Since the results in roulette games are entirely random, there are only two possible outcomes for the players — they either win or lose. Therefore, the probability of winning with a given bet type is calculated by dividing the number of ways to win by the total number of all possible outcomes. Another way to put it would be to say the probability of winning is equal to the number of ways to win, divided by the total of the ways to win and the ways to lose.
Let us first demonstrate how it works by using a coin toss as an example. As you know, when you are flipping a coin, there are only two possible outcomes as the coin will land either on heads, or on tails. The chances of it landing on each of the two sides are practically equal. Now, let us apply the formula from above to calculate the likelihood of collecting a payout with a Split bet in the game of roulette. Since with Split bets players cover only two numbers that are adjacent on the layout, there are only two ways to win out of 37 possible outcomes, i.
Another way to put it would be to say there are two ways to win and 35 ways to lose with your Split bet. In contrast, the likelihood of winning with the very same bet in American roulette drops down to 5. The greater the number of outcomes you cover with a single bet, the higher the probability of winning will be. For instance, let us assume you are interested in experimenting with one of the more exotic roulette bets , like Voisin du Zero, which covers a sequence of seventeen random numbers on the single-zero wheel.
The probability of hitting one of these winning numbers is equal to As you can probably see for yourself, figuring out the probability of winning with different roulette bet types does not require profound mathematical knowledge.
The rules that apply at casino tables are designed in such a way so as to tilt the advantage in favour of the house. Because of this, it is of extreme importance for roulette players to learn how to calculate the odds of winning with each type of bet. Unlike probability, odds are never expressed in terms of percentages but are typically presented as pairs of numbers. The odds for a random event, like a die toss or a roulette spin, denote the likelihood of this event taking place.
To calculate the odds for winning with a given roulette bet, you need to figure out what its probability is. If we use the coin flip example from above, the calculation will go as follows: 0. The odds in this case are even. However, there is an easier way to figure out the odds for winning with roulette bets and it is to simply divide the number of ways to win by the number of ways to lose. As you can see, probability differs from odds in that it is a likelihood of 1 out of 37 outcomes.
Some roulette players tend to confuse the odds for winning with the odds against winning because the ratio is written in reverse on many occasions, like so 36 to 1. This is not exactly the same thing because the odds against a given event reflect the probability of the said event not happening. These reversed odds are normally used by gambling establishments to list the payouts of the winning bets.
The smaller the likelihood of winning with a given roulette bet, the greater the return offered by the house. This is so because when it comes to the majority of casino games, roulette included, the players are practically competing against the house. Therefore, the house is betting against its patrons so the odds paid are the odds against the player winning, hence the inverted ratio.
You will be able to read more detailed information regarding the house odds in the section to follow. As far as casino games are concerned, there is always a disparity between the mathematical probability of winning with your bets and the ratio these bets are paid at. It is precisely this disparity between the true odds of winning and the casino odds that gives the house advantage over players in the long run.
For every game the casino offers, the payout odds on bets are established in such a way so that the casino can generate profits on each wager you make. This house advantage is expressed in percentages which reflect the overall return the casino can expect over time, or in other words, the average percentage players will inevitably lose in the long term. Being a commercial business, the casino needs its edge to cover the costs associated with hosting the games.
In some games of chance like craps, there are wild fluctuations in the house edge for different bet types. This is not the case in roulette where the edge remains constant, with a single exception which is the Five-Number bet. The latter can be made in double-zero games only and gives the house an advantage of 7. To calculate the house edge in roulette, we multiply the difference between the true odds against winning and the casino odds by the probability of winning.
On a double-zero wheel, the odds against winning with a Straight Up bet are 37 to 1 but the house pays only 35 to 1 which results in a house edge of 5. As you can see, the difference between the odds against winning and the payout in American roulette is equal to two units.
Using the formula from above, we can calculate the house edge like so:. The house edge in European roulette is significantly smaller because there is only one zero pocket on the wheel so the calculation will run as follows:.
Please bear in mind that you can expect such losses only over extended periods of time which involve tens of thousands of spins. Everything is possible in the short term, so players can certainly be ahead if they bet on roulette recreationally for a day or two.
Columns — The numbers on the layout are organized into three columns of twelve numbers each. This bet pays out 2 to 1 when you win. Dozens — There are 36 numbers on the table, so you can bet on the first dozen , the second dozen , or the third dozen This bet also pays out 2 to 1. You can also bet on specific numbers and sets of numbers on the inside of the layout.
These bets win less often, but they pay out more when you do win. The house edge on the inside bets is the same as the house edge on the outside bets. Split bet — This is a bet on any two adjacent numbers. You place the chip on the line between the two numbers in order to make this wager.
This bet pays out at 17 to 1. Street bet — This bet covers three numbers. You place your bet on the line outside of the three numbers in the row where you want to win. This bet pays out at 11 to 1. Corner bet — Some people call this a square bet or a quarter bet. A win on this type of bet pays out at 8 to 1. The problem is that it has a higher house edge, making it the worst bet on the table. This bet is on the numbers 0, 00, 1, 2, and 3, and you place the chip on the outside corner line between the 1 and the 0.
This bet pays out 6 to 1, but only masochists place this bet. Six-number bet — Some people call this a line bet. It covers two adjoining rows of numbers. It pays out at 5 to 1. These payouts all have one thing in common—they pay out less than the true odds of hitting a win. Your odds of winning are always less than the payout amounts. For example, the odds of winning a straight-up bet are 37 to 1.
There are 37 numbers on the wheel that lose, and 1 bet on the wheel that will win. But the bet only pays out 35 to 1, not 37 to 1, so the house wins more often than it loses. I could list all of them, but you get the idea by now.
This bet pays out at 17 to 1. Street bet — This bet covers three numbers. You place your bet on the line outside of the three numbers in the row where you want to win. This bet pays out at 11 to 1. Corner bet — Some people call this a square bet or a quarter bet. A win on this type of bet pays out at 8 to 1. The problem is that it has a higher house edge, making it the worst bet on the table.
This bet is on the numbers 0, 00, 1, 2, and 3, and you place the chip on the outside corner line between the 1 and the 0. This bet pays out 6 to 1, but only masochists place this bet. Six-number bet — Some people call this a line bet. It covers two adjoining rows of numbers. It pays out at 5 to 1. These payouts all have one thing in common—they pay out less than the true odds of hitting a win. Your odds of winning are always less than the payout amounts. For example, the odds of winning a straight-up bet are 37 to 1.
There are 37 numbers on the wheel that lose, and 1 bet on the wheel that will win. But the bet only pays out 35 to 1, not 37 to 1, so the house wins more often than it loses. I could list all of them, but you get the idea by now. The casino has an unassailable mathematical advantage on every bet. No betting system or strategy can overcome this advantage.
Of course, in the short run, anything can and often will happen. The mathematically true results only come around the closer you get to an infinite number of spins. So the best way to approach roulette is as a lark. You can relax and socialize while you play. And if you do win, walk away and smile, because you beat the odds. Understanding Roulette Payouts.
Play Now. Zero game, also known as zero spiel Spiel is German for game or play , is the name for the numbers closest to zero. All numbers in the zero game are included in the voisins, but are placed differently. The numbers bet on are The bet consists of four chips or multiples thereof. Three chips are bet on splits and one chip straight-up: one chip on split, one on split, one on split and one straight-up on number This type of bet is popular in Germany and many European casinos.
It is also offered as a 5-chip bet in many Eastern European casinos. As a 5-chip bet, it is known as "zero spiel naca" and includes, in addition to the chips placed as noted above, a straight-up on number This is the name for the 12 numbers that lie on the opposite side of the wheel between 27 and 33, including 27 and 33 themselves. On a single-zero wheel, the series is Very popular in British casinos, tiers bets outnumber voisins and orphelins bets by a massive margin.
Six chips or multiples thereof are bet. One chip is placed on each of the following splits: , , , , , and The tiers bet is also called the "small series" and in some casinos most notably in South Africa "series ". A variant known as "tiers " has an additional chip placed straight up on 5, 8, 10, and 11m and so is a piece bet. In some places the variant is called "gioco Ferrari" with a straight up on 8, 11, 23 and 30, the bet is marked with a red G on the racetrack.
These numbers make up the two slices of the wheel outside the tiers and voisins. They contain a total of 8 numbers, comprising and Five chips or multiples thereof are bet on four splits and a straight-up: one chip is placed straight-up on 1 and one chip on each of the splits: , , , and A number may be backed along with the two numbers on the either side of it in a 5-chip bet.
For example, "0 and the neighbors" is a 5-chip bet with one piece straight-up on 3, 26, 0, 32, and Neighbors bets are often put on in combinations, for example "1, 9, 14, and the neighbors" is a chip bet covering 18, 22, 33, 16 with one chip, 9, 31, 20, 1 with two chips and 14 with three chips.
Any of the above bets may be combined, e. The " Final 4, for example, is a 4-chip bet and consists of one chip placed on each of the numbers ending in 4, that is 4, 14, 24, and Final 7 is a 3-chip bet, one chip each on 7, 17, and Final bets from final 0 zero to final 6 cost four chips. Final bets 7, 8 and 9 cost three chips. Some casinos also offer split-final bets, for example final would be a 4-chip bet, one chip each on the splits , , , and one on A complete bet places all of the inside bets on a certain number.
Full complete bets are most often bet by high rollers as maximum bets. The maximum amount allowed to be wagered on a single bet in European roulette is based on a progressive betting model. For instance, if a patron wished to place a full complete bet on 17, the player would call "17 to the maximum".
To manually place the same wager, the player would need to bet:. The player calls his bet to the croupier most often after the ball has been spun and places enough chips to cover the bet on the table within reach of the croupier. The croupier will immediately announce the bet repeat what the player has just said , ensure that the correct monetary amount has been given while simultaneously placing a matching marker on the number on the table and the amount wagered.
The player's wagered 40 chips, as with all winning bets in roulette, are still his property and in the absence of a request to the contrary are left up to possibly win again on the next spin. Based on the location of the numbers on the layout, the number of chips required to "complete" a number can be determined. Most typically Mayfair casinos in London and other top-class European casinos with these maximum or full complete bets, nothing except the aforementioned maximum button is ever placed on the layout even in the case of a win.
Experienced gaming staff, and the type of customers playing such bets, are fully aware of the payouts and so the croupier simply makes up the correct payout, announces its value to the table inspector floor person in the U. Also typically at this level of play house rules allowing the experienced croupier caters to the needs of the customer and will most often add the customer's winning bet to the payout, as the type of player playing these bets very rarely bets the same number two spins in succession.
There are also several methods to determine the payout when a number adjacent to a chosen number is the winner, for example, player bets 40 chips on "23 to the maximum" and number 26 is the winning number. The most notable method is known as the "station" system or method.
When paying in stations, the dealer counts the number of ways or stations that the winning number hits the complete bet. In the example above, 26 hits 4 stations - 2 different corners, 1 split and 1 six-line. If calculated as stations, they would just multiply 4 by 36, making with the players bet down. Over the years, many people have tried to beat the casino, and turn roulette—a game designed to turn a profit for the house—into one on which the player expects to win.
Most of the time this comes down to the use of betting systems, strategies which say that the house edge can be beaten by simply employing a special pattern of bets, often relying on the " Gambler's fallacy ", the idea that past results are any guide to the future for example, if a roulette wheel has come up 10 times in a row on red, that red on the next spin is any more or less likely than if the last spin was black.
All betting systems that rely on patterns, when employed on casino edge games will result, on average, in the player losing money. Certain systems, such as the Martingale, described below, are extremely risky, because the worst-case scenario which is mathematically certain to happen, at some point may see the player chasing losses with ever-bigger bets until he runs out of money. The American mathematician Patrick Billingsley said  that no betting system can convert a subfair game into a profitable enterprise.
At least in the s, some professional gamblers were able to consistently gain an edge in roulette by seeking out rigged wheels not difficult to find at that time and betting opposite the largest bets. Whereas betting systems are essentially an attempt to beat the fact that a geometric series with initial value of 0.
These schemes work by determining that the ball is more likely to fall at certain numbers. Edward O. Thorp the developer of card counting and an early hedge-fund pioneer and Claude Shannon a mathematician and electronic engineer best known for his contributions to information theory built the first wearable computer to predict the landing of the ball in This system worked by timing the ball and wheel, and using the information obtained to calculate the most likely octant where the ball would fall.
Ironically, this technique works best with an unbiased wheel though it could still be countered quite easily by simply closing the table for betting before beginning the spin. In , several casinos in Britain began to lose large sums of money at their roulette tables to teams of gamblers from the USA. Upon investigation by the police, it was discovered they were using a legal system of biased wheel-section betting.
As a result of this, the British roulette wheel manufacturer John Huxley manufactured a roulette wheel to counteract the problem. The new wheel, designed by George Melas, was called "low profile" because the pockets had been drastically reduced in depth, and various other design modifications caused the ball to descend in a gradual approach to the pocket area.
Thomas Bass , in his book The Eudaemonic Pie published as The Newtonian Casino in Britain , has claimed to be able to predict wheel performance in real time. The book describes the exploits of a group of University of California Santa Cruz students, who called themselves the Eudaemons , who in the late s used computers in their shoes to win at roulette. This is an updated and improved version of Edward O. Thorp 's approach, where Newtonian Laws of Motion are applied to track the roulette ball's deceleration; hence the British title.
In the early s, Gonzalo Garcia-Pelayo believed that casino roulette wheels were not perfectly random , and that by recording the results and analysing them with a computer, he could gain an edge on the house by predicting that certain numbers were more likely to occur next than the 1-in odds offered by the house suggested. This he did at the Casino de Madrid in Madrid , Spain , winning , euros in a single day, and one million euros in total.
Legal action against him by the casino was unsuccessful, it being ruled that the casino should fix its wheel. To defend against exploits like these, many casinos use tracking software, use wheels with new designs, rotate wheel heads, and randomly rotate pocket rings. At the Ritz London casino in March , two Serbs and a Hungarian used a laser scanner hidden inside a mobile phone linked to a computer to predict the sector of the wheel where the ball was most likely to drop.
The numerous even-money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a martingale betting strategy , wherein the gambler doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet.
The problem with this strategy is that, remembering that past results do not affect the future, it is possible for the player to lose so many times in a row, that the player, doubling and redoubling his bets, either runs out of money or hits the table limit. A large financial loss is certain in the long term if the player continued to employ this strategy. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence.
Regardless of the specific progression, no such strategy can statistically overcome the casino's advantage, since the expected value of each allowed bet is negative. The Reverse Martingale system, also known as the Paroli system, follows the idea of the martingale betting strategy , but reversed. Instead of doubling a bet after a loss the gambler doubles the bet after every win. The system creates a false feeling of eliminating the risk of betting more when losing, but, in reality, it has the same problem as the martingale strategy.
By doubling bets after every win, one keeps betting everything he has won until he either stops playing, or loses it all. The Labouchere System involves using a series of numbers in a line to determine the bet amount, following a win or a loss. Typically, the player adds the numbers at the front and end of the line to determine the size of the next bet. When he wins, he crosses out numbers and continues working on the smaller line. If he loses, then he adds his previous bet to the end of the line and continues to work on the longer line.
This is a much more flexible progression betting system and there is much room for the player to design his initial line to his own playing preference. This occurs because as the player loses, the average bet size in the line increases. The system, also called montant et demontant from French, meaning upwards and downwards , is often called a pyramid system. It is based on a mathematical equilibrium theory devised by a French mathematician of the same name.
Like the martingale, this system is mainly applied to the even-money outside bets, and is favored by players who want to keep the amount of their bets and losses to a minimum. The betting progression is very simple: After each loss, you add one unit to the next bet, and after each win, one unit is deducted from the next bet.
Starting with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. If this is followed by a win, the next bet would be 1 units. This betting system relies on the gambler's fallacy—that the player is more likely to lose following a win, and more likely to win following a loss. There are numerous other betting systems that rely on this fallacy, or that attempt to follow 'streaks' looking for patterns in randomness , varying bet size accordingly.
Many betting systems are sold online and purport to enable the player to 'beat' the odds. From Wikipedia, the free encyclopedia. This article is about the casino game. For other uses, see Roulette disambiguation. Game of chance. Massachusetts Institute of Technology. Retrieved 20 October London: Academic. Retrieved 8 February Scarne's new complete guide to gambling Fully rev. Retrieved 22 September Advantage Play for the Casino Executive.
Science The Guardian , guardian. New York: Palgrave Macmillan. The New York Times.
Your preference should be to play on exclusively Australian-based online casinos, such as Planet 7 Oz. Not only is it an online casino focused on Australian players, they also invest heavily in the servers to host their games so that they are reliable and consistent. It should also be pointed out that Planet 7 Oz are top notch when it comes to rewarding players with massive bonus bets. The thing about Roulette is that you can make a lot of money by betting on one number, or you can win a small amount by betting on many numbers.
With the more numbers you bet, the more chances you have at winning, but you also have a higher risk of losing altogether. Many rookie players lose their cash by making simple mistakes such as selecting a specific number, without understanding the easier methods to win like hedging a bet on multiple numbers, or by playing the outside of the felt.
Before we dig into the felt and expose some details on the possible Roulette bets you can make, it is a good idea to know what all respective payouts are:. As you can see, there are indeed some great rewards to be had for making a more definitive number selection for your bet.
Remember as we touched base on the green zero and double zero inclusion to Roulette? We can thank the Martingale Strategy as being the main reason for that inclusion. Provided your pockets are deep enough, today is the day you stop laughing, because the Martingale strategy is based on probability theory.
This strategy was introduced by a French mathematician called Paul Pierre Levy. It relies on the theory of mean reversion, so you will need a significant money supply to maintain positive results. When you see a failing bet, you double down on your previous bet and continue until you see a winning bet again. What this means is that each flip of the coin prior, has no impact on the next flip. So as long as you maintain the same outcome I.
This strategy is based on the premise that you will only need one bet to turn your winnings around. Roulette is unlike any other casino game. This sounds too good to be true, but the downside is that the payout ratio is much lower. Not as attractive in terms of big paydays but this bet is undoubtedly one of the safest and best roulette bets you can make. When you start betting more substantial amounts, the reward begins to become more attractive in terms of gains but does bring higher risk.
Betting on columns is considered the second-best Roulette bet in the game. Playing the outside, you can double your money while bringing the possible numbers down to almost a one-third chance. What you need to remember when it comes to columns, is that each column does not contain consecutive numbers.
For example, column one or the first column includes the numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, 28 and Each column also has a differing number of red and black numbers. In the common Australian Roulette games which is based on the European standard , the zero is not included and is represented as green — to claw back some house edge!
If you have studied the felt, you would have noticed two critical facts about the setup of the board. The third column on the board is made up of eight red numbers and four black numbers. Try guess what the second column might include? Yep, you guessed it — the second column is the opposite, consisting of eight black numbers and four red numbers.
What this means is that our third best roulette bet gives you a chance at attempting to hedge your bets by being savvy. Consider the third column; it has more red numbers than the other columns — therefore covering a large portion of the red section of the wheel. At the same time, you are hedging a loss by betting on a black outcome, which also gives you just under half of the wheel.
So, when a red number shows up on the third column you win double your bet — but lose your black bet which is the same amount — so you are breaking even. This is the same when a number on black is selected; you win your bet on black but lose your column bet.
The beauty in this strategy is when a black number on the third column is selected — because you are winning both of your bets. This is where the strategy sets you ahead and gives you some decent payouts. With this method, you are hedging your bet by offsetting most of the risks and giving yourself a steady chance at scoring double wager payouts. In a game of roulette the house should keep at least 2.
The casino has no need to cheat the players. One of the other differences between European roulette and both American and Sands roulette is that the European roulette table has an additional betting area. This secondary betting area is used to place specially designed bets.
They are more complicated than the normal bets made in American and Sands roulette. The green slots on the wheel make it impossible for anyone, anywhere, to ever design a betting system that is guaranteed to win. If you really want to guarantee yourself a win every time, then put a chip on each of the 2-to-1 outside bets and on each of the green number bets. You may have heard about a system called the Martingale System. Experienced roulette players just turn their heads and roll their eyes when someone mentions the Martingale System.
The only way you can make money with the Martingale System is to write a book about it and get people to buy your book. You start out betting the minimum. If you lose, you double your bet. If you win on your doubled bet, you go back to betting the table minimum.
If you lose again, you double the size of your bet again. Every betting system in every form of gambling tries to leverage probability theory. The Martingale System and other roulette betting strategies also rely on probability estimates. The secret to not going broke when you gamble is to set reasonable expectations and maintain your self-discipline. You should never drink or take drugs when you gamble.
They lower your inhibitions and impair your judgment. Probability theory came out of statistics. It tries to give us rules by which to guess what happens next in any situation. The guesses are seldom accurate predictions. Gamblers love probability theory because they think it helps them pick the best betting strategies.
The more bets you place, the less likely it becomes to double your money. The closer you are to the short term, the more likely you are to get better than expected results. The dealer spins the wheel and releases a ball that whirls around the outside of the wheel and finally settles in a slot. With only 37 slots on a European roulette wheel you have a 1-in probability of the ball landing on a specific slot.
Nor can it predict whether the ball will land on red, black, or green any number of times over the next spins. Nonetheless, a lot of gambling guides tell you that you have the best chances of winning if you do this because of such-and-such probabilities. In the real world the Probability Fairy is always on vacation. The ball could land on red over the next 20 spins. Or it could land on black or green or some random mix of color combinations.
You have no way of knowing how many of the next [X] spins will turn out a certain way. Talking about probabilities in this way is just dishonest. What you can do is look at the wheel and ask yourself how much it costs to bet on the largest possible set of numbers.
The idea here is to get as much coverage as you can without losing money too fast. So the only way to win in roulette—and this is completely random, never guaranteed—is to bet on less than all the numbers on the wheel.