. Your chances of winning are 18 to 37. To make the calculation, you will have to use fractions, so you will need equal denominators. For the purpose, you should multiply the numerator and the denominator of the fraction that represents the house odds by 18/18. This will be the result – 1/1 x 18/18 = 18/18. From this, we get the following: 19/18 – 18/18 x 18/37 = 1/18 x 18/37 = 1/37 = 0.0270270. In order to calculate the house edge percentage, you need to multiply your result by 100. Thus, you get 0.0270270 x 100 = 2.70%.

There are many different bets one can place in a game of European roulette and their payouts vary accordingly. Players’ chances of winning with some of them are greater, but the house will always have the same advantage for all types of bets, namely 2.70%.

While there is no way to completely offset the advantage of the casino, being able to calculate the house edge will help players place smarter bets, implement a suitable betting strategy and minimise there losses in the long run.

European Roulette House Edge
Bet Type Bet Payout Bet Probability House Edge
Straight 35/1 2.70% 2.70%
Split 17/1 5.41% 2.70%
Street 11/1 8.11% 2.70%
Square or Corner 8/1 10.81% 2.70%
Six Line 5/1 16.2% 2.70%
Column 2/1 32.4% 2.70%
Dozen 2/1 32.4% 2.70%
Red / Black 1/1 48.64% 2.70%
Odd / Even 1/1 48.64% 2.70%
High / Low 1/1 48.64% 2.70%
American Roulette House Edge
Bet Type Bet Payout Bet Probability House Edge
Straight 35/1 2.63% 5.26%
Split 17/1 5.26% 5.26%
Street 11/1 7.89% 5.26%
Square or Corner 8/1 10.53% 5.26%
Five Line 6/1 13.16% 7.89%
Six Line 5/1 15.79% 5.26%
Column 2/1 31.58% 5.26%
Dozen 2/1 31.58% 5.26%
Red / Black 1/1 46.37% 5.26%
Odd / Even 1/1 46.37% 5.26%
High / Low 1/1 46.37% 5.26%
French Roulette House Edge *
Bet Type Bet Payout Bet Probability House Edge
Straight 35/1 2.70% 2.70%
Split 17/1 5.41% 2.70%
Street 11/1 8.11% 2.70%
Trio (0,1,2 / 0,2,3) 11/1 8.11% 2.70%
Four-Number (0,1,2,3) 8/1 10.81% 2.70%
Square or Corner 8/1 10.81% 2.70%
Six Line 5/1 16.2% 2.70%
Column 2/1 32.4% 2.70%
Dozen (P12, M12, D12) 2/1 32.4% 2.70%
Red / Black 1/1 48.64% 2.70%
Impair (Odd) / Pair (Even) 1/1 48.64% 2.70%
Manque (Low) / Passe (High) 1/1 48.64% 2.70%

* In French roulette, when even money bets are placed and the ball ends up in the zero pocket, only half of the bet is returned to the player. This is known as the “half-black” or “en prison” rule and reduces the house edge when placing even money bet to 1.35%.