The house edge is the casino’s expected share of the total amount wagered over repeated play. It does not mean the casino wins every bet or a player loses exactly that percentage in a session. Re-betting winnings increases total turnover and exposure.
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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.
A single-zero wheel has 37 pockets. A winning one-unit straight-up bet pays 35 units profit and returns the original unit, while each losing outcome costs one unit. The expected net result is (1 × 35 − 36 × 1) / 37 = −1/37 units per unit wagered. The house edge is therefore 1/37:
House edge = 1/37 ≈ 0.027027. As a percentage: (1/37) × 100 ≈ 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%
The same is true 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%
Roulette Number Sequences
American Roulette
European Roulette
French Roulette
Classic Roulette Bets
As we can see, the edge of the house for a corner bet is exactly the same as that for a straight-up bet.
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.
The exception
One exception is the double-zero five-number bet on 0, 00, 1, 2 and 3. Its winning probability is 5/38, payout 6:1 and odds against winning 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!”.
Ordinary double-zero bets generally have a 5.26% edge, compared with the five-number bet’s 7.89%. Other exceptions depend on the rules: half-back on zero gives eligible single-zero even-money bets a 1.35% edge, while half-back on both zeros gives eligible double-zero even-money bets a 2.63% edge. Neither benefit applies automatically to all bets.
The bottom line is that a reasonable player will always abstain from making this bet!
Further reading: Gambling Commission explanation of house edge.
