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Probability The probability of winning with each bet
Here are a bunch of charts and tables for different probabilities in both ๐ European and American roulette.
There's also some handy (but not necessarily easy) information at the bottom about working out roulette probabilities, ๐ plus a little bit on the gambler's fallacy.
1. European roulette
Probability of each bet type winning on a European roulette wheel.
Bet ๐ Type Fraction Ratio Percentage Even (e.g. Red/Black) 1/2.06 1.06 to 1 48.6% Column 1/3.08 2.08 to 1 32.4% Dozen 1/3.08 ๐ 2.08 to 1 32.4% Six Line 1/6.17 5.17 to 1 16.2% Corner 1/9.25 8.25 to 1 10.8% Street 1/12.33 11.33 ๐ to 1 8.1% Split 1/19.50 18.50 to 1 5.4% Straight 1/37.00 36.00 to 1 2.7%
A simple bar chart to highlight ๐ the percentage probabilities of the different bet types in roulette coming in.
The same color in a row
How unlikely is it ๐ to see the same color 2 or more times in a row? What's the probability of the results of 5 ๐ spins of the roulette wheel being red? The following chart highlights the probabilities of the same color appearing over a ๐ certain number of spins of the roulette wheel.
A graph to show the probability of seeing the same color of red/black ๐ (or any evens bet result for that matter) over multiple spins.
Number of Spins Ratio Percentage 1 1.06 to 1 48.6% ๐ 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% ๐ 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% ๐ 10 1,346 to 1 0.074% 15 49,423 to 1 0.0020% 20 1,813,778 to 1 0.000055%
Example: The probability of the same ๐ color showing up 4 times in a row is 5.60% .
As the graph shows, the probability of seeing the same ๐ color on consecutive spins of the roulette wheel more than halves (well, the ratio probability doubles) from one spin to ๐ the next.
I stopped the graph at 6 trials/spins, as that was enough to highlight the trend and produce a prettier ๐ probability graph.
Other probabilities
Event Ratio Percentage The same number (e.g. 32 ) over 2 spins. 1,368 to 1 0.073% The result ๐ being 0 . 36 to 1 2.7% The 0 appearing at least once over 10 spins. 2.7 to 1 27.0% ๐ The same color over 2 spins. 3.23 to 1 23.7% Guessing color and even/odd correctly. 3.11 to 1 24.3% Guessing ๐ color and dozen correctly. 5.16 to 1 16.2% Guessing dozen and column correctly. 8.25 to 1 10.8%
Rank Casino Rating Payment ๐ Methods Payout Time Links No casinos available :(
2. American roulette
Here are a few useful probabilities for American roulette.
Alongside the charts, ๐ I've included graphs that compare the American roulette probabilities to those of the European roulette probabilities. The difference in odds ๐ and probability for these two variants is explained in the American vs. European probability section below.
Probability of each bet type ๐ winning on an American roulette wheel.
Bet Type Fraction Ratio Percentage Even (e.g. Red/Black) 1/2.11 1.11 to 1 47.4% Column 1/3.16 ๐ 2.16 to 1 31.6% Dozen 1/3.16 2.16 to 1 31.6% Six Line 1/6.33 5.33 to 1 15.8% Corner 1/9.50 8.50 ๐ to 1 10.5% Street 1/12.67 11.67 to 1 7.9% Split 1/19.00 18.00 to 1 5.3% Straight 1/38.00 37.00 to 1 ๐ 2.6%
A simple bar chart to highlight the percentage probabilities of winning with the different bet types in American and European ๐ roulette.
The same color in a row
When playing on an American roulette wheel, what's the probability of seeing the same color ๐ appear X times in a row? The table below lists both the ratio and percentage probability over successive numbers of ๐ spins.
A graph to show the probability of seeing the same color of red/black on an American roulette table (compared to ๐ the odds on a European table).
Number of Spins Ratio Percentage 1 1.11 to 1 47.4% 2 3.45 to 1 22.4% ๐ 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% ๐ 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% ๐ 15 73,732 to 1 0.0014% 20 3,091,873 to 1 0.000032%
Example: The probability of the same color showing up 6 times ๐ in a row on an American roulette wheel is 1.13% .
The probability of seeing the same color appear on successive ๐ spins just over halves from one spin to the next.
You'll also notice that it's less likely to see the same ๐ color appear on multiple spins in a row on an American roulette wheel than it is on a European wheel. ๐ This is not because the American wheel is "fairer" and dishes out red/black colors more evenly โ it's because there ๐ is an additional green number (the double zero - 00) that increases the likelihood of disrupting the flow of successive ๐ same-color spins.
Other probabilities
Event Ratio Percentage The same number (e.g. 32 ) over 2 spins. 1,444 to 1 0.069% The result ๐ being 0 or 00 . 18 to 1 5.26% The 0 or 00 appearing at least once over 10 spins. ๐ 0.9 to 1 52.6% The same color over 2 spins. 3.45 to 1 22.4% Guessing color and even/odd correctly. 3.22 ๐ to 1 23.7% Guessing color and dozen correctly. 5.33 to 1 15.8% Guessing dozen and column correctly. 8.5 to 1 ๐ 10.5%
3. Why is there a difference between European and American roulette?
The probabilities in American and European roulette are different because ๐ American roulette has an extra green number (the double zero - 00), whereas European roulette does not.
Therefore, the presence of ๐ this additional green number ever so slightly decreases the probability of hitting other specific numbers or sets of numbers, whether ๐ it be over one spin or over multiple spins.
To give a simplified example, lets say I have a bag with ๐ 1 red, 1 black and 1 green ball in it. If I ask you to pick out one ball at ๐ random, the probability of choosing a red ball would be 1 in 3.
Now, if I added another green ball so ๐ that there are now 2 green balls in the bag, the probability of picking out a red ball has dropped ๐ to 1 in 4.
This exact same idea applies to all the probabilities in American roulette (thanks to that extra 00 ๐ number), just on a slightly bigger scale.
Fact: This difference in the probabilities also has a knock-on effect for the house ๐ edge too. So essentially, in American roulette you have a slightly worse chance of winning, but the payouts remain the ๐ same.
Note: You can find out more about the differences between these two games in my article American vs European roulette.
4. ๐ Mathematics
a. Formats
There are a number of ways to display probabilities. On the roulette charts above I have used; ratio odds, ๐ percentage odds and sometimes fractional odds. But what do they mean?
Percentage odds (%) This is easy. This tells you the ๐ percentage of the time an event occurs. Ratio odds (X to 1) For every time X happens, the event will ๐ occur 1 time.
Example: The ratio odds of a specific number appearing are 36 to 1, which means that for every ๐ 36 times the number doesn't appear, it will appear 1 time. Fractional odds (1/X) The event occurs 1 time out ๐ of X amount of trials.
Example: The fractional odds of a specific number appearing are 1/37, which means that it will ๐ happen 1 time out of 37 spins.
As you can see, fractional odds and ratio odds are pretty similar. The main ๐ difference is that fractional odds uses the total number of spins, whereas the ratio just splits it up in to ๐ two parts.
The majority of people are most comfortable using percentage odds, as they're the most widely understood. Feel free to ๐ use whatever makes the most sense to you though of course. They all point to the same thing at the ๐ end of the day.
b. Calculating
From my experience, the easiest way to work out probabilities in roulette is to look at ๐ the fraction of numbers for your desired probability, then convert to a percentage or ratio from there.
For example, lets say ๐ you want to know the probability of the result being red on a European wheel. Well, there are 18 red ๐ numbers and 37 numbers in total, so the fractional probability is 18/37. Simple.
With this easy-to-get fractional probability, you can then ๐ convert it to a ratio or percentage.
Single spin
Calculation: Count the amount of numbers that give you the result you want ๐ to find the probability for, then put that number over 37 (the total number of possible results).
For example, the probability ๐ of:
Red = 18/37 (there are 18 red numbers)
Even = 18/37 (there are 18 even numbers)
Dozen = 12/37 (there are 12 ๐ numbers in a dozen bet)
8 Black = 1/37 (there is only one number 8 )
) Red and Odd = 9/37 ๐ (there are 9 numbers that are both red and odd)
Dozen and Column = 4/37 (there are only 4 numbers in ๐ the same dozen and column)
As well as working out the probability of winning on each spin, you can also find ๐ the likelihood of losing on each spin. All you have to do is count the numbers that will result in ๐ a loss. For example, the probability of losing if you bet on red is 19/37 (18 black numbers + 1 ๐ green number).
Note: To reduce a fraction down to 1/X, just divide each side by the number on the left. e.g. ๐ a bet on red has the probability of 18/37, divide each side by 18 and you've got 1/2.05.
Multiple spins
Calculation: Work ๐ out the fractional probability for each individual spin (as above), then multiply those fractions together.
For example, let's say you want ๐ to find the probability of making correct guesses on specific bet types over multiple spins:
Probability = (9/37) x (18/37) x (12/37) = 1/26.06
To ๐ keep it simple, I reduced the all fractions for the results above down to the 1/X format.
c. Converting
Having probabilities in ๐ a fraction format like 18/37 or 1/2.05 is okay, but sometimes it's more useful to see the probability as a ๐ percentage or a ratio. Luckily, it's pretty easy to convert to either of these from a fraction.
Fraction to ratio
Conversion: Reduce ๐ the fraction to the 1/X format, then take 1 away from X. This will give you the X to 1 ๐ ratio.
For example, what is a dozen bet (12/37) as a ratio?
Reduce the fraction to 1/X. 12/37 = 1/3.08 (you divide ๐ both sides by the left-hand side number, which in this example is 12 ) Take 1 away from X. 3.08 ๐ - 1 = 2.08 Ratio = 2.08 to 1
Fraction to percentage
Conversion: Divide the left side by the right side, then ๐ multiply by 100.
For example, what is a corner bet (4/37) as a percentage?
Divide the left side by the right side. ๐ 4 รท 37 = 0.1081 Multiply by 100. 0.1081 x 100 = 10.81% Percentage = 10.81%
5. Important fact about probability
The ๐ result of the next spin is never influenced by the result of previous spins.
A quick example
The probability of the result ๐ being red on one spin of the wheel is 48.6%. That's easy enough.
Now, what if I told you that over ๐ the last 10 spins, the result had been black each time. What do you think the probability of the result ๐ being red on the next spin would be? Higher than 48.6%?
Wrong. The probability would be exactly 48.6% again.
Why?
The roulette wheel ๐ doesn't think "I've only delivered black results over the last 10 spins, I better increase the probability of the next ๐ result being red to even things up". Unfortunately, roulette wheels are not that thoughtful.
If you had just sat down at ๐ the roulette table and didn't know that the last 10 spins were black, you wouldn't have a hard time agreeing ๐ that the probability of seeing a red on the next spin is 48.6%. Yet if you are aware of recent ๐ results, you're tempted to let it affect your judgment.
Each and every result is independent of the last, so don't expect ๐ the results of future spins to be affected by the results you've seen over previous spins. If you can learn ๐ to appreciate this fact, you will save yourself from some disappointment (and frustration) in the future.
Believing that a certain result ๐ is "due" because of past results is known as the gambler's fallacy.
What about those graphs above?
In the graph of the ๐ probability of seeing the same color over multiple spins of the wheel, it shows that the probability of the result ๐ being the same color halves from one spin to the next.
However, this is only if you're looking at the entire ๐ set of trials/spins from the start.
If the last spin was red, the chances of the next spin being red are ๐ still 48.6% โ they do not drop to 23.7%. On the other hand, if you hadn't spun the wheel to ๐ see the first red result and wanted to know the probability of seeing red over the next 2 spins (and ๐ not just on the next 1 spin), the probability would be 23.7%.
Further reading
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