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Message: <blockquote data-quote="Nifft" data-source="post: 3816953" data-attributes="member: 6562">Here's an easier way of thinking, to help us figure it out: What are the numbers that lead to your wand NOT burning out? That's all the numbers in the range 2-20, or a 0.95 probability. The chance of still having your wand after ONE use is 95%. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile    :)"  data-smilie="1"data-shortname=":)" />Now we can multiply out by the number of uses:2 tries = .95^2 = 0.9025 = 90.25%3 tries = .95^3 = 0.8574 = 85.74%4 tries = ... = 0.81455 tries = 0.77386 tries = 0.73517 tries = 0.6983...12 tries = 0.540413 tries = 0.513314 tries = 0.4877So your d20 die is expected to last ~14 charges. That's the half life of this phase of the wand's deterioration.Next we move on to the d12. Here we are happy with 2-12, which are 0.9166 of the available choices. We have only a 0.4985 chance of lasting through 8 uses.d10 is easy: 90% chance of success each try. We last 7 before hitting 0.4783.d8 lasts for 6 uses before sinking to 0.4488.d6 breaks .5 after 4 uses (4 tries = 0.4823).d4 is expected to last a mere 3 uses (3 tries = 0.421875).- - -So, we have 14 + 8 + 7 + 6 + 4 + 3 = roughly 42 expected charges. This is on the high side though, since I'm merely taking the highest integer below the 50% mark.An actual statistician could no doubt tell you lots more. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile    :)"  data-smilie="1"data-shortname=":)" />Cheers, -- N</blockquote>

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