Understanding Roulettes Odds and Probability

Understanding Roulette’s Odds and Probability

Understanding Roulettes Odds and Probability

Blaise Pascal, a French polymath who lived in the 17th century, is credited with developing the game of roulette after failing to build a mechanism with perpetual motion.

This is appropriate given that the mathematics that underlies the game possesses a certain elegance that a wide range of individuals can appreciate.

Starting with the inconsequential, some people have found it intriguing that the sum of the numbers of a roulette wheel equals 666, which is purportedly the “number of the beast.”

Whether or if there are connections to Satan, there is a more interesting beauty to be found in the interplay between the probabilities and odds of the different bets.

As is the case with a great number of games, both those played in casinos and those played in other settings, what appears to be such a straightforward game at first appearance is, in reality, a brilliantly designed game that strikes the ideal balance between the player’s chances and those of the house.

Not Due to Talent, NoR to Luck, But Due to Mathematics

Let’s say we’re dealing with a typical European roulette wheel with just one zero. We are sorry to have to break this to anyone who believes they have a roulette strategy, system, or betting plan that “works,” but in this instance, what you do as a player does not make the slightest difference to the long-term projected outcome. In the short run, things are influenced by luck, which is why players can and do win, sometimes tremendous amounts of money. But nothing indeed beats the cold, hard math of the game when it comes down to it in the end.

The house edge, also known as the casino’s advantage over the player and which is the direct outcome of the intricate and impeccably developed mathematics that underpin roulette, will not shift in any way. No matter what we gamblers decide to do. You can cover all numbers except for your ex-date girlfriend’s of birth, bet ten chips on eight numbers every third spin following consecutive reds, and obscure all numerals except for your ex-date girlfriend’s of birth, or you can bet 10 pounds on black each time. The final result you can anticipate in the long term will not be affected by your choice.

This is due to the fact that the odds shift in accordance with the probabilities of each and every event that can be wagered on while playing roulette. This occurs for each conceivable wager. What exactly do we imply by saying this? If you place your bet on a single number, you put up half as much money, stand to win half as much money, and have half as good of a chance of winning as a player who places the same amount of money on two different numbers. Put another way, the reward for the less likely result is boosted in inverse proportion to its chances of winning. If you bet on even numbers, you have a significantly better chance of winning than on zero.

Probabilities, odds, and the advantage held by the house

The following table details the most important aspects of the primary wagers that can be placed when playing single zero roulette. As can be seen, the advantage the house enjoys over players is unaffected by the type of wager set. This indicates that a player who bets on red 10,000 times with a £10 wager each time can anticipate losing the same amount of money as a person who bets on lucky number seven 10,000 times with a £10 wager each time.

In either case, the player should anticipate losing a maximum of 2,700 pounds on average. Even though it might seem like a lot, that is only 2.7% of the large stake of £100,000 (the house edge on all bets in single-zero roulette).

Straight up – any single number (including zero35/1One in 372.70%
Split – any two adjoining numbers17/1One in 18.52.70%
Street – any three horizontal numbers11/1One in 12.332.70%
Corner – any four adjoining numbers (including 0,1,2,3)8/1One in 9.252.70%
Six line – six numbers from horizontal rows (two)5/1One in 6.172.70%
Any 12 numbers (various groupings, including 1-12 and 13-24)2/1
One in 3.08
Any 18 numbers (various groupings including red, odd or low numbers)Even moneyOne in 2.062.70%

Furthermore, the operation of any combination of the bets described above is the same. Just betting on a color or betting on your 18 favorite individual numbers, both of which pay out the same amount and have the same chance of success, are equivalent to betting on three distinct six-line wagers. In other words, the risk-to-reward ratio is the same for every stake, and there is no bet in roulette that is superior to or inferior to any additional bet.


The variance is one aspect that does change. The term “variance” refers to the degree to which the average of your short-term results deviates from the predicted value of the long-term average. Picture a pair of twins intending to play a game of roulette in a casino. Steady Eddie places a £10 wager on low numbers (an even money bet with an expected success rate of slightly less than one in two) for 37 consecutive spins. Instead, Risky Rafe decides to wager £10 on the number 13 for each of the 37 spins. There is a one in 37 chance that this wager will result in a victory; if it does, the payout will be 35 to 1 odds.

Even if the twins played an unlimited number of spins, they would still have the same results, which would be a little loss equal to 2.7% of their bankroll. Their outcomes may diverge significantly after 37 spins. Steady Eddie will almost definitely come out on top after a couple of spins. Believe it or not, the longest-ever consecutive run of one color (which has the same probability as supporting either high numbers or low numbers) is believed to have been 32, which means that even with the worst luck imaginable, we may anticipate Eddie not lose all of his money in the bets he places.

Given that the low numbers (1-18 inclusive) have an 18 in 37 probability of winning, you would anticipate him to win 18 times on average, given this information. It is doubtful that there will be a significant divergence from 18, given that he has an almost 50 percent probability of winning with each spin. In addition, the payoff for each win is even money, which means that his overall results will remain mostly the same in terms of net winnings or losses.

That means that, for instance, if the twins visit the casino 1,000 times in their lifetime and use the same technique, the vast majority of the time, Eddie would probably win or lose less than fifty pounds, and he will probably lose more often than he wins. It is anticipated that both twins will end up approximately 2.7% in the red over the course of their 1,000 visits to Risky Rafe, which would cover a total of 37,000 spins. On the other hand, Rafe’s path leading up to that time will be rather different.

When you bet on a single number, the payoff is much more than usual, but your odds of winning are significantly lower. This might result in significant variation. Rafe should have a chance to win once out of every visit, but he should also expect to lose little each time, much like his brother. Their monetary results ought to be similar, with 18 £10 wins out of 37 at evens yielding a return of £360 and a loss of £10; this is precisely the same as one wins out of 37 at 35/1.

On the other hand, Rafe can lose every one of his turns with only a moderate amount of unfavorable luck. Something like this may occur multiple times throughout the thousand visits that we have been discussing. On these visits, Rafe blows all £370, and Eddie is responsible for paying back the cab ride. As we have shown, this is an outcome that Eddie himself is extremely unlikely to ever occur at any point in his life.

On the other hand, Eddie’s chances of winning over twenty or thirty pounds on a visit are extremely low. In all of those 1,000 visits, he has an extremely low chance of winning more than £60 or £70, and he will never score a net win of £250 or more. That would need him to win 31 out of 37 spins, which is improbable given that he has approximately a 48% chance of winning each time.

On the other hand, for Rafe to land a significant win, all that is required is for him to win twice rather than the typical one. An outcome like that would result in a net success of £350 for the night, and over the course of their consistent visits, Rafe is almost guaranteed to have nights like that. Sometimes he’ll even have fortuitous sessions that bring him three or even four wins in a row. Both would result in financial gains that his sibling could never hope to achieve (even if he won all 37 spins). Rafe is responsible for the champagne and the taxi on these nights.

A Guide to Improving Your Chances When Playing Roulette

You are not able to alter the odds or the house advantage. Still, you may modify the variation of your outcomes by choosing whether you want a high number of tiny wins and losses or a higher number of regular casualties with the possibility of a big victory occasionally occurring. Or can you?

Regarding roulette, there is one thing you can do to enhance your odds. While it is not a revolutionary strategy, it is incredibly straightforward and has a hundred percent success rate. You can make the proper choice. To begin, and this is the most important step, you should only play American roulette or any other game variation containing one zero. The zero or zeroes provide the casino an advantage over the player when playing certain games. The house edge increases from 2.70% to 5.26% when you double the number of zeroes, which indicates that you will lose almost twice as much money over the course of playing the game.

There is an additional number on the wheel where you will suffer a loss, but the odds at which your wagers are paid out remain the same. Keep an eye out for the French roulette game, which might also be called the La Partage roulette game. The regulations of La Partage and En Prison are discussed in greater detail in other sections of our website; nevertheless, in a nutshell, both roulette variants provide you a second chance to win should the ball land at zero, so reducing the advantage the house has over the player to less than 1.5%.