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Message: <blockquote data-quote="Spatzimaus" data-source="post: 2669448" data-attributes="member: 3051">nycdan, as we explained before, simply adding the 50% expectation value (i.e., the median) for each individual die DOES NOT WORK.  It's a variation on the Central Limit Theorem; the more dice you add to the chain, the closer the median approaches the mean.  And the mean number of rolls for an individual die is simply the number of sides on the die; the mean on a d20 is 20, on a d12 is 12, and so on.The reason for this is the distributions aren't symmetric; while the median falls at 14ish on the d20, and 8ish on the d12, the distributions skew to the high side; that is, if one of the two dice goes high, it'll go high by a larger margin than a die that goes low could possibly make up for.  As a result, the median of the sum is higher than the sum of the medians, both of which are less than the sum of the means.And scottin, the equation isn't Random(20) + Random(12) + Random (10) + Random(8).  That's just the wrong math.  You're not equally likely to run out of d20 charges in 1 as 20, and it's possible to go higher than 20.It's nice that you're both trying to help with the math on this, and more feedback is always good, but you're making math mistakes that we discussed in this thread two weeks ago.  The math behind the medians we gave has been proven both explicitly (working all possible combinations) and iteratively (running millions of test cases).And Thaniel: That's very strange, because you should have had at LEAST one wand go for 100 or more charges, assuming your dice aren't biased in any way.  I suppose you could have just been unlucky on the rolling, but to have NONE of your wands last longer than 36 implies to me that your d20 is a bit iffy, since it's really the most important die in this process.  Ever tested it?  (This isn't an idle point.  One of my d20s rolls a LOT of natural 20s, well above 5%.  Naturally, as of 3E it's now my favorite.)Primitive Screwhead: Which die progression are you using?The simplest way is to price it by the mean.  That is, if you're using the 20-12-8-6-4 progression (which I feel is the best, and has a mean of 50), then it'd go like this:All five charges still in: 100%d20 gone: 60%d12 gone: 36%d8 gone: 20%d6 gone: 8%d4 gone: BOOM!And if you included a way to repair, just move back up a step.  You could price by median, in which case we'd need to rederive the medians for the 4-, 3-, and 2-step progressions (the final 1-step is easy).  But it's really not worth it.Now, IMC we have "expended" wands and staff still retain 50% of their original value (the expensive materials, which can be salvaged), which changes this as you'd expect.</blockquote>

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