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.
Well, the probability is easy to work out. Se below for details.
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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 2.06x2.06, or 4.24.
The odds of seeing 10 reds in succession are 1 in (2.06)10 = 1 in 1376.
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?
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.
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.
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