The probability of winning on each bet

Here are a few**charts and tables**for different probabilities in both European and American roulette.

Below is also some useful (but not necessarily easy) information about calculating roulette probabilities, as well as a little bit about player error.

## 1. European Roulette

Probability of each bet type winning on a European roulette wheel.

bet type | fraction | relationship | percentage |
---|---|---|---|

Straight (e.g. red/black) | 1/2.06 | 1,06 bis 1 | 48,6 % |

Split | 1/3.08 | 2.08 bis 1 | 32,4 % |

dozen | 1/3.08 | 2.08 bis 1 | 32,4 % |

six line | 1/6.17 | 5.17 bis 1 | 16,2 % |

Corner | 1/9.25 | 8.25 to 1 | 10,8 % |

Street | 1/12.33 | 11.33 bis 1 | 8,1 % |

Splits | 1/19.50 | 18.50 bis 1 | 5,4 % |

Just | 1/37.00 | 36.00 bis 1 | 2,7 % |

A simple bar chart to highlight the percentage odds of different bet types in roulette.

### The same color in a row

How unlikely is it to see the same color twice or more in a row? What is the probability of the results of 5 spins of the roulette wheelrot? The following table shows the probabilities of**same color**appears over a certain number of spins of the roulette wheel.

A chart showing the probability of seeing the same color red/black (or any other).*evenings*Betting outcome for that matter) across multiple spins.

number of turns | relationship | percentage |
---|---|---|

1 | 1,06 bis 1 | 48,6 % |

2 | 3.23 to 1 | 23,7 % |

3 | 7.69 to 1 | 11,5 % |

4 | 16.9 to 1 | 5,60 % |

5 | 35.7 to 1 | 2,73 % |

6 | 74.4 to 1 | 1,33 % |

7 | 154 to 1 | 0,65 % |

8 | 318 to 1 | 0,31 % |

9 | 654 to 1 | 0,15 % |

10 | 1.346 to 1 | 0,074 % |

fifteen | 49.423 bis 1 | 0,0020 % |

20 | 1.813.778 bis 1 | 0,000055 % |

Example:The probability of the same color appearing four times in a row is`5,60 %`

.

As the graph shows, the probability of seeing the same color on consecutive spins of the roulette wheel is greater thanThe half(so the*ratio probability*doublings) from one spin to the next.

I paused the graph at 6 trials/spins as that was enough to highlight the trend and create a nicer probability graph.

### Other probabilities

incident | relationship | percentage |
---|---|---|

The same number (ex.32) over 2 turns. | 1.368 to 1 | 0,073 % |

The result is0. | 36 to 1 | 2,7 % |

That0Appears at least once over 10 spins. | 2.7 to 1 | 27,0 % |

The same color over 2 spins. | 3.23 to 1 | 23,7 % |

Guesscolour and even oddcorrect. | 3.11 bis 1 | 24,3 % |

guess colorand dozencorrect. | 5.16 to 1 | 16,2 % |

About a dozenand pillarcorrect. | 8.25 to 1 | 10,8 % |

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## 2. American Roulette

Here are a few useful probabilities for**American roulette**.

Alongside the charts, I have included graphs comparing the odds of American roulette to roulette*European*Roulette Probabilities. The difference atopportunitiesand probability for these two variants is explained in theAmerican vs. European Probabilitysection below.

Probability of each bet type winning on an American roulette wheel.

bet type | fraction | relationship | percentage |
---|---|---|---|

Straight (e.g. red/black) | 1/2.11 | 1.11 bis 1 | 47,4 % |

Split | 1/3.16 | 2.16 bis 1 | 31,6 % |

dozen | 1/3.16 | 2.16 bis 1 | 31,6 % |

six line | 1/6.33 | 5.33 to 1 | 15,8 % |

Corner | 1/9.50 | 8.50 to 1 | 10,5 % |

Street | 1/12.67 | 11.67 to 1 | 7,9 % |

Splits | 1/19.00 | 18.00 bis 1 | 5,3 % |

Just | 1/38.00 | 37.00 bis 1 | 2,6 % |

A simple bar chart to highlight the percentage odds of winning the different bet types in American and European roulette.

### The same color in a row

When playing on aAmerican rouletteWheel, what is the probability that the same color will appearXtimes in a row? The table below lists both the ratio and the percentage probability over consecutive numbers of spins.

A chart showing the odds of seeing the same color red/black at an American roulette table (compared to the odds at a European table).

number of turns | relationship | percentage |
---|---|---|

1 | 1.11 bis 1 | 47,4 % |

2 | 3.45 to 1 | 22,4 % |

3 | 8.41 to 1 | 10,6 % |

4 | 18.9 to 1 | 5,04 % |

5 | 40.9 to 1 | 2,39 % |

6 | 87.5 to 1 | 1,13 % |

7 | 186 to 1 | 0,54 % |

8 | 394 to 1 | 0,25 % |

9 | 832 to 1 | 0,12 % |

10 | 1.757 to 1 | 0,057 % |

fifteen | 73,732 to 1 | 0,0014 % |

20 | 3.091.873 bis 1 | 0,000032 % |

Example:The probability of the same color appearing 6 times in a row on an American roulette wheel is`1,13 %`

.

The chance of seeing the same color on consecutive spins is slightly more than halved from one spin to the next.

You will also find that the same color is less likely to appear on multiple spins in a row on an American roulette wheel than on oneEuropean wheel. It's not because the American wheel is more "fair" and distributes red/black colors more evenly - it's because there's an extra green number (the double zero -00), which increases the likelihood of breaking the flow of consecutive spins of the same color.

### Other probabilities

incident | relationship | percentage |
---|---|---|

The same number (ex.32) over 2 turns. | 1.444 to 1 | 0,069 % |

The result is0or00. | 18 to 1 | 5,26 % |

That0or00Appears at least once over 10 spins. | 0,9 bis 1 | 52,6 % |

The same color over 2 spins. | 3.45 to 1 | 22,4 % |

guess colorandeven/odd correct. | 3.22 to 1 | 23,7 % |

guess coloranddozen right. | 5.33 to 1 | 15,8 % |

About a dozenandcolumn correct. | 8.5 to 1 | 10,5 % |

## 3. Why is there a difference between European and American roulette?

The probabilities in American and European roulette are different because in American roulette an additional green number (the double zero -00), while European roulette does not.

Therefore, the presence of that extra green number very slightly decreases the likelihood of hitting other specific numbers or groups of numbers, whether on one spin or multiple spins.

To give a simplified example, let's say I have a bag with 1 red, 1 black, and 1 green ball in it. If I ask you to randomly pick a ball, the odds of picking oneroter Ballwould1 von 3.

If I now add another green ball so that there are now 2 green balls in the bag, the probability increases that aroter Ballhas fallen to1 von 4.

Exactly this idea applies to all probabilities in American roulette (thanks to this extra00number), only on a slightly larger scale.

Fact:This difference in probabilities also affects thehouse edgeto. Essentially, you have a slightly worse chance of winning in American roulette, but thatpayoutsstay the same.

Note:You can learn more about the differences between these two games in my articleAmerican vs European Roulette.

## 4. Mathematics

### a. Formate

There are a number of ways to display probabilities. On the*Roulette-Charts*above I used; Ratio odds, percentage odds and sometimes fractional odds. But what do they mean?

- Odds in percent (%)
- That's easy. This gives you the percentage of time that an event occurs.
- Odds Ratio (X to 1)
- For each time X occurs, the event occurs 1 time.

Example: The odds ratio of a particular number that appears is 36 to 1, meaning that for every 36 times that number does not appear, it will appear 1 time. - Teilquoten (1/X)
- The event occurs 1 time out of X attempts.

Example: The odds of appearing a specific number are 1/37, which means it will happen 1 time in 37 spins.

As you can see, fractional odds and ratio odds are quite similar. The main difference is that fractional odds use the total number of spins while the ratio just splits them into two parts.

The majority of people are most comfortable with percentage odds as they are the most widely used. However, feel free to use whatever makes the most sense to you. They all point to the same thing at the end of the day.

### b. calculation

From my experience, the easiest way to calculate odds in roulette is tolook at thefractionof numbersfor your desired probability and then convert from there to a percentage or ratio.

For example, let's say you want to know the probability that a is redEuropeanRad. Well, there are a total of 18 red numbers and 37 numbers, so is the fractional probability18/37. Easy.

With this easy-to-obtain fractional probability, you can then convert it to a ratio or percentage.

#### single spin

Calculation:Count the number of numbers that give you the outcome you want the probability of, and then multiply that number over 37 (the total number of possible outcomes).

For example the probability of:

- Red = 18/37 (there are 18 red numbers)
- Even = 18/37 (there are 18 even numbers)
- Dozen = 12/37 (there are 12 numbers in a Dozen bet)
- 8 black = 1/37 (there is only one number8)
- Red and odd = 9/37 (there are 9 numbers that are both red and odd)
- Dozen and column = 4/37 (there are only 4 numbers in the same dozen and column)

Not only can you find the probability of winning on each spin, but also the probability of losing on each spin. All you have to do is count the numbers that result in a loss. For example, if you bet on red, the probability of losing is 19/37 (18 black numbers + 1 green number).

Note:To reduce a fraction to 1/X, simply divide each side by the number on the left. e.g. a bet on red has the probability of18/37, divide each side18and you have1/2.05.

#### Multiple turns

Calculation:Then calculate the breakage probability for each individual spin (as above).**multiply**these factions together.

For example, let's say you want to find the probability of correct guesses in specific casesWeather conditionsover several turns:

- Twist 1: Red = 18/37
- Spin 2: Dozen Bet = 12/37
- Probability = (18/37) x (12/37) =1/6.34

- Spin 1: Straight Bet (z.B.32) = 1/37
- Spin 2: Straight Bet (z.B.fifteen) = 1/37
- Probability = (1/37) x (1/37) =1/1369

- Twist 1: Black and Straight = 9/37
- Spin 2: Odd = 18/37
- Rotation 3: Column = 12/37
- Probability = (9/37) x (18/37) x (12/37) =1/26.06

To keep it simple, I've reduced all fractions to 1/X format for the results above.

### c. Convert

Having probabilities in a fractional format like 18/37 or 1/2.05 is fine, but sometimes it's more useful to see the probability as a*percentage*or a*relationship*. Luckily, it's pretty easy to convert from a fraction to either of these two.

#### break to relationship

conversion:Reduce the fraction to the format 1/X, then subtract 1 from X. This gives you the ratio of X to 1.

For example, what is a bet on a dozen (12/37) as a ratio?

- Reduce the fraction to 1/X.12/37 = 1/3.08 (You divide both sides by the left side number, which is in this example12)
- Take 1 away from X.3,08 - 1 = 2,08
- ratio =2.08 bis 1

#### fraction to percent

conversion:Divide the left side by the right side, then multiply by 100.

For example, what is aCornerBet (4/37) in percent?

- Divide the left side by the right side.4 ÷ 37 = 0,1081
- Multiply by 100.0,1081 x 100 = 10,81 %
- percent =10,81 %

## 5. Important fact about probability

The result of the next spin isoh noinfluenced by the outcome of previous spins.

### A quick example

The probability of the outcome isrotfor one revolution of the wheel is 48.6%. That's easy enough.

What if I told you that the outcome of the last 10 spins was like this?Schwarzevery time. How likely do you think the outcome is?roton the next spin would be? Higher than 48.6%?

Not correct. The probability would again be exactly 48.6%.

### Why?

The roulette wheel doesn't think "I've only returned black results for the last 10 spins, I better increase the probability that the next result is red to even things out". Unfortunately, roulette wheels are not that well thought out.

If you just sat down at the roulette table and didn't know that the last 10 spins were black, you wouldn't have a hard time agreeing that the probability of seeing a red on the next spin is 48.6%. However, if you are aware of recent results, you are tempted to let them influence your judgment.

Each individual result is independent of the last one, so don't expect the results of future spins to be affected by the results you've seen on previous spins. Appreciating this fact will save you some disappointment (and frustration) in the future.

Believing that a particular result is "due" based on previous results is referred to as "that".*Player's error*.

### What about the graphics above?

On the graph of the probability of seeing the same color over multiple spins of the wheel, it shows the probability that the outcome is the same colorThe halffrom one turn to the next.

However, this only applies if you look at the entire set of tries/spins from the start.

If the last spin was red, the probability of the next spin being red is still 48.6% - it doesn't go down to 23.7%. On the other hand, if you hadn't spun the wheel to see the first red result and wanted to know the probability of seeing redover the next 2 turns(and not only on the next 1 spin), the probabilitywant23.7%.

## Continue reading

- Roulette Winning Simulator
- American roulette house edge-wizardofodds.com
- Gambler Expectation- hundertprozentgambling.com