What are the odds of the ball landing in the same colour 10x in a row?
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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?
Roulette Odds and the 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.
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.
There are either 37 or 38 possible outcomes per spin, depending on whether you are on on a European or an American wheel. The odds of winning at roulette = No. Ways to Win / (Total Ways to Win AND Lose). So for a bet on red in European roulette, this would be 18/37 =48.6%
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