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Indeed and the example above confirms that those are just fallacies.
Although the probability of hitting the same number three times in a row in Roulette is 1/50653, it can still happen! The number being "
zero" makes it more odd. Well done on documenting it OP.
That being said, it's always recommended to check the fairness of the game and verify each round's result.
Yup, gamblers fallacy, previous outcome doesn't influence the next result. However, there are instances, like in this one that probabilities is really very odd.
I've also been playing roulette for many years now, but I avoided double 00 because the house edge are high as compare to single 0 but still you can't discount the fact that this can happen.