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mb34i t1_ja86g31 wrote

Reply to comment by hinoisking in ELI5: why does/doesn’t probability increase when done multiple times? by Reason-Local

The probability of rolling a 6 on a die depends on the die; if it's perfectly manufactured then it's 1/6, if it's crooked then it's different than 1/6. The probability doesn't change because in theory the die does not change physically, when you roll it.

In practice, dice can get chipped / worn out, so the probability CAN change. But for the purpose of statistical problems, you're considering "perfectly manufactured" dice that are brand new.

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earlandir t1_ja8jl7l wrote

Wow, you are saying if the dice are warped they no longer behave like perfect dice!? Incredible insight. /s

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breckenridgeback t1_ja8oscq wrote

The insight here is that, provided you are not certain of the fairness of the die, each roll would give you information about its fairness (and therefore about future rolls). The rolls themselves are still independent even on an unfair die, but you will develop progressively better estimates of the actual underlying probabilities.

(Of course, in basic statistics we ignore this sort of thing and just assume the die is fair or loaded in some known way. But this is an important caveat in real-world statistics!)

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