Rounds to see all faces with two dice

HardProbability Expected Value~10m

Each round you roll two fair $6$ -sided dice and note the two faces shown. What is the expected number of rounds until every one of the $6$ faces has appeared at least once? Round to two decimal places.

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Inclusion–exclusion: $\mathbb{E}[N]=\sum_{k=1}^6(-1)^{k+1}\binom6k\frac{1}{1-q_k}$ with $q_k=((6-k)/6)^2$ (a round avoiding a fixed $k$ -set).
Sum the six terms; it comes to $\approx 7.60$ (not $14.7/2$ ).

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7.6 (± 0.01)

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Rounds to see all faces with two dice

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