We have talked extensively about the house edge of a casino game, but it is worth clarifying exactly what that means before we explain in a little more detail the house edge for each individual bet in roulette. If you have not yet done so, start with our guide to the rules of roulette and the different wheels — everything below builds on it.
What the House Edge Really Means for Your Bankroll
The house edge is the way the casino makes its money. It varies from game to game, and even within a game depending on particular bets or configurations — as we have already seen with roulette's different wheels. Even a house edge of less than 2% is enough to generate enormous profits when played across millions of wagers over a year.
For our purposes, we need to look at ways of minimising the house edge as much as possible so that we can maximise our chances of winning. If you want to give yourself the best possible chance, it is vital you understand the importance of the house edge and how it is worked out.
The Expectation Formula: How the House Edge Is Calculated
The same formula applies to work out the house edge for any casino game. The amount we are going to win or lose over the long run is called the Expectation, and it is calculated like this:
The loss is whatever stake we put down as our bet. The win is whatever profit we make back if the bet wins. The probability is the chance of that particular loss or win happening. Let us look at a couple of examples in practice so it becomes clearer.
House Edge on Outside Bets: Red, Black, Odd and Even
We can start by looking at the even-money bets, such as Red/Black or Odd/Even. On the European table there are 36 numbers plus the single zero, so we have a total of 37 spaces. There are 18 red spaces and 18 black spaces on the wheel. The chance of hitting a black on the next roll is therefore 18/37, and the chance of not hitting a black must be 19/37. The same odds apply to red, odd or even. Let us imagine we place a $1 bet:
Expectation = −0.5135 + 0.4865
Expectation = −0.027, a house edge of 2.7%
If we do the same calculation for the American wheel, we get a different house edge. This time the chance of hitting a black is 18/38, due to the extra 00 number, and the chance of not hitting a black is 20/38:
Expectation = −0.5263 + 0.4737
Expectation = −0.0526, a house edge of 5.26%
That is almost double the house edge of European roulette!
House Edge on Inside Bets: The True Cost of a Straight-Up Number
Let us look at the inside bets and see how the calculations work out. These bets have a much higher payout but a far lower chance of winning. A straight-up bet on a single number costs us a single unit and returns at 35:1 — if we put $1 on number 17, for example, we would get $36 back if the next number turns out to be 17.
On the European wheel there are 37 spaces, so the chance of a single number coming in is 1/37, and the chance of it not winning is 36/37. This makes the calculation as follows:
Expectation = −0.9729 + 0.9459
Expectation = −0.027, a house edge of 2.7%
We can do the same calculation for the American wheel. Now the chance of hitting a number is 1/38 with the extra 00, and the chance of not hitting a particular number is 37/38:
Expectation = −0.9737 + 0.9211
Expectation = −0.0526, a house edge of 5.26%
Again, the house edge on the American wheel is almost double that of the European table — mathematical proof that the European wheel is always the best one to play. As an example, if you were to play $10,000 over time, you would lose on average $270 on the European table. If you played the same amount on the American table, you would lose $526.
Roulette Payout and Probability Charts: European vs American
Here are two charts showing the payout ratio and the probability of every bet on the two tables. Notice that the house edge for outside and inside bets is identical within each wheel — in the long run it makes no difference which bets you play, although in the short term the difference in variance can be significant.
| Bet | Payout Ratio | Probability |
|---|---|---|
| Red or Black | 1:1 | 48.6% |
| Odd or Even | 1:1 | 48.6% |
| 1-18 or 19-36 | 1:1 | 48.6% |
| Dozen | 2:1 | 32.4% |
| Column | 2:1 | 32.4% |
| Six Line | 5:1 | 16.2% |
| 0 – 1 – 2 – 3 | 8:1 | 10.8% |
| Corner | 8:1 | 10.8% |
| Street | 11:1 | 8.1% |
| Split | 17:1 | 5.4% |
| Straight Up | 35:1 | 2.7% |
| Bet | Payout Ratio | Probability |
|---|---|---|
| Red or Black | 1:1 | 46.37% |
| Odd or Even | 1:1 | 46.37% |
| 1-18 or 19-36 | 1:1 | 46.37% |
| Dozen | 2:1 | 31.58% |
| Column | 2:1 | 31.58% |
| Six Line | 5:1 | 15.79% |
| 0 – 1 – 2 – 3 | 8:1 | 10.53% |
| Corner | 8:1 | 10.53% |
| Street | 11:1 | 7.89% |
| Split | 17:1 | 5.26% |
| Straight Up | 35:1 | 2.63% |
The Gambler’s Fallacy: Why the Wheel Has No Memory
Now that we are familiar with working out odds and probability, let us consider the chances of a string of events occurring in sequence. This is one of the most common areas of misunderstanding in a casino, and it has led many players to bet away their entire bankroll in disbelief that such an “unlikely” event could occur. You will often find these people at the bar, moaning to anyone who will listen about how incredibly unfortunate they are. Let us be sure never to become that person, and consider what has come to be known as the Gambler’s Fallacy.
If you were watching a roulette wheel and saw 10 reds rolled in sequence, you might wonder about the chances of such an event occurring. You might also think it is about time a black number came in — after all, the chance of a black is almost 50%, so surely after so many reds in a row it has got to be a sure thing? This classic way of thinking is the first step on the path to a busted bankroll.
The casino knows it, too. One of the ways casinos exploit this weakness is by displaying the results of previous spins. They may highlight numbers that have come up frequently, or announce that the number 18 has not appeared for 100 spins. This type of data is utterly meaningless for “predicting” the next number. It is there only to confuse players into thinking there is some kind of logical sequence to the wheel.
The wheel, just like a coin, has no memory. It does not know what took place before and does not try to make things “even out” over time. The chances of any event occurring on the wheel are identical from one spin to the next. If a crowd told you the wheel had been red 10 times in a row, that has no bearing on the next spin whatsoever — just as a coin that has come up tails 100 times in a row still has a 50% chance of tails on the next toss. Overestimating or underestimating the chances of an event because of previous results is the Gambler’s Fallacy.
The Maths of Streaks: Calculating Consecutive Events
The bet on Red or Black is not quite 50/50 because of the green zero, so let us use a coin toss as our real-life example: two outcomes, each with a chance of 1/2, or 50%, or 0.5. The payout is even money, just as it is on Red or Black. To work out the chances of consecutive events occurring, all we have to do is multiply the chances of each individual event together.
For example, the chance of 2 heads in a row from 2 consecutive coin tosses is:
The chance of 4 heads in a row is:
But if we get through the first 3 tosses successfully, what are the chances of the fourth? Remember that the chance of any single coin toss is always 50/50. The formula is therefore very simple:
This is because those events that were previously unknown have now taken place. They are in the past, we already know what happened — so the “chances” of those events have already been decided at 1. The only coin toss we are uncertain of is the one yet to happen.
Let us imagine the same scenario, but this time we interrupt the bet after two successful coin tosses:
The first two events have already taken place and been heads, so we put them down as 1. We have two bets left, each with a chance of 0.5, and multiplying them together gives 0.25 — a 1 in 4 chance. The critical thing to understand is that all previous events have absolutely no bearing on the next one (assuming they are independent, such as a coin toss or a roulette spin).
Just for interest, here are the chances of a red or black occurring in particular sequences:
| Number of Spins | Chance as a Percentage |
|---|---|
| 1 | 48.6% |
| 2 | 23.7% |
| 3 | 11.5% |
| 4 | 5.6% |
| 5 | 2.73% |
| 6 | 1.33% |
| 7 | 0.65% |
| 8 | 0.31% |
| 9 | 0.15% |
| 10 | 0.074% |
Summary: The Two Rules That Protect Your Bankroll
To find out the chances of a sequence of events taking place, multiply the chances of the individual events together. And remember: the roulette wheel has no memory. Previous events have no bearing on future ones and cannot change the odds of an event occurring in any way at all. Even after 10 reds — or 100 reds — the chance of the next spin being red will always be 48.6%. For more on the maths behind the game, see our guides to roulette odds and roulette strategies.
Frequently Asked Questions About Roulette Payouts and House Edge
What is the house edge in roulette?
The house edge is the built-in mathematical advantage the casino holds on every bet. In roulette it comes from the green zero pockets: 2.7% on the European wheel and 5.26% on the American wheel. Over $10,000 wagered, that means an average loss of $270 on a European table versus $526 on an American one.
How is the roulette house edge calculated?
Using the expectation formula: Expectation = (Loss × probability) + (Win × probability). For a $1 bet on black on a European wheel: (−1 × 19/37) + (1 × 18/37) = −0.027, which is a 2.7% house edge.
Do inside bets have a higher house edge than outside bets?
No. The house edge is identical for outside and inside bets on the same wheel — 2.7% for every bet on a European table and 5.26% on an American table. What changes is the variance: inside bets pay more but win far less often, so short-term swings are much bigger.
What is the Gambler’s Fallacy?
It is the mistaken belief that past results affect future ones on independent events — for example, thinking black is “due” after 10 reds in a row. The wheel has no memory: the chance of red on any single spin is always 48.6% on a European wheel, regardless of what came before.
Should I follow the previous-spin displays casinos show at the table?
No. Boards showing hot numbers, or numbers that have not appeared for many spins, are meaningless for predicting the next result. Each spin is independent, and the displays exist only to encourage players to see patterns that are not there.