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Roulette Odds of Winning and Your Bets Consider the following scenario: You put money $20 each on Red, Even, the first half numbers 1-18, and the individual numbers 2, 4, 6, 8, and 10. That’s a $160 worth of bets. The ball lands on red 27.
- Red or Black – This bet pays out even odds (1 to 1) if the ball lands on the color you chose. Odd or Even – This bet pays out even odds (1 to 1) if the ball lands on odd or even, depending on which you chose.
- To make this even clearer, let us see the odds for probably the most commonly placed bet in roulette – red/black. If we place our chips on red, the probability would be 18 out of 37, while the odds would be 19:18 against us because there would be 19 ways to lose against 18 ways to win.
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?
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.
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 Same Number Comes Up in a Row | True Odds to One in FRENCH Roulette | True Odds to One in AMERICAN Roulette |
---|---|---|
37 | 38 | |
2˟ | 1,369 | 1,444 |
50,653 | 54,872 | |
4˟ | 1,874,161 | 2,085,136 |
69,343,957 | 79,235,168 | |
6˟ | 2,565,726,409 | 3,010,936,384 |
94,931,877,133 | 114,415,582,592 | |
8˟ | 3,512,479,453,921 | 4,347,792,138,496 |
129,961,739,795,077 | 165,216,101,262,848 | |
10˟ | 4,808,584,372,417,850 | 6,278,211,847,988,230 |
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.
Roulette Odds And Payouts
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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.
Roulette Betting Odds Red
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
Vegas Roulette Odds
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
Roulette Odds 6 Red In A Row
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
See The Martingale StrategyYou 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.
FAQs Roulette Probabilities
Craps Odds
- 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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Roulette Odds Of 5 Reds In A Row
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