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Message: <blockquote data-quote="babomb" data-source="post: 2635223" data-attributes="member: 1316">The problem with my previous approach was that it failed to take into account the combinatorics. For example, there is only one way to get a wand with 4 uses, but 4 ways to get a wand with 5 uses and 10 ways to get one with 6, and so on. The number of possiblities increases rapidly as you go upward, partly offsetting the decreased probability of each given permutation.Unfortunately, since different dice are involved, there doesn't seem to be a "nice" way to calculate this. So, I wrote a program that goes through each possiblity and calculates the probability. That is, for example, the program calculates the probability for each of the 4 ways to have a wand with 5 uses and adds them together. I have also made the algorithm general, so I can plug in any numbers and kinds of any dice I want and compute the result.I can't say for certain that it is entirely correct. However, I have verified that the computer counts the same number of possibilities predicted by the theory. In addition, in the degenerate case of exactly one die, it finds the same medians as I posted previously. So I think it's right. The algorithm is much too complicated to post here, but I can upload the source somewhere, if you want.Apparently, the wands in question have a median of 44.7449 uses. Adding just the d6 brings the median to 50.8943. Adding the d4 as well gives a median of 54.9645.By the way, the most probable result on the d20-d12-d10-d8 is 36 uses (1.85055%).</blockquote>

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