Roulette: chances and probabilities

Now you know all the basic stakes in roulette and payout ratios for them. So let’s move on to the most interesting part of this article. It’s time to count the odds in roulette to find out the value of each bet in the long run.

I calculated the so-called RTP (Return to Player) for each bet in the table below. RTP is the percentage of payments . This indicator indicates the value of the bet.

Domestic betting: chances and probabilities

All the information you need about the odds and probabilities of internal bets is given in the table below. Some bets are only available in the American or European versions of roulette, so some table cells are left blank.

RateNumber of roomsPayout ratioChance to win (Heb.)Chance to win (Amer.)RTP rates (Heb.)RTP rates (Amer.)
Straight app136: 11/371/3897.3%94.74%
Split218: 12/372/3897.3%94.74%
Street312: 13/373/3897.3%94.74%
Line66: 16/376/3897.3%94.74%
Angle49: 14/374/3897.3%94.74%
Trio312: 13/3797.3%
Basketball49: 14/3797.3%
Top line57: 15/3892.1%

Note that the payout percentage of the top line in American roulette is lower than the payout percentage of all other bets. This is all because the rate covers 5 numbers and the payout ratio is only 7: 1. If the ratio was 7.2: 1, the percentage of payments at this rate would be equal to others in American roulette. That’s why a top line bet will never be a good idea .

External bets: chances and probabilities

In the table below, I have provided you with all the information you need about the odds and probabilities of external betting .

RateRTP (Hebrew)RTP (Hebrew + “La Partage”)RTP (Hebrew + “En Prison”)RTP (Amer.)RTP (American + Surrender)
Red / black97.3%98.6%98.6%94.74%97.2%
Even / odd97.3%98.6%98.6%94.74%97.2%
Large / small97.3%98.6%98.6%94.74%97.2%

Due to these rules, odds at the level of odds have a higher payout percentage compared to other bets . Therefore, if you play roulette where one of the above rules applies, remember that these bets will generally be more profitable.

Oral bets: chances and probabilities

Oral rates are special. They consist of smaller bets covering certain sectors of the roulette board. This means that the odds and probabilities of verbal bets can be divided by the odds and probabilities of each of the lower bets .

Therefore, I will not list the payout percentage of these rates, as I did for standard internal and external rates. Any oral bet on roulette with one zero has an RTP of 97.3% . Oral bets consist of internal bets, which means that the payout percentage of the total bet will not change when special rules are applied that affect the payout percentage of the odds level.

Oral bets are almost always used only in European (French) roulette. However, when used (as modified) in American roulette, they would have a payout percentage of 94.74% , provided they do not include a top-line bet, as it has a slightly different RTP and can change it for the overall bet.

Percentage advantage of casino in roulette (share of casino)
The fate of the casino is the overall percentage advantage of the casino . Calculate it for any game is quite simple:

Casino share = 100% – RTP (payout percentage)

Accordingly, here is the standard share of a casino for roulette:

  • European roulette (roulette with one zero) – 2.7%;
  • American roulette (roulette with double-zero) – 5.26%.

However, as you probably already understand, there are some exceptions : they are some bets and special roulette rules, as they can reduce the advantage of the casino over the players.

The following are the rates and rules that can change the fate of the casino:

  • La Partage and En Prison rules reduce the share of a single zero roulette casino for odds (red / black, even / odd, big / small) to 1.35% ;
  • the “Surrender” rule reduces the share of casino roulette with double-zero for betting at the level of odds (red / black, even / odd /, big / small) to 2.6% ;
  • the top line bet, which covers numbers 0, 00, 1, 2 and 3 on a double-zero roulette, has the highest percentage advantage of the casino among all – 7.9% .

The lower the share of the casino, the better for the players . In terms of the payout percentage and the casino’s interest advantage, the odds on equal odds in French roulette with the “La Partage” or “En Prison” rule are considered the best for players, as they statistically lose only 1.35% of their bets.

What is the fate of casino roulette compared to other casino games?

Due to the share of casinos and the percentage of payouts, it is quite simple to compare different casino games and determine which of them are the least profitable casinos and the most profitable for players. So, will the fate of the casino in roulette withstand comparison with other casino games?

Below are the percentage benefits of the casino for different games.

  • European roulette – 2.7%.
  • American roulette – 5.26%.
  • French roulette (with the rule “La Partage” or “En Prison” – 1.35%.
  • Blackjack (according to the main strategy ) – less than 0.5%.
  • Slots – from about 1% to 8% (average 4%).
  • Baccarat – about 1% (when betting on the bank).
  • Video Poker (Valts and Better) – less than 0.5%.

As you can see, everything is recognizable by comparison, because there are quite a few games that are more profitable for the player in the long run. American roulette is much worse for the player, so if you are going to play roulette, find a casino where there will be a roulette with one zero and, ideally, using rules that reduce the casino’s percentage advantage.

How to calculate RTP and the share of casinos in roulette?

As already mentioned, roulette is a fairly simple game, so calculating the percentage of payouts and the share of the casino is not difficult. In this part of the article, I will explain why casinos always have an advantage in roulette , as this advantage is mathematically related to the course of the game and the chances of winning.

For calculations I use European roulette without special rules. Although this formula is suitable for other types of roulette, if you make minor changes to the benefits of the casino in each case.

Mathematical expectation or expected value ($ 1 bet on straight up) = Possible win * Odds of winning = $ 36 * (1/37) = $ 36/37 = $ 0.973

For other bets, the expected value will be the same.

  • $ 1 in red / black = $ 2 * (18/37) = $ 36/37 = $ 0.973
  • $ 1 per split = $ 18 * (2/37) = $ 36/37 = $ 0.973
  • $ 1 per column = $ 3 * (12/37) = $ 36/37 = $ 0.973

I could do this calculation for each type of bet in European roulette, but is it really necessary? Payouts for each bet are calculated according to the same formula, which means that each European roulette has a payout percentage of 97.3% (statistically, a player wins $ 0.973 for every $ 1 invested).

The payout percentage in European roulette is the same for all types of bets. However, if special rules are applied that may make certain bets less profitable for the casino, the payout percentage increases and the casino share decreases.

Calculations for American roulette are quite similar. All you have to do is replace the number “37” with “38”, because there are 38 possible game results in a double-zero roulette.

Each result in American roulette is slightly less likely than in Europe (except for “00”, which is not on roulette with one zero), while the payouts remain the same. That is why American roulette has a lower payout percentage – only 94.74% .

And one bet in American roulette has an even lower payout percentage – 92.1%. The reason for this is the non-standard chances of winning (5:38) and the payout ratio (7: 1) for the “top line” bet. The RTP calculation for this bet is as follows: $ 1 on top line = $ 7 * (5/38) = $ 35/38 = $ 0.921

The share of the casino can be calculated using the payout percentage:

Casino share = 1 – RTP

Accordingly, the fate of the casino in roulette is as follows:

  • 1 – 97.3% = 2.7% for European roulette;
  • 1 – 94.74% = 5.26% for American roulette.

Of all the casino games, roulette does not offer the highest chances of winning, and the games are more exciting. However, there are many who want to argue that roulette is a classic among casino board games that brings a lot of fun.

Moreover, the rules of the game are very simple, and the chances of winning are quite high . It can be played even by beginners who know absolutely nothing about roulette, although I recommend that you first learn the basics and rules of the game to make only the right decisions.

That’s why I decided to write this article. I hope it will be useful to you, and I wish you success at the roulette table if you decide to try your luck in this game.

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