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It's a Wand! It's a Crossbow Bolt! It's a Floor Wax!
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<blockquote data-quote="babomb" data-source="post: 2639628" data-attributes="member: 1316"><p>Maybe. Arguably, there's no meaning to saying the median is a result that is impossible to occur. I looked on the 'Net only briefly, and didn't see a better approach, but I don't doubt that there is one. Still, I believe the results are a reasonable approximation. A real mathematician might get mad at me, but sometimes close enough is close enough.</p><p></p><p></p><p></p><p>Brute force isn't pretty, but it always works, at least. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink ;)" data-smilie="2"data-shortname=";)" /> </p><p></p><p></p><p></p><p>A 5d10 wand would have a median of 46.3745. The most probable outcomes are 40 and 41, occuring 2.05887% of the time each. There is over a 20% chance for the wand to be in the range [37,46], so it is less of a gamble.</p><p></p><p></p><p></p><p>Yes, I think so. It has a slightly higher median than the d20-d12-d10-d8 variety (44.7765) and a slightly smaller standard deviation, but still pretty high. You'll get pretty much the same results with either. </p><p></p><p>While the PCs can be sure there's a reasonable amount of charges most of the time (over 91% have at least 23 uses), there's enough variability to create some anxiety/excitement, and that builds as the wand dies down (pun intended). The most probable result is 36, with 1.96235%. And, given a sufficient number of wands, the mean charges per wand will be about 50. So, yes, I believe such wands would have the desired effect.</p></blockquote><p></p>
[QUOTE="babomb, post: 2639628, member: 1316"] Maybe. Arguably, there's no meaning to saying the median is a result that is impossible to occur. I looked on the 'Net only briefly, and didn't see a better approach, but I don't doubt that there is one. Still, I believe the results are a reasonable approximation. A real mathematician might get mad at me, but sometimes close enough is close enough. Brute force isn't pretty, but it always works, at least. ;) A 5d10 wand would have a median of 46.3745. The most probable outcomes are 40 and 41, occuring 2.05887% of the time each. There is over a 20% chance for the wand to be in the range [37,46], so it is less of a gamble. Yes, I think so. It has a slightly higher median than the d20-d12-d10-d8 variety (44.7765) and a slightly smaller standard deviation, but still pretty high. You'll get pretty much the same results with either. While the PCs can be sure there's a reasonable amount of charges most of the time (over 91% have at least 23 uses), there's enough variability to create some anxiety/excitement, and that builds as the wand dies down (pun intended). The most probable result is 36, with 1.96235%. And, given a sufficient number of wands, the mean charges per wand will be about 50. So, yes, I believe such wands would have the desired effect. [/QUOTE]
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It's a Wand! It's a Crossbow Bolt! It's a Floor Wax!
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