Casino Margin

As much fun as it is, the game of roulette is not exactly fair. This is because players will always, whatever amounts they bet on whatever combination of numbers, have a greater chance of losing money than they do of winning. This means that the casino always has a certain “edge” over the player, and it is this percentage of "unfairness" that we call the house edge.

Where the house edge comes from

So how come the casino has an edge over the player? Spinning the roulette wheel once is roughly the same as choosing a number from 0-36 (or 00-36) randomly, like a random generator would do, for instance. If this process is repeated over and over a large amount of times, the outcomes will average out and every number will have been chosen approximately an equal number of times. This is called the "Law of Large Numbers" and it means that no number has any greater chance to be the outcome of a spin of the roulette wheel than any other number does. The house edge then comes from the advantage that the casino gains from the number 0 (and the 00 in American roulette), and the payouts accorded a win.

For example, take the “red or black” bet. This may seems at first glance like a 50/50 bet, and it is payed out 1 to 1. But your chances of winning the bet are not actually 50%, because there are on or two numbers on the wheel that are neither red nor black. That is, it is not 50% because of the 0 and 00 slots. This is why 0 and 00 are referred to a the house numbers. It doesn’t mean that you can’t bet on those numbers, you can bet on them. It just means that these are the additions to the wheel from which the house derives it’s edge.

What does this amount to?

So what does this mean for your odds of winning? Let’s take a look at a couple of examples.

Singles bets (bets on a single number) pay out 35-to-1.
So if you were to constantly bet 1 chip on the same number over and over again, that number would win once in every 37 spins on average on a French roulette table. But you would only be paid out 36 chips every time you won. This means that, on average, you would have to lose 36 chips to win 35, resulting in a net average loss.

This loss in average payout is similar to all inside bets: splits pay only 17-to-1, streets (or lines) pay 11-to-1 and corners (or carré) pay only 8-to-1.

Outside bets always lose on 0 and 00.
The bets Red, Black, Even, Odd, High, Low, and all column and dozen bets do not include the 0 and 00. This means that, whenever you bet any of these there is a 1 in 37 (for French tables) or 2 in 38 (for American tables) chance you lose by default, regardless of which outside bet you took.

Should we bet 1 chip on red and 1 on black, we would win nothing and lose nothing without the 0 and 00 slots. With those slots, however, we would lose both chips once (or twice) every 37 (or 38) spins. So, once again, the average is a net loss.

How to calculate the house edge

The actual advantage of the casino can be calculated as a percentage of how much of every bet a player stands to lose on average. This can differ per bet: there are certain ways to decrease the house edge, as well as rule variations that either bring the house edge up or down. The actual edge for a specific bet is calculated as follows:

Expected value = (number of favourable outcomes / total possible outcomes) × (amount of winnings) – (number of adverse outcomes / total possible outcomes) × bet

This will, for roulette, always be a negative number, often somewhere between -0.01 and -0.1. If you divide this number by the amount of chips betted and multiply it by -100%, we get the percentage we call the house edge. So what this in effect represents is the amount of money you will lose, on average, as a percentage of the total amount of money you betted. Remember that this is an average and actual results will likely be worse or better, depending on nothing but luck!

Here is an example of the house edge when we bet a single chip on any single number on an American roulette wheel (with both 0 and 00). As we saw above, winnings are 35 chips, there are 37 losing outcomes and 1 winning outcome, and of course 38 total possible outcomes. We calculate the expected value as follows:

Expected value = (1 / 38) × 35 – (37 / 38) × 1 = -0.0526

This means in this case the house edge is equal to 5.26%. On a French roulette wheel the house edge for a singles bet would be 2.7%.

Special rules

When calculating the house edge, one should definitely take into account the "En Prison" (imprisoned) Rule. If this rule is in effect, all even money bets that lose because the ball lands on 0 or 00 will ride again on the next spin and the player will win back his bet (losing nothing) if the bet wins. A loss the second time will mean he truly loses his bet. This has a large positive impact on the house edge: for instance, a bet of 1 chip on Black in French roulette where the En Prison rule holds will have a house edge of 1.4%, compared to 2.7% (almost double!) when En Prison is not in effect.

The Best Odds

Of course, since the house edge represents the total expected loss, a smaller house edge is a better one. So can we determine what kind of bets are better than others? As we have seen above, a French roulette wheel was better than an American one when it comes to betting singles. This is generally the case: French roulette wheels offer better odds. So if you are looking to beat the odds on roulette, this type of wheel is your best shot. But having a good time in a casino should of course not depend on the type of table you are at.

But let us consider the different house edges for different bets on a French roulette wheel:
(For a list of different bets, click here)

As you can see, the evened odds bets are literally your best bet, since you stand to lose the least amount of money!