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Hypothetical Statistics Question
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<blockquote data-quote="Amaroq" data-source="post: 1897245" data-attributes="member: 15470"><p>As noted above, all different.</p><p></p><p>d9 + 2 generates an equal, 1 in 9 chance of rolling each of the numbers you're looking for. The distribution curve is a flat line.</p><p></p><p>d4 + d6 + 1 generates a flat-capped distribution curve;</p><p>3: 1 in 24</p><p>4: 2 in 24</p><p>5: 3 in 24</p><p>6: 4 in 24</p><p>7: 4 in 24</p><p>8: 4 in 24</p><p>9: 3 in 24</p><p>10: 2 in 24</p><p>11: 1 in 24</p><p>In other words, your people are most likely to roll a 6, 7, or 8 (half the time, total), and least likely to roll a 3 or 11 (once in 24 rolls, each)</p><p></p><p>2d5 + 1 will generate a fairly similar curve, but with a peak at 7:</p><p>3: 1 in 25</p><p>4: 2 in 25</p><p>5: 3 in 25</p><p>6: 4 in 25</p><p>7: 5 in 25</p><p>8: 4 in 25</p><p>9: 3 in 25</p><p>10: 2 in 25</p><p>11: 1 in 25</p><p></p><p>You can figure out each curve by counting the number of ways in which you can roll any given number; the 'in N' is calculated by multiplying each of the terms after a 'd' in them:</p><p>For example, for d4 + d6 + 1, the 'in N' is (4 * 6), or 24.</p><p>The '3' in d4 + d6 + 1 can only be acheived if both the d4 and the d6 show 1. That's 'one way' out of (4 * 6) possibilities, or 1 in 24.</p><p>The '4' can only be achieved if either [the d6 shows 1 and the d4 shows 2], or [the d4 shows 1 and the d6 shows 2]; that's 2 ways, or 2 in 24. </p><p>Etc.</p><p></p><p>The question 'which is most fair to all parties involved' is fairly meaningless without something to compare it to. If you decide to create two creatures, each doing 3-11 points, and one uses d9 + 2 and the other uses d4+d6+1, is it fair? The former does his 'extreme' results more frequently, while the other does the 'average' results more frequently, but the odds of one doing more damage than the other in any given roll should be the same.</p><p></p><p>What you're left with is 'what do you prefer'? Would you rather have a large amount of random variance in the utility of this spell or monster? If so, choose d9 + 2. Would you rather have the largest amount of 'predictability'? If so, choose 4d3 - 1. Would you rather have a mixture of the two, with some predictability but a reasonable chance of extreme result? Then 2d5+1 might be 'right' for you. Another concern is 'how easy is it to roll'? Eh, d4+d6+1 is close enough to 2d5+1 for me, plus there's no odd division or rerolls to slow down calculation of the total. I'll just use that.</p><p></p><p>Of course, our question back to you is, why not use 2-12 and good ol' 2d6? <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=":)" /></p></blockquote><p></p>
[QUOTE="Amaroq, post: 1897245, member: 15470"] As noted above, all different. d9 + 2 generates an equal, 1 in 9 chance of rolling each of the numbers you're looking for. The distribution curve is a flat line. d4 + d6 + 1 generates a flat-capped distribution curve; 3: 1 in 24 4: 2 in 24 5: 3 in 24 6: 4 in 24 7: 4 in 24 8: 4 in 24 9: 3 in 24 10: 2 in 24 11: 1 in 24 In other words, your people are most likely to roll a 6, 7, or 8 (half the time, total), and least likely to roll a 3 or 11 (once in 24 rolls, each) 2d5 + 1 will generate a fairly similar curve, but with a peak at 7: 3: 1 in 25 4: 2 in 25 5: 3 in 25 6: 4 in 25 7: 5 in 25 8: 4 in 25 9: 3 in 25 10: 2 in 25 11: 1 in 25 You can figure out each curve by counting the number of ways in which you can roll any given number; the 'in N' is calculated by multiplying each of the terms after a 'd' in them: For example, for d4 + d6 + 1, the 'in N' is (4 * 6), or 24. The '3' in d4 + d6 + 1 can only be acheived if both the d4 and the d6 show 1. That's 'one way' out of (4 * 6) possibilities, or 1 in 24. The '4' can only be achieved if either [the d6 shows 1 and the d4 shows 2], or [the d4 shows 1 and the d6 shows 2]; that's 2 ways, or 2 in 24. Etc. The question 'which is most fair to all parties involved' is fairly meaningless without something to compare it to. If you decide to create two creatures, each doing 3-11 points, and one uses d9 + 2 and the other uses d4+d6+1, is it fair? The former does his 'extreme' results more frequently, while the other does the 'average' results more frequently, but the odds of one doing more damage than the other in any given roll should be the same. What you're left with is 'what do you prefer'? Would you rather have a large amount of random variance in the utility of this spell or monster? If so, choose d9 + 2. Would you rather have the largest amount of 'predictability'? If so, choose 4d3 - 1. Would you rather have a mixture of the two, with some predictability but a reasonable chance of extreme result? Then 2d5+1 might be 'right' for you. Another concern is 'how easy is it to roll'? Eh, d4+d6+1 is close enough to 2d5+1 for me, plus there's no odd division or rerolls to slow down calculation of the total. I'll just use that. Of course, our question back to you is, why not use 2-12 and good ol' 2d6? :) [/QUOTE]
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