How many times must you roll a die to be within $99\%$ confidence that it is fair? What if you were to use a die with more sides?

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    $\begingroup$ math.stackexchange.com/questions/57624/… might help $\endgroup$ – Shuri2060 Mar 18 '16 at 19:12
  • $\begingroup$ Is a die that comes up with heads $\frac{1}{100000000000}$ times more than it comes up tails fair? Because even if you say "the die is either exactly fair or biased exactly in this way, with probability 50% each", you're going to have to do a lot of trials before you get any noticeable information on which case we're in. $\endgroup$ – Milo Brandt Mar 18 '16 at 19:24
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    $\begingroup$ If my die landed on heads, I'd be rather concerned! $\endgroup$ – Dr. John A Zoidberg Mar 18 '16 at 19:26
  • $\begingroup$ Dice can land on $\;1,2,3,4,5,6\;$, coins can land on heads or tails. $\endgroup$ – DonAntonio Mar 18 '16 at 19:27
  • $\begingroup$ In other words, we need a definition of fair. Do you mean, for example, that the prob of any side coming up must be within $10^{-6}$ of $\frac{1}{6}$? $\endgroup$ – almagest Mar 18 '16 at 19:30