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What is the expected number of times one must throw two fair dice before all numbers from 2 to 12 have appeared at least once?

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    This sounds interesting. With one die its easy, see e.g. here: http://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf p.92011-05-31
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    What do you mean by "expected". In other words, at what probability threshold do you draw the line - the probability of all numbers appearing approaches, but never hits 1.2011-05-31
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    @crasic: You could reformulate it: On average, how many times must two 6-sided dice be rolled until all numbers from 2 to 12 appear at least once?2011-05-31
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    One approach would be to consider the probability transitions among states consisting of subsets of $\{2,...,12\}$ given by the chance of a new number appearing (given the previously obtained sums). This amounts to $2^{11} = 2048$ states to keep track of, easily reduced by half owing to symmetry, something a computer program could manage. One would get, for each number of rolls, the probability that all sums have appeared (an absorbing state). The expected number of rolls needed to reach the absorbing state could then be calculated numerically.2011-05-31
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    http://math.stackexchange.com/questions/25568/a-question-about-dice/25576#255762011-05-31

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