Calculating Optimal Bet Sizing, Expectations, and Odds in Live Roulette

When entering into a game of roulette, having some knowledge of the internal hardwiring helps a lot. With some money in your hand, if you know details of the workings, then you can calculate the odds of the roulette, the expected player returns, and that is helpful. Using the above details, you can then calculate and manage your bankroll through optimizing the bet size.

roulette odds

Understanding the probability of winning each bet can help you in making informed choices, particularly with a live roulette game than with others. That is, various other types of gambling games also exist in any single casino. This is because various types of roulette games have different types of odds, and these are relatively high risk compared to games like slot machines.

For example, the American version of roulette has a higher house edge than the European version and the French roulette.

Calculating Probabilities in Live Roulette

The way to calculate the probability of winning in a live roulette can be life-saving. Despite the style of roulette you are playing, the probabilities remain the same. This is because the spaces are all of the same sizes and the ball is likely to land on one space or the other. The exact details of the probability calculation can be done as below.

  • If there are 37 spaces, the probability of a ball landing on any one of them is 1/37;
  • If there are 18 red spaces, it means the probability of landing on red is 18/36;
  • If there are 20 black or green spaces, the probability is calculated to be 20/37;

Now, using these calculated values and a chart of bet type and payout odds you can place your bets and improve your chances of winning. Below are some of the values.

  • With Red/Black Bet Type and Payout Odds 1/1, European Odds are 48.6%, French is 48.6%, and American is 47.3%;
  • With a Dozen Bets and Payout Odds 2/1, European Odds are 32.4%, French is 32.4%, and American is 31.5%;

The calculations like above can be done for Column Bets, Double Street, Odd/Even and all other types of bets. These different types of bets in a live roulette can change the probability and the chance of winning. Next, we introduce some mathematical terms and jargon that are pretty useful in understanding how these roulettes or any such game of probability works.

You might also want to read about the Fibonacci strategy of betting.

What is Random Variable and Expected Value in Roulette?

In a game of probability, anything that has a random outcome is known as a random variable. In this case, the net winnings of roulette when making a bet on a game can be considered as a discrete random variable. The word “discrete” means that it can only have numbers we use in counting. For simplification, a wager of $1 on red balls and the ball lands on red, will give you $1 on your wager. So, the net win is $1 only. But, when you lose, the net win is -$1.

The expected value is a better representation of how good a game is. It is the average of the net winnings over a number of bets. For example, the net win you would have if you continued to place the bet on the same red balls over the next 100 bets, the net win is the expected value of that particular roulette. One thing to remember is that the house edge always gives the advantage to the casino in the long run.

Roulette Payouts

Despite the vast majority of wager options on roulette the majority of the bets are straightforward. You must make sure the chips are placed in the right spots on the table. In the case of a live casino, you can miss out on a really big payout. The odds of these games are x to 1, so for every bet you place, you can either win x pounds for every 1 pound or lose the same. In simpler terms, if you bet on a payout of 35 to 1, on winning the bet, you get back 35 + 1 = 36 back.

You can understand the payout system very easily as there is not much complexity in these terms. What is complex is to understand how the odds are calculated and how to place your bets?

Odds & Payouts on Inside Bets

There are two types of bets, broadly, outside and inside. Thus, besides the outside bets, you can also choose to place your money on inside bets. These bets are less likely to succeed though, but they have a higher payout as well. That is, the higher the risks, the higher the payout. The inside bets are made on a single number or a small group of numbers, and then you can further split them into different wagering types. We have listed them below with a further explanation for ease.

  • Straight Up

This is a popular form of wagering and simple as well. In this, you place your bet on a single number on the table, and if you win, the payout will be 35 to 1 ratio. Simple right?

  • Split Bet

This is a little interesting. If you place your chips on the line between two numbers, then you are trying to cover both the numbers. And, if the ball lands on either of the numbers, you will receive a payout of 17 to 1. This is also quite popular among players.

  • Street Bet

This is a type of bet in live roulette that is most prized by players. This is interesting because it covers three numbers. Thus, in order to place your bet, you have to place your chips on the line outside the three numbers that are together in a row. The payout is 11 to 1 here.

  • Square Bet or Corner Bet

Known by either of the names in different places but they refer to the same thing. This wager is made on a corner by placing your chips in the form of a square and covering a range of numbers. The payout reduces further here to 8 to 1, as the probability of winning increases.

If something you can notice from the above is that as the probability of winning increases, the payout decreases. This is the top rule of any roulette game. Higher the risks, higher the pay, or lower the risks lower the pay.

There are a few more types as well.

  • Double Street Bet

This is an extended version of the above Street Bet. With this type of wager, you can cover two rows that are adjoining to each other. That means, now you can cover 6 numbers, further improving your chances of winning. Thus, the payout further reduces to 5 to 1.

  • Basket Bet

This is also known as a five-number bet. As one can understand by now, in this case, you can place a bet on five numbers at a time. This is perceived by many as the worst type of bet one can possibly place in a live roulette game. First, you can only make one of them. For example, if the wager is on the numbers 0, 00, 1, 2, and 3, you have to place the chips on the outside corner of the line between 0 and 1. Second, the payout for a successful wager is 6 to 1, but the house edge on this is much higher. A higher house edge means the chances of winning are very very rare. The Basket Wager is only available in American Roulette.

Thus, we learn about three things: House Edge, Probability and Payouts. As the probability of winning a bet increases, the House Edge is deliberately reduced and the payout is reduced as well. So, a player who is trying to increase their chances of winning a bet by placing the chips on more numbers, the chances of winning are reduced by a lot.

What is the Kelly Criterion? How to Calculate Optimal Bet Size?

As understood from the above summary, a player has to find the optimal or middle ground between the House Edge, the Wagering Numbers, and the Payout in order to improve their chances of winning.


We have looked at the odds and payouts for live dealer roulette above quite elaborately. So, we want to calculate our bet size to do something good. One thing to note is that our odds of winning will always be less than the payout amounts because most casinos maintain the House Edge as well, clearly described above. Specifically, American Roulette in casinos across the USA maintains an edge of 5.26%. In European and French casinos, their Roulette Games maintain an edge of 2.70%. Thus, understanding the odds can always be helpful, if not guarantee the winning chances. After all, the outcome is always a random variable.

There are various strategies, which despite being a random variable can help you manage and build your bankroll, using an optimal bet sizing. The most popularly used sizing method or optimal strategy is called the Kelly Criterion. This can be used within multiple games and gambling sports, besides the live roulette. The formula is described as follows.

F = bp – (1-p)b

In the above mathematical formula, “F” is the fraction of the current bankroll to bet, “b” is the net odds, and “p” is the probability of winning

Thus, from the above-calculated values of probability, and odds that we have mentioned before with examples, we can calculate the fraction of the bet sizing value now. To make things more favorable, a Live Dealer Roulette has been found to obey and give the best results using the Kelly Criterion by many experts. If you use it with a certain specific type of bets only, then the above rule holds.

As a thumb rule, to be able to use the Kelly Criterion, you should always stick to placing bets on red or black only. The key is always to avoid under-betting.

Though over-betting can kill your bankroll quickly, one must not bet less, and even better chances are to learn the optimal bet size. Under-betting has serious worse effects when long-term betting is done. In addition to that, it has very fewer chances of success. When continue to wager the same amount every time, this is known as under-betting. At the same time, one must be cautious that they do not deplete their bankroll quickly. Here is where Kelly Criterion can help you find that fine line between under-betting and over-betting. Mathematics can do stuff that guessing simply cannot.

Here is a small example. For example, if a wager has a 51% probability of winning, with even pricing on red and black, you should always bet with an edge of 2%. When the chances of winning increase to 53%, you should bet with an edge of 6%, and so on. In this manner, it helps you build your bankroll in a more managed and careful manner such that you do not risk under-betting or over-betting at the same time. In other words, the roulette game is approached using the best strategy possible, such that you have a lot of fun and over the long-term, you can end up making millions in winnings too.

This is why roulette is a game of fun when you know about the inner hard wirings a little bit more than a complete novice. In the same spirit, some of the real live casinos with live roulette games are LeoVegas, RoyalPanda, and

The Odds of Same Number Being Spun Several Times in a Row

The odds of the same number coming out on a single zero (European and French) and double zero in American can be learned from a chart. As per current records maintained by the mainstream media, the number 19 is spun 7 times in a row in Rio Casino in Las Vegas. At the same time, the chances of this happening are 94 billion to 1. In pure mathematical calculations, placing a wager of $1 will land you a win of $64,339,296,875 for the next seven spins. Only if luck was that favorable and rules didn’t limit anyone from doing that.

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