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Message: <blockquote data-quote="ichabod" data-source="post: 1324540" data-attributes="member: 1257">This is a geometric distribution, which is a special case of the negative binomial distribution. The probability that X (the number of charges you get from the wand) is equal to x is q^(x-1)*p, where p is the probability that the wand is used up, and q = 1-p. According to my reference material*, the mean is q/p. So in your case the mean is 0.98/0.02 = 49. My reference gives the second moment as q/p^2, so the variance would be 49 also, giving you a standard deviation of about 7. By rule of thumb that means 2/3 of the wands will end up with between 42 and 56 charges, and only 1 in 20 will have less than 35 or more than 63.On the other hand, this is a pretty skewed distribution, so that isn't such a good rule of thumb. It turns out 1 in 20 wands will have 3 or less charges. 1 in 10 will have 6 or less. 1 in 4 will have 15 or less, 1 in 4 will have 69 or more, 1 in 10 will have 114 or more, and 1 in 20 will have 145 or more.That makes this probably not a good house rule.*Univariate Discrete Distributions, 2nd ed., Johnson, Kotz, and Kemp.</blockquote>