Understanding the Roulette House Edge

The house edge (also known as house take, or house advantage) is the major source of income for casinos. In fact, establishments such as these have predetermined payout odds for every table game they offer in order to score profit from each bet placed by their visitors. In some cases the house edge may appear to be insignificant, but, this does not mean it does not have the potential to ”consume” the bankroll of a player bit by bit.

As we already pointed out, players are able to choose from a variety of bets at the roulette table. With that many betting options available, there are people who doubt that the advantage of the house remains one and the same. This is especially valid for people, who have knowledge of games such as craps, where the edge of the house ranges between less than 1% and more than 16%. Therefore, people with little or no knowledge of roulette may require a more profound understanding of the way the house edge is estimated.

How to calculate the house advantage

Let us use the French roulette wheel as an example again. Despite that the wheel offers 37 possible winning numbers, a player will receive a payout of 35 to 1 for a bet on a single number. Or, for winning a bet of 1 unit the casino will pay him/her 35 units plus the initial bet. For a straight-up bet the probability of success is 1/37 (1 chance out of 37), but the player will receive 36 units, while the difference of 1 unit (37 minus 36) represents the house advantage. If we multiply the house edge by the probability of success and present the result as a percentage, we will come to the following:

1 x 1/37 = 0.0270270 x 100 = 2.70270 , or a rounded 2.70%.

Another way to come to this result is to multiply the difference between the actual odds for a loss and the house odds by the probability of success:

HOUSE EDGE = (Odds against Success – House Odds) x Probability of Success

If expressed as a percentage:

House Percentage = House Edge x 100.

Since

Odds against Success = Ways to Lose / Ways to Win

and

Probability of Success = Ways to Win / Ways to Win + Ways to Lose,

for one straight-up bet the odds against success are 36:1 (36/1), the house odds are 35:1 (35/1) and the probability of success is 1/37. If we use these numbers in the House Edge formula above, we will come to the following:

House Edge = (36/1 – 35/1) x 1/37 = 1/1 x 1/37 = 1/37 = 0.0270270.

Therefore,

House Percentage = 0.0270270 x 100 = 2.70%

French Roulette Straight Up Bet Payout 35 to 1

The same is valid for other inside bets. Let us take corner bets (four numbers), for example. In this case the odds against success are 33 to 4, the house odds are 8 to 1, while the probability of success is 4/37 (4 / 4 + 33). In order to place these numbers into the formula above and be able to subtract fractions, we need equal denominators. Right now we have 33/4 and 8/1. Therefore, we have to multiply the numerator and the denominator of the fraction expressing the house odds by 4/4. Or 8/1 x 4/4 = 32/4. This way we will come to the following:

33/4 – 32/4 x 4/37 = 1/4 x 4/37 = 1/37 = 0.0270270

The House Percentage is 0.0270270 x 100 = 2.70%

As we can see, the edge of the house for a corner bet is exactly the same as that for a straight-up bet.

French Roulette Corner Bet 8 to 1

Someone may ask what the case with even-money outside bets will be. Let us bet 1 unit on black. There are 18 black numbers, which means we have 18 ways to be successful. Also, there are 18 red numbers and one green single zero, which means there are 19 ways to lose. So, the odds against success are 19 to 18 and we are aware that the house odds are 1 to 1. The probability of success is 18/37 (18 / 18 + 19). In order to place these numbers into the formula and be able to subtract fractions, we need equal denominators. Therefore, we have to multiply the numerator and the denominator of the fraction expressing the house odds by 18/18. Or 1/1 x 18/18 = 18/18. We will come to the following:

19/18 – 18/18 x 18/37 = 1/18 x 18/37 = 1/37 = 0.0270270

The House Percentage is 0.0270270 x 100 = 2.70%

Again we come to one and the same result.

French Roulette Color Bet payout 1 to 1

The exception

The only exception is the sucker bet, which can solely be placed on the American roulette wheel. Since it is a bet on five numbers (00, 0, 1, 2, 3), the probability of success is 5/38. The house odds are 6/1 and the odds against success are 33/5. We have to multiply the numerator and the denominator of the fraction expressing the house odds by 5/5. Or 6/1 x 5/5 = 30/5. We will come to the following:

33/5 – 30/5 x 5/38 = 3/5 x 5/38 = 3/38 = 0.0789474

The House Percentage is 0.0789474 x 100 = 7.89%

Or, we can say ”Ouch! That hurts!”. The house edge in this case is even greater than with any other bet placed on the double-zero wheel (5.26%).

The bottom line is that a reasonable player will always abstain from making this bet!

French Roulette Sucker Bet Payout 6 to 1

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