# Average number of rolls of die to see each side at least once [duplicate]

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You have a weighted n-sided die. Every side of the die is weighted differently where side n1 has a weight of w1, n2 has a weight of w2, ...

Estimate the average number of rolls needed to see every face at least once.

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## marked as duplicate by joriki, Arkamis, Austin Mohr, Norbert, Chris EagleOct 30 '12 at 18:50

Voting to close as duplicate: although that question is a special case of this one, the answers address the general case. –  Chris Eagle Oct 30 '12 at 18:49

It's correct that this is the coupon collector's problem, but that expected number can't be right - consider the case where all of the weights are 1 (or so nearly so as to be negligibly different, while still meeting the 'weighted differently' constraint). The formula would suggest that it takes only $n$ rolls to 'collect' all $n$ sides. –  Steven Stadnicki Oct 29 '12 at 18:23
But it can't be correct, because the original problem has $w_k=\frac{1}{n}$ and your answer would give us $n^2$ in that case, when it should be $nH_n = O(n\log n)$ –  Thomas Andrews Oct 29 '12 at 18:28