Roulette Explained: Odds, Bets & House Edge

Roulette is one of the easiest casino games to recognise and one of the most useful for understanding probability.

A ball is released around a spinning wheel. It eventually settles into one numbered pocket, and wagers are settled according to that result.

There are no player decisions comparable to hitting or standing in blackjack.

Instead, roulette is mainly about choosing which outcomes to cover and understanding the relationship between probability and payout.

How a Roulette Wheel Works

A roulette wheel contains numbered pockets divided between red, black and green.

The exact number of pockets depends on the version of roulette being played.

European Roulette

A standard European roulette wheel contains 37 pockets:

• numbers 1 to 36;
• 18 red numbers;
• 18 black numbers; and
• one green zero.

The zero is central to the mathematics of roulette.

American Roulette

A standard American roulette wheel contains 38 pockets.

It has the same numbers 1 to 36 plus:

• one zero; and
• one double zero.

That additional pocket changes the probabilities without proportionally improving the standard payouts, producing a larger house advantage on many common bets.

The Betting Table

Roulette wagers are usually divided into two broad groups: inside bets and outside bets.

The names describe where the wagers appear on the traditional table layout rather than whether one category is inherently "better."

Inside Bets

Inside bets cover individual numbers or small groups of neighbouring numbers on the layout.

Common examples include:

• Straight up — one number;
• Split — two adjacent numbers;
• Street — a row of three numbers;
• Corner — four numbers meeting at a corner; and
• Six line — two adjacent rows covering six numbers.

Covering fewer numbers generally means a lower probability of winning the wager but a larger payout when it succeeds.

Outside Bets

Outside bets cover larger groups of numbers.

Common examples include:

• red or black;
• odd or even;
• 1–18 or 19–36;
• dozens; and
• columns.

These bets win more frequently than a wager on one individual number, but their payouts are correspondingly smaller.

A higher hit probability does not automatically mean a better long-term mathematical proposition.

Probability Comes From the Wheel

Roulette probabilities can be calculated directly from the number of pockets covered by a wager.

On a European wheel, a straight-up wager covers one of 37 possible outcomes.

Its probability of winning on a fair spin is therefore approximately:

1 / 37 ≈ 2.70%

A wager on black covers 18 of the 37 pockets:

18 / 37 ≈ 48.65%

Notice that black is not a 50% proposition even though there are equal numbers of red and black pockets.

The green zero is the reason.

Probability and Payout Are Different

Understanding roulette becomes easier when probability and payout are kept separate.

Probability answers:

How often should this outcome occur across a very large number of fair spins?

Payout answers:

How much does the game pay when the wager wins?

The difference between the true odds and the offered payouts is what creates the standard roulette house advantage.

Why Zero Matters

Imagine a roulette game containing only 18 red pockets and 18 black pockets with no zero.

A red-or-black wager would then be an even 18-versus-18 proposition.

Real European roulette adds the zero.

The player still normally receives an even-money payout for winning a red-or-black wager, but there are now 37 possible wheel outcomes rather than 36.

When zero appears, ordinary red and black wagers both lose under standard rules.

That small green pocket is enough to create the mathematical advantage.

House Edge in European Roulette

Consider a €1 straight-up wager on a single number.

There are 37 possible pockets, while a winning straight-up wager normally pays 35 to 1.

If every possible number occurred once across a hypothetical set of 37 perfectly distributed spins, one straight-up wager repeated on the same number would produce one win and 36 losses.

That mismatch between probability and payout creates a standard theoretical house edge of approximately 2.70% on many European roulette wagers.

The percentage describes long-run mathematical expectation. It does not mean every €100 session loses exactly €2.70.

Why American Roulette Is Mathematically Different

American roulette adds the double-zero pocket, giving the wheel 38 possible outcomes.

For a standard red-or-black wager, 18 pockets still win, but 20 outcomes do not.

Under standard rules this produces a larger house advantage than the equivalent wager on a single-zero European wheel.

This illustrates an important principle:

Small rule changes can materially change the mathematics of a casino game.

Does Choosing More Numbers Improve Your Chances?

It improves the probability that a particular wager wins, but that is only half the story.

A bet covering 18 numbers wins much more frequently than a bet covering one number.

But it also pays much less when successful.

Roulette payouts are structured so that simply covering more numbers does not automatically remove the house edge.

This is why "wins more often" and "better mathematical value" should not be treated as identical ideas.

Each Spin Is a New Event

Suppose a European wheel has landed on red five times consecutively.

Many people instinctively feel that black has become more likely.

But if the spins are independent and the wheel is fair, the physical composition of the wheel has not changed.

For the next spin there are still:

• 18 red pockets;
• 18 black pockets; and
• one green zero.

The probability of black on the next spin remains approximately 48.65%.

The Gambler's Fallacy

The belief that an independent outcome becomes "due" because it has not occurred recently is known as the gambler's fallacy.

Roulette makes this particularly tempting because previous results are often displayed prominently.

A screen might show:

Red – Red – Red – Red – Red – Red

That sequence contains information about the previous six spins.

It does not create another black pocket on the wheel for spin number seven.

But Aren't Long Streaks Unlikely?

Yes — and this is where probability can feel counterintuitive.

A specific sequence of six reds is less likely before the sequence begins than a single red on one spin.

But once five reds have already occurred, those five results are known history.

The probability question for the next independent spin starts again from the unchanged wheel.

These are different questions:

1. What is the probability of a six-red sequence before any of the six spins occur?
2. After five reds have already occurred, what is the probability that the next spin is red?

Confusing those two questions is one of the main reasons streaks can feel predictive.

Hot and Cold Numbers

A "hot" number is usually one that has appeared frequently in a recent sample. A "cold" number is one that has appeared less often.

Those labels can accurately describe historical results.

The problem appears when they are treated as evidence that an independent future spin has changed probability.

On a fair wheel, a number does not become more likely simply because it appeared several times recently, nor does it become due because it has been absent.

What About Roulette Betting Systems?

Roulette has inspired many systems for changing wager sizes according to previous results.

Some increase the stake after a loss. Others change the stake after a win or move through predefined sequences.

These systems can certainly change the pattern of money won and lost during a session.

They can also change how quickly the size of a wager grows.

What they do not do is alter the number of pockets on the wheel.

The Martingale Example

One of the best-known roulette systems is the Martingale.

In its familiar form, a player increases an even-money wager after a loss with the intention that a later win recovers previous losses and produces a small net gain.

The apparent simplicity hides two practical problems.

First, stakes can increase rapidly during a sufficiently long losing sequence.

Second, neither the player's available money nor the permitted table stake is unlimited.

Most importantly, increasing the stake does not change the probability of the next spin.

A staking pattern changes financial exposure. It does not remove the zero or alter the wheel's underlying house advantage.

Can Money Management Still Be Useful?

Yes, but for a different reason.

Setting a spending limit can control how much money is exposed to gambling.

Setting a time limit can control how long a session continues.

Choosing smaller wagers can make a fixed entertainment budget last through more individual rounds.

Those are risk-management decisions.

They should not be described as methods for turning a negative-expectation game into a guaranteed profitable one.

Common Roulette Myths

"Black Is Due"

Previous red results do not increase the number of black pockets on the next independent spin.

"This Number Is Hot"

A number can genuinely have appeared frequently in a recent sample without having a higher probability on the next fair spin.

"This Number Hasn't Appeared All Night"

Historical absence does not create a debt that randomness must repay.

"A System Can Remove the House Edge"

Changing the timing or size of wagers does not change the probabilities and payouts that created the underlying house edge.

"Outside Bets Are Safer, So They Must Be Better Value"

Outside bets generally win more frequently than straight-up bets, but their payouts are smaller.

Frequency of winning and long-term expected value are different concepts.

Roulette Is a Useful Probability Lesson

Roulette strips probability down to something visible.

You can see the pockets. You can count how many outcomes a wager covers. You can compare those outcomes with the offered payout.

That makes roulette a useful example for understanding several ideas that appear throughout casino mathematics:

• probability;
• true odds versus payouts;
• house edge;
• independent events;
• short-term variance; and
• the gambler's fallacy.

Our Casino Game Maths Guide explores these concepts beyond roulette.

A Practical Way to Read a Roulette Table

Instead of asking which number is going to win, start with questions that can actually be answered.

1. Is the wheel European, American or another variant?
2. How many pockets are present?
3. How many outcomes does the wager cover?
4. What payout is offered?
5. What happens when zero or double zero appears?
6. Are any special rules applied to particular wagers?
7. How much money are you prepared to lose before stopping?

Those questions explain the game without pretending to predict the ball.

Probability Explains Roulette Better Than Patterns Do

Roulette naturally produces streaks, clusters and surprising sequences.

Some evenings may contain many red results. A particular number may appear twice within a few spins. Another number may remain absent for a long period.

None of that requires the wheel to be following a hidden cycle.

Random sequences are allowed to look uneven.

A pattern can describe what happened without predicting what happens next.

That is perhaps the most useful idea to take away from roulette.

For a deeper look at why random casino results can feel surprisingly non-random, read Why Casino Games Feel Less Random Than They Really Are.

For another type of game where player decisions genuinely affect mathematical expectation, continue with our Blackjack Guide.

You can also return to Casino Game Guides to explore the rest of Fresh Game Guide.

If you choose to play roulette or another gambling game, treat spending limits as real limits rather than a system for recovering previous losses. See our Responsible Play Guide for more.