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Assuming monitoring a 1000 rolls in a fairly balanced roulette wheel and writing them down, is it safe to assume that the number that appeared the least is the one more likely to be the next?

In other words, the likeliness of numbers appearing is in the order of the the least amount of appearances

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    $\begingroup$ This is the gambler's fallacy. $\endgroup$ – Matt Samuel Oct 9 at 18:04
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No, as long as the spins are independent of each other. You assumed the wheel to be fair, so by assumption every number has the same probability, no matter how often you spun the wheel before.

If the wheel is not fair, then the conclusion might be different, but rather the opposite of what you were thinking. It would make more sense to assume that the number occuring the least has a lower probability of occuring and therefore you should, if anything, assume that that number will occur less likely.

See also: https://en.wikipedia.org/wiki/Gambler%27s_fallacy

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