Although roulette is a game of chance you can give yourself a better chance of winning if you follow a strategy when it comes to what you bet on and how much. Newcomers will tend to concentrate on their lucky numbers and although that can work as part of a strategy – or just as a stroke of beginner’s luck – if you want to win more often.
Albert Einstein supposedly once said: “No one can win at roulette unless he steals money from the table while the croupier isn’t looking.”
Although I wouldn’t normally question Einstein, this statement isn’t true. In fact, you can use Einstein’s specialist subject, physics, to help you win. Or you can find a biased wheel that makes some numbers more likely to come up.
What Einstein actually meant was that there is no mathematical trick that can help you win at roulette. Each spin is an independent trial and, in the long run, the casino will win. This is different to a game such as Blackjack where the probabilities change as cards are dealt.
But some believe that it is possible to exploit the way the roulette wheel, and the betting cloth, is laid out to give themselves an advantage. The idea is that you can make bets on the layout in a way that you are guaranteed to win. But is this really possible?
Roulette wheel layout
Like a dartboard, the layout of a roulette wheel did not come about by accident. It was carefully planned and exhibits certain properties. In fact, there are two different layouts. An American wheel and a European wheel. The two layouts are shown below.
Notice that the American wheel has two zeroes. This is important as it doubles the advantage for the casino. On a European wheel you would expect to lose, in the long run, 2.7% of any money you bet with. On an American wheel you can expect to lose 5.26% (if you are interested in the mathematics of roulette, the video at the end will show you how these odds are calculated).
The numbers are arranged in a different order on each wheel but there are some similarities in the patterns. On both wheels, the red and black numbers alternate around the wheel, although if you removed the zeroes, the American wheel would have consecutive reds and blacks. The wheels are also structured so that the low numbers (1-18) and the high numbers (19-36) should alternate as much as possible.
On a European wheel, this is only violated where the 5 sits next to the 10 (both low numbers). On the American wheel, there are many examples where this rule is violated. It is for this reason that the American wheel is considered not as balanced as the European wheel. Both wheels also try to distribute odd and even numbers as evenly as possible. But again there are a number of violations of this rule on both wheels.
On the European wheel there are two other interesting symmetries. First, all the low red numbers and black high numbers are on one side of the zero, and the high red numbers and low black numbers are on the other side. Second, the sequence 29-7-28-12-35-3-26-0-32 contains no numbers between 13 and 24 (the second dozen). You can place a bet on the whole of the second dozen, with odds of 2-1.
So, can we beat the maths?
A simple search on Google will return many (possibly millions) of systems for playing (and supposedly winning) roulette. Some easy, some complicated, some well described, some not so.
A system should really be a combination of a playing strategy and a money management strategy. Perhaps the best known money management strategy is the Martingale system. This system is guaranteed to win money as long as you have enough of a bankroll to double your bet after every loss and you do not hit the table limit, which you will quickly do so. The Martingale system is probably the quickest way to bankruptcy known to man.
Whatever betting strategy, and money management strategy, you choose, they all suffer from the same fate. Assuming that each number on the wheel has the same probability of being selected – meaning the wheel is not biased – the maths means the casino will always win. The system may look good, and may work in the short term, but when one of the numbers comes up that you have not bet on you will lose and the casino will move towards its win expectation (2.7% or 5.26%).
Some systems involve betting on many numbers, perhaps 20. In this case, you will win quite often as you are covering more than half of the numbers. But when one of the numbers does not turn up (and it will almost half the time) you lose all of the 20 bets you have made. This will often wipe out any wins to date.
Any system, so far devised, can be analysed to show that there is a win expectation for the casino. The following video shows the maths.
You might as well place a single chip on the same number every time and hope that it appears more than it should during the short time that you are playing.
We can dress up the layout of the wheel, the layout of the betting cloth, our number selection and our money management system however we like, but the maths is always there, quietly working against us. You might as well just have fun, pick random numbers and trust to Lady Luck. Either that, or do as Einstein suggested and steal chips (not that we’d recommend it).
For the most part, calculating roulette payouts is just a matter of multiplication. Each bet pays out at certain odds, and that determines what you multiply the bet by to get the payout. Also, as with most table games, the payouts are done on an X to Y basis, as opposed to an X for Y basis.
This post wants to cover roulette payouts in some degree of detail, though, including how much each bet pays off.
More importantly, I want to explain how the croupier is able to calculate payouts for roulette so quickly. Guess what? They have a system for that.
Payout Odds in Gambling
When you’re gambling on something, you get paid off using odds. Some games offer even odds, which means that if you bet $100, you win $100 when you win.
Most games, though, have various payouts for various kinds of bets.
The top jackpot on a video poker machine pays off at 800 for 1.
And that’s an important distinction. There’s a big difference between a payoff of 800 for 1 and a payoff of 800 to 1.
With table games like roulette, the payoffs are in the form of 2 to 1, 3 to 1, 35 to 1, etc.
This means that if you win the bet, you get to keep the amount you bet, and you get the winnings along with it.
If you bet $100 on a single number at the roulette table and win, you get a payoff of $3,500. But you also get to keep your $100.
With gambling machines, payouts are made on a “for” basis instead of a “to” basis. This means your winnings are traded for what you risked.
If you bet $5 on a slot machine and win a $10 payout, you don’t get your $5 back on top of that.
This is an important distinction you should make. Most gamblers don’t stick just with roulette, so if you’re going to play other games — and you probably will — you should understand how that works.
Specific Payouts in the Game of Roulette
In roulette, you have a huge variety of bets you can place. You bet on a single number. Or you can bet on two numbers — if either of those numbers come up, you win. Or you can bet on three numbers, and if any of those three numbers come up, you win.
The more likely it is for you to win, the lower the payout is.
A bet on black wins almost half the time. The payoff for that bet is only 1 to 1, or even money.
A bet on a single number pays off at 35 to 1, which is a big payoff, but it also only wins 1 out of every 38 spins on average.
The Difference Between the Odds of Winning and the Payout Odds
The casino makes its money from the difference between the odds of winning and the payout odds.
You know how you can express the payout on a bet as odds?
35 to 1 is an example of how you’d express a payoff on the single number bet.
The odds of winning can also be expressed in the same way.
On a standard American roulette wheel, you have 37 ways to lose a single number bet and only one way to win.
This means the odds of winning are 37 to 1.
Since the odds of winning are lower than the payoff for the bet, the casino makes a profit in the long run.
Once out of every 38 spins, they’ll pay off a single number bet, but they’ll only pay off 35 to 1 on that bet. The rest of the money goes into the casino’s pocket.
The casino deals in long-term averages, especially when it comes to roulette.
Roulette Bets and Their Payoffs
Here’s a list of bets you can make at the roulette table and how much each of them pays off.
The Outside Bets
These are the bets on the outside of the betting surface, and they’re the bets that pay off the most often. As a result, you win less with these bets.
Here are the outside bets you can make:
- Red(or Black) – You can bet on the color of the number, and the payout is even money — 1 to 1
- Even (or Odd) – You can bet that the number will be even or odd, and the payout is again even money — 1 to 1
- Low (or High) – You can bet that the number will be 1-18 (low) or 19-36 (high). The payout is even money on this one, too
- Columns – The numbers on the betting surface are organized into three columns. You can bet that the ball will land on one of the numbers in that column. The payoff, if you guess right, is 2 to 1
- Dozens – The numbers can be divided into 1st third (1-12), 2nd third (13-24), and 3rd third (25-36). If you guess right, you get a 2 to 1 payout
On all these outside bets, 0 and 00 count as losses. Those numbers are green, and they’re not considered even or odd, high or low.
The Inside Bets
These are the bets on the inside of the betting surface. They pay out better but have a bigger chance of losing.
Here are the inside bets you can make:
- Straight Up – This is a bet on a single number and pays off at 35 to 1
- Split – This is a bet on two numbers that are next to each other. It pays off at 17 to 1
- Street – This is a bet on three numbers, and it pays off at 11 to 1
- Corners – This is a bet on four numbers, and it pays off at 8 to 1
- The 5-Number Bet – You can only bet on 0, 00, 1, 2, and 3 if you want to bet on five numbers, and it pays off at 6 to 1. This is the only bet on the roulette table with a different house edge from the other bets — 7.89% (the other bets have a house edge of 5.26%)
- Line – This is a bet on six numbers and pays off at 5 to 1
All these bets would be a break-even proposition in the long run IF the wheel didn’t have a green 0 and a green 00.
How the Croupier Makes the Payouts So Quickly
The first thing the croupier does after the decision is to clear all the losing bets off the roulette table. Since he’s intimately familiar with the layout of the betting surface, this doesn’t take long at all.
Also, all the players at the roulette table have chips that are specifically colored so that they have the same color. You can’t use the roulette chips at the other table. This enables the croupier to tell your bet from someone else’s. It’s the color of the chips.
To calculate the payouts, you just multiply the bet by the payout odds.
If someone bet two chips on a single number and it won, you’d multiply 2 by 35 and get 70. That’s how many chips you’d give the player in winnings.
He doesn’t really have a magical system, either. He knows the payouts for the various bets, and he’s able to do the multiplication in his head. It’s easy multiplication, but even if it weren’t, he’d eventually just be able to memorize the correct payout relative to the number of chips bet.
Also, he doesn’t really think of the chips as money. They’re just betting units.
Can Any of This Information Help Me Win at Roulette?
Naw.
Roulette’s a negative expectation game.
How To Win At Roulette Every Time
You might get lucky in the short run, but if you play long enough, the math behind the payouts will eventually reduce your bankroll to 0.
Conclusion
And that’s how to calculate roulette payouts. You just memorize which bets are possible and how much they pay off. Once you know that, calculating the payouts is just a matter of multiplication.
Croupiers are able to do it quickly because they do it all day every day.
How Much Money Do You Win On Roulette
I’m able to make change in my head because I worked for years on cash registers that didn’t calculate change. I know how to subtract from 100 without any effort at all.
Calculating roulette payouts is a similar skill.