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(Discussion) Character Points Change Issue
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<blockquote data-quote="orsal" data-source="post: 1597274" data-attributes="member: 16016"><p>I very much doubt that anybody ever ran a program on all 6^24 possible sets of die rolls. If you could check a million every second, you'd have to run the computer nonstop for 150 thousand years to do that. Neither D&D nor high-speed computing have been around that long. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite1" alt=":)" title="Smile :)" loading="lazy" data-shortname=":)" /> </p><p></p><p>However, for a straight 4d6, drop lowest, no exchanges or refunds, you don't need to consider 6 ability scores at once. Just consider a single ability score. There are only 1296 combinations, and very crude programs can handle that. (That's how I did the spreadsheet I mentioned earlier.) You can then get a distribution for either score on the 3-18 scale or point buy count for a single ability; find its average, and multiply by 6 to get the average for a whole character. The average points come out to 29.13 if you count everything less than 8 as 0 points, 28.71 if you count negative points (between -1 and -5) for lower scores.</p><p></p><p>If you get into a "reroll the whole character if you don't get something at least this good overall" formula, it becomes more complicated, because you can't consider each of the six attributes in isolation anymore. That's when you need to know a little mathematics. It would be fairly simple to tweak the spreadsheet to calculate averages for a "reroll if no attribute is above X" rule, but rather harder for a "total must be at least Y" rule if you want to be exact. (An approximation, however, shouldn't be too difficult with a little basic statistics, which I sometimes teach so I should be able to do it.)</p></blockquote><p></p>
[QUOTE="orsal, post: 1597274, member: 16016"] I very much doubt that anybody ever ran a program on all 6^24 possible sets of die rolls. If you could check a million every second, you'd have to run the computer nonstop for 150 thousand years to do that. Neither D&D nor high-speed computing have been around that long. :) However, for a straight 4d6, drop lowest, no exchanges or refunds, you don't need to consider 6 ability scores at once. Just consider a single ability score. There are only 1296 combinations, and very crude programs can handle that. (That's how I did the spreadsheet I mentioned earlier.) You can then get a distribution for either score on the 3-18 scale or point buy count for a single ability; find its average, and multiply by 6 to get the average for a whole character. The average points come out to 29.13 if you count everything less than 8 as 0 points, 28.71 if you count negative points (between -1 and -5) for lower scores. If you get into a "reroll the whole character if you don't get something at least this good overall" formula, it becomes more complicated, because you can't consider each of the six attributes in isolation anymore. That's when you need to know a little mathematics. It would be fairly simple to tweak the spreadsheet to calculate averages for a "reroll if no attribute is above X" rule, but rather harder for a "total must be at least Y" rule if you want to be exact. (An approximation, however, shouldn't be too difficult with a little basic statistics, which I sometimes teach so I should be able to do it.) [/QUOTE]
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