Why does something like the gambler’s fallacy hold true in an instance like the monte carlo roulette incident?

Question

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…

In: Other

Answer 1

Red is no more likely than black for the 27th spin. There’s slightly less than a 50% chance that it lands on Red and a slightly less than 50% chance it lands on black(thanks to the Green zeros)

The odds of getting to that pattern are 1 in 66 million, but the odds on the next spin are always the same

If you do a few billion roulette spins, you’ll likely have at least one string of 30 blacks in a row and another string of 30 reds in a row, simply because you have a large enough sample that suddenly unlikely combinations become near certainty. But just because I know that somewhere in the billions of spins will be 30 blacks in a row, that doesn’t mean I should go all in on the first one to reach 29 in a row.