In case you’re wondering what the monte carlo incident is, it was a game of roulette that landed on black 26 times in a row… the odds of that happening is 1 in 66.6 million
The gamblers fallacy is a fallacy that people who gamble tend to think if something has a long streak it’s going to change.
If the odds of it being 26 blacks in a row is 1 in 66.6 million why would that be a fallacy? Obviously it could always be a 27th black but thats incredibly unlikely and statistically speaking red would be far more likely…
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The odds of being black 26 times in a row is 1 in 67 million, but so is the odds of it being black, red, black, black, red, red, red, black, red, red, black, black, black, black, red, black, black, red, black, red, red, red, black, red, black, black. *Any* chain of 26 results has a 1 in 67 million chance of occurring. 26 blacks is just (almost) unique in being “interesting” to humans as a long streak. But that’s just psychology, it has nothing to do with probability.
The same thing is true for a chain of 27. 27 blacks has the exact same probability as 26 blacks followed by one red. Which means that if you’ve already got a chain of 26 blacks, both red and black are equally likely for the 27th roll.
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