Roulette Color Probability

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How many times in a row has a little ball landed in the same pocket of a Roulette wheel, i.e. how many times has a single number occurred in a row? And how about the same color? What is the probability of these events and a potential impact on a play?

The odds of winning can also be expressed in the same way. On a standard American roulette wheel, you have 37 ways to lose a single number bet and only one way to win. This means the odds of winning are 37 to 1. Since the odds of winning are lower than the payoff for the bet, the casino makes a profit in the long run.

Record Occurrence of a Single Number in Roulette

The probability that any single number occurs is 1/37 in French Roulette and 1/38 in American Roulette (there are 36 numbers + zero + double zero in American Roulette). There is no doubt that it is a great coincidence when the same number comes up again and again.

But knowing this doesn’t change the odds of winning on the next spin. For example, you could wait for 10 consecutive reds, and have two options: Option 1: Expect the color streak will continue, and bet on red. Option 2: Expect black is due, and bet on black. Let’s assume green zero doesn’t exist. So which option would you take? In roulette, what is the probability/chance of the same colour appearing 13 times in consecutively? I was wondering than in roulette, the record is something like 22 same colour in a row, but what actually is the chance of it coming in about 13 times. The following chart highlights the probabilities of the same colour appearing over a certain number of spins of the roulette wheel. Example: The probability of the same colour showing up 4 times in a row is 5.6%. A graph to show the probability of seeing the same colour of red/black (or any 'evens' bet result for that matter) over multiple spins. These can be placed in both single-zero and double-zero roulette, although you have an extra 3-number bet in double-zero roulette courtesy of that extra 00 number. The payouts and probability for this bet are the same for the respective roulette tables as the street bet above. 2 Numbers - 17:1 (5.41%) Also known as: Split bet.

The longest reliable series was registered at the hotel El San Chuan in Puerto Rico on 9 June 1959. During the course of the American Roulette, number ten occurred even six times in a row! The probability of such (successive) events is determined by a multiplication of individual events. Therefore the probability that the same number comes up six times in a row is:

(1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38) ˟ (1/38), that is:

(1/38)6 = 0.000000000332122593261671.

That is a very small number indeed, roughly three billionths only. If we convert this probability into true odds that would have to be offered to us by a casino, we get the value 3,010,936,384 to one. The true (fair) odds are calculated as a reciprocal of the probability, that is 1 ÷ probability. If such a bet on a series of outcomes was possible in Roulette, we would win $3 billion for a $1 bet(!)

It is important to add that the above-mentioned calculation of probability deals with a multiple (successive) events, i.e. we can ask this question: What is the probability that the same number in Roulette comes up 6 times in a row?

Since it would be a different case if e.g. number 10 occurred and after that before the new spin we asked what was the probability that number ten came up again? In this case the answer would be 1/38 (in terms of American Roulette), because any number could occur with the same probability 1/38 in every new spin. That is what we call a simple event in contrast with a multiple event(s) whereas the probabilities of individual events are multiplied (→ Articles on Probability).

The true odds for a 1 to 10fold repetition of the same number are shown in the table below. It is the same mechanism as if a sporting bet company or a casino offered the odds for a victory of some home team in some football match (→ The Odds Determination and Calculation).

The odds are reciprocal values of the probabilities – the higher they are, the lower the probabilities are. The case of the above-mentioned record series is marked green. Consider also the difference that is made by one extra number in American Roulette (the double zero).

Record Repetition of the Same Color in Roulette

There are no exceptions that the same color appeared more than 20 times in a row in practice. The record was registered in 1943, when red color came up 32 times in a row! The probability of such event in French Roulette is (18/37)32 = 0.000000000096886885 with the corresponding odds 10,321,314,387:1.

The probability of the 32fold repetition of the same color in American Roulette is much more lower: (18/38)32 = 0.00000000004127100756 and the odds are 24,230,084,485:1. Thus this is even less likely than occurrence of a single number six times in a row. Again it is clearly demonstrated what kind of importance (a negative one for players) has just one extra number in American Roulette.

Now imagine that you used the Martingale betting strategy (→ see the first test of the Martingale system), whereas the next bet is doubled if your bet loses...

→ Testing & Simulations of Roulette Bets & Strategies

What are the roulette odds of the ball landing in the same colour ten times in a row? What about landing on the same number twice? Let´s take a look, and then we´ll explain how this relates to the Gambler´s Fallacy, or the Monte Carlo Fallacy- the belief that the odds of a black number coming in increase, the more times you see red.

Let´s look at a European Roulette wheel. Over a single spin, the odds of a red number coming up are 18/37, or 1 in 2.06. Over 2 spins, the odds of 2 reds coming in are 1 in 2.06×2.06, or 4.24.

The odds of seeing 10 reds in succession are 1 in (2.06) to the power of 10 = 1 in 1376.

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Pretty low odds that you´ll ever see this, in other words. But that doesn´t mean it isn´t going to happen. In fact, the longest number of reds in a row was recorded in an American Casino in 1943 when 32 came up in a row. Now imagine that you were betting the Martingale that day! The odds of seeing that are 1 in 11 million, or thereabouts by the way.

Another huge streak (this time on black) was seen by the players at the Casino in Monte Carlo who saw 26 blacks in a row on the table on 18 August 1913. The odds of this happening? A mere 1 in 145,000.

And this gave name to the Monte Carlo Fallacy, otherwise known as the Gambler´s Fallacy, as the longer the streak went on, more and more people started piling their chips on to red. And they lost a lot of money.

So what happened?

Gambler´s Fallacy

The important thing to understand and to get your head around, is that these are odds over multiple spins. And here´s the thing. In roulette, you can´t bet on what is going to happen over 10 spins, you can only bet on the next spin. And thus the odds are always the same – 18/37, whether the red came in 10 times previously or not. The wheel has no memory from spin to spin. It is not a living thing.

Tip for Martingale Players

Martingale System Players are often susceptible to long runs as they double their bet after a loss. Start your first bet low if you employ this strategy to give yourself the most room for manouevre

You are Betting on One Spin Not Multiple Spins
When you are betting on one spin, the odds are for one spin, and for one spin only.

One things for sure about the Gambler´s Falllacy- the casinos love it! Don´t get sucked in, keep your thinking hat on.

One thing’s for sure- there are plenty of people who have worked out that the odds are with the casino on roulette, and have opted to scam the casinos instead, like the roulette scam in Ohio. Just be warned- that’s illegal. They got busted.

Roulette Color Probability Chart

FAQs Roulette Probabilities

Roulette Color Probability Games

• What are the odds of seeing 10 reds in a row on a roulette wheel?
  The odds of seeing 10 reds one after another are 1 in (2.06)¹⁰ = 1 in 1376. But remember, you cannot bet on 10 spins, only on a single spin. Here the odds are 1 in 2.06
• What is the definition of the Gambler’s Fallacy in roulette?
  The Gambler’s Fallacy is the incorrect belief that a certain event like flipping a coin or the ball landing on a black number is more or less likely, due to a previous sequence of events.
  This is incorrect for mutually exclusive events because each event is independent with a result that has no relation to past events. Think about it this way. Is the wheel thinking after each spin, “I spun a red last spin. Let´s throw in a black to even things up.” No.

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