Statistical Probabilities Behind the Game

James Gibson, Guest Author at

Understanding the Roulette Wheel

Before we have a look at the maths behind roulette, we’ll give you a summary of the roulette wheel. This is important because the wheel can vary; it can also affect your odds of winning.

There are two main versions of the roulette wheel: European and American. Both of them have 36 numbered pockets of which half are black and half are red.

The European wheel has 0 (zero) pocket coloured green. This means that in European versions of roulette, there are 37 numbered pockets in total.

American roulette games have a 00 (double zero) pocket that’s green in addition to the 0 pocket. Therefore, American versions of roulette have 38 pockets altogether.

What this means is that if you play European roulette, each numbered pocket has a 1/37 chance of winning. When you play an American version, the odds are slightly lower at 1/38.

It should come as no surprise that many players prefer European roulette because of its slightly better winning chances. However, you’ll still find plenty of American roulette games available to play.

Most roulette sites have both versions of the game available to play. The best ones have live versions of these games too. They also let you play non-live roulette games for free.

If you want to try the two different versions of roulette yourself, play free demos. With these, you can practise as much as you want without having to pay.

House Edge and RTP

House edge and RTP are two terms that you’ll come across a lot when gambling, especially online. They’re opposites and they’re both to do with payout percentages.

If a roulette game has a house edge of 4%, this means that the house (i.e. the casino) takes 4% of your money on average over long-term play.

Spend $100 on a roulette game whose house edge is 4% and, statistically speaking, you should lose 4% of this, i.e. $4. This would leave you with $96. The casino would keep the $4.

It’s important to point out that house edge is a long-term average. If you play just a few games of roulette, the casino could end up taking a lot more of your money.

On the other hand, the casino could end up owing you money if you’re lucky. The more you play, the closer your average loss per game gets to the house edge.

As for RTP, which stands for ‘return to player’, this is the exact opposite of house edge. It’s a measure of how much of your bet you should in theory keep over long-term play.

The house edge and RTP always add up to 100. Going back to the roulette game with a 4% house edge, its RTP would therefore be 96%.

If you’re serious about trying to make money from roulette, you should focus on games with a low house edge or high RTP. Online European roulette games typically have an RTP of 97.3% or a house edge of 2.7%.

As for American roulette games, the RTP is lower because of the extra 00 pocket. The RTP for a standard American roulette game is 94.74%, which makes its house edge 5.26%.

How House Edge and RTP Are Calculated

Before an online casino game is released, it undergoes a significant amount of testing. This involves simulating a large number of rounds, usually in the millions. The purpose of this is to determine the house edge and RTP.

For example, let’s say developers simulate a million rounds of a new roulette game. Each round has a $1 bet placed on a random number. That’s a total of $1 million spent.

If the game returned $970,000, the game’s house edge would be 3% because exactly 3% of the $1 million has been lost. Its RTP would, therefore, be 97%.

Online casino games typically have a lower house edge or higher RTP than their real-life counterparts. This is because physical casinos have more costs than online ones. Therefore, their games have to pay out less money.

If you want to make money from roulette, you’re more likely to do so with online versions of the game. Just remember that even if the house edge or RTP is favourable, you’re still likely to make a loss overall.


When you play a real-life version of roulette with physical props, gravity and luck determine which numbered pocket the ball lands in. The outcome is completely random. In online games, something else makes sure outcomes are random.

This something is an RNG or random number generator. It’s a piece of software that generates complex sequences of numbers. A game then uses these to determine outcomes such as the pocket the ball lands in.

With an RNG in place, each pocket on the wheel has an equal chance of being the winning one. Also, no outcome from past rounds can affect any future outcomes.

In other words, if a particular number has won a lot of times recently, this doesn’t mean the number will keep coming up. Likewise, it also doesn’t mean the number won’t come up again for a while.

Any patterns that you might see when looking at results are coincidental. All outcomes are random and independent of one another. Every time you play, each pocket has the same, equal chance of winning no matter what.

Some people believe that numbers can be ‘hot’ or ‘cold’. Hot numbers have won recently, cold numbers haven’t. They use this information to decide what numbered pockets to bet on.

However, the idea that numbers can be ‘hot’ or ‘cold’ is a misconception. Again, patterns are just random, and they don’t mean anything. Every spin’s result is unaffected by all previous results.

Calculating Odds

One of the best aspects of roulette is that it has multiple betting options. You can bet on a single number if you like or include multiple numbers in your bet.

We mentioned earlier that when you play European roulette, each number has a 1/37 chance of winning; and for American roulette, the odds are 1/38.

But what about if you’re betting on more than one number? When you play a typical game of roulette, you’ll have lots of betting options available.

These are displayed in the betting table. It arranges all the numbers on the wheel into three columns and a dozen rows with extra spaces for the 0 and 00 bets.

The bets in roulette can be grouped into two categories: inside and outside. Inside bets have large payouts with low chances of winning; betting on a single number counts as an inside bet.

As for outside bets, these involve a large selection of numbers. They’re more likely to win and so the payouts they give are lower.

The list below shows the main bets for roulette, starting with inside bets.

  • Straight/Single – covers just one number
  • Split – covers two numbers that are horizontally or vertically adjacent in the betting table
  • Street – covers a row of three numbers
  • Corner/Square – covers a square of four numbers
  • Six Line/Double Street – covers two adjacent rows
  • Trio/Basket – covers at least one 0 and two other numbers; for European roulette it’s 0-1-2 or 0-2-3; for American roulette it’s 0-1-2, 0-00-2 or 00-2-3
  • First Four – covers 0-1-2-3 in European roulette only
  • Top Row – covers 0-00-1-2-3 in American roulette only

The outside bets are as follows.

  • 1-18 – covers the numbers 1-18
  • 19-36 – covers the numbers 19-36
  • Red or Black – covers all red or black numbers
  • Odd or Even – covers all odd or even numbers
  • Dozen Bet – covers numbers 1-12, 13-24 or 25-36
  • Column Bet – covers one column of 12 numbers in the betting table
  • Snake Bet – covers the numbers 1, 5, 9, 12, 14, 16, 19, 23, 27, 30, 32, and 34

Calculating the odds for a roulette bet is simple. The odds depend on two factors: the type of roulette you’re playing and how many numbers the bet covers.

The table below shows the odds for roulette’s inside bets.

Bet Odds
Straight/Single 1/37 for European, 1/38 for American
Split 2/37 for European, 2/38 or 1/19 for American
Street 3/37 for European, 3/38 for American
Corner/Square 4/37 for European, 4/38 or 2/19 for American
Six Line/Double Street 6/37 for European, 6/38 or 3/19 for American
Trio/Basket 3/37 for European, 3/38 for American
First Four 4/37 for European
Top Row 5/38 for American

The next table is the same but for the outside bets.

Bet Odds
1-18 18/37 for European, 18/38 for American
19-36 18/37 for European, 18/38 for American
Red or Black 18/37 for European, 18/38 for American
Odd or Even 18/37 for European, 18/38 for American
Dozen Bet 12/37 for European, 12/38 or 6/19 for American
Column Bet 12/37 for European, 12/38 or 6/19 for American
Snake Bet 12/37 for European, 12/38 or 6/19 for American

It’s also worth looking at the payouts for roulette bets. Generally speaking, the fewer numbers a bet covers, the bigger its payout. The table below shows the payouts for inside bets.

Bet Odds
Straight/Single 35/1
Split 17/1
Street 11/1
Corner/Square 8/1
Six Line/Double Street 5/1
Trio/Basket 11/1
First Four 8/1
Top Row 6/1

And the same for outside bets.

Bet Odds
1-18 1/1
19-36 1/1
Red or Black 1/1
Odd or Even 1/1
Dozen Bet 2/1
Column Bet 2/1
Snake Bet 2/1

If you want to play it safe, stick with outside bets. If you want to take a risk and go for a large payout, place inside bets.

Roulette Strategies

Many people who play roulette for real money want to make a profit. Like other casino games, there’s no guarantee you’ll win. There are some strategies but none of them can definitely produce a win for you.

There’s one in particular that many players use for roulette and it’s called the Martingale strategy. The way it works is straightforward: double your bet after a loss.

If you do this, your next win will recoup all the money you’ve spent. Plus, you’ll end up with a profit equal to your initial bet.

The Martingale strategy isn’t just for roulette. It can be used for any sort of game where there are two main outcomes and they both have a near 50% chance of happening.

In roulette, the presence of the 0 (and 00) pocket reduces the odds of the winning ball being red or black to slightly below 50%. Even so, roulette is still suitable for the Martingale strategy.

There’s also the reverse Martingale strategy which has you halve your bet after a loss and double it after a win. The problem with this is that it relies on winning streaks to be successful.

Another roulette math strategy is the Labouchere system. It’s more complicated than the Martingale strategy but has a key difference: whereas Martingale recovers your losses with a single win, Labouchere does this with multiple wins.

It involves writing down a sequence of numbers that add up to determine your profit. Your bet is the first and last numbers in the sequences added together.

If you win, you cross off the first and last numbers. If you lose, you add the sum of the first and last numbers to the end of the sequence.

Whenever you have just one number, that’s how much you bet. If you win, you start the cycle again with a new sequence of numbers.

The Labouchere system can be complicated when you have lots of losses and your sequence of numbers grows bigger as a result.

We mentioned playing free versions of roulette earlier. This is ideal for anyone who wants to practise strategies and see how they work. With demo games, you can play as much as you like with no risk to your budget.


Now you should have a better understanding of the math behind roulette. The next time you play the game, think carefully about what bets you’ll place and how likely each one is to win.

With any casino game, knowing the math can help you both in the long run. When you’re aware of how the game works and what the odds are for different bets, you’ll make better betting decisions.

About the author

Name James Gibson
Job Freelance Writer Specialising in iGaming

James Gibson is a freelance content writer with passion for slot and game guides. He proclaims responsible gambling and aims at providing accurate and confirmed information.

Moderation is key. Gambling is best enjoyed when you stick to limits and you’re the one in control.

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