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Why I Am Starting to Prefer 4d6 Drop the Lowest Over the Default Array.
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<blockquote data-quote="FormerlyHemlock" data-source="post: 7135240" data-attributes="member: 6787650"><p>Hey, hey, hey. I didn't say "in fundamental ways that I will quickly reverse-engineer." I'm not claiming to be a mathematical prodigy who can instantly reconstruct distributions based on a handful of samples from the distribution--I'm saying that a distribution consisting of normalized stats will feel hinky, especially if I'm actually doing the stat generation by drawing cards or whatnot. I do think I will notice a distribution which is normalized in obvious ways (such as your sum-to-74 thing), even if I'm just looking at the outputs from the distribution, but even then I might not know exactly what the similarity is ("they all sum to 74!")--I just think I'll be able to tell them from the real thing.</p><p> </p><p></p><p></p><p>I believe that was on a different topic. That was about someone trying to compare point-buy vs. rolled stats' overall utility/power levels--see recent discussion with Lanefan for another treatment of that topic.</p><p></p><p>To address your confusion directly: the space of all arrays that sum to 74 is a narrow slice of attribute space, and it would be boring to be confined to that space, but that doesn't mean that all arrays within that space have equivalent utility. Summing attribute totals is, IMO, a bad way to measure utility of the array. 3 + 18 play out very differently from 10 + 11, and have different utilities. 3 + 18 has nearly the same utility as 8 + 18 despite having different totals; but from a creative standpoint, 8 + 18 can sometimes be quite different from 3 + 18 and it would be a pity if it never occurred. E.g. I'll probably roleplay a Str 3 wizard quite differently from a Str 8 wizard--the Str 3 guy is probably ancient, or some sort of cripple--even though in terms of the actual die rolls you'd make during the game they are basically identical. But the hypothetical PCs themselves are quite different.</p><p></p><p></p><p></p><p>A method which gives arrays that always sum to 74 bores me, yes. Not interested.</p><p></p><p></p><p></p><p>Well, let's see. I accidentally looked at the source code for your first link, so I have to discount that one, but looking at the samples drawn from your second link, they all seem kind of homogenous, so I'm going to guess that they're not actually 4d6 drop lowest--I think they are normalized.</p><p></p><p>[a moment later, after looking at source code]</p><p></p><p>And, yep, they are. So I did quickly notice in this case.</p><p></p><p> If you were my DM and were just spitting out streams of stats, I don't know how long it would take me to catch on for absolute SURE that you weren't using 4d6 drop lowest, but judging from this experiment it appears I would have definite suspicions. The arrays produced are hinky.</p></blockquote><p></p>
[QUOTE="FormerlyHemlock, post: 7135240, member: 6787650"] Hey, hey, hey. I didn't say "in fundamental ways that I will quickly reverse-engineer." I'm not claiming to be a mathematical prodigy who can instantly reconstruct distributions based on a handful of samples from the distribution--I'm saying that a distribution consisting of normalized stats will feel hinky, especially if I'm actually doing the stat generation by drawing cards or whatnot. I do think I will notice a distribution which is normalized in obvious ways (such as your sum-to-74 thing), even if I'm just looking at the outputs from the distribution, but even then I might not know exactly what the similarity is ("they all sum to 74!")--I just think I'll be able to tell them from the real thing. I believe that was on a different topic. That was about someone trying to compare point-buy vs. rolled stats' overall utility/power levels--see recent discussion with Lanefan for another treatment of that topic. To address your confusion directly: the space of all arrays that sum to 74 is a narrow slice of attribute space, and it would be boring to be confined to that space, but that doesn't mean that all arrays within that space have equivalent utility. Summing attribute totals is, IMO, a bad way to measure utility of the array. 3 + 18 play out very differently from 10 + 11, and have different utilities. 3 + 18 has nearly the same utility as 8 + 18 despite having different totals; but from a creative standpoint, 8 + 18 can sometimes be quite different from 3 + 18 and it would be a pity if it never occurred. E.g. I'll probably roleplay a Str 3 wizard quite differently from a Str 8 wizard--the Str 3 guy is probably ancient, or some sort of cripple--even though in terms of the actual die rolls you'd make during the game they are basically identical. But the hypothetical PCs themselves are quite different. A method which gives arrays that always sum to 74 bores me, yes. Not interested. Well, let's see. I accidentally looked at the source code for your first link, so I have to discount that one, but looking at the samples drawn from your second link, they all seem kind of homogenous, so I'm going to guess that they're not actually 4d6 drop lowest--I think they are normalized. [a moment later, after looking at source code] And, yep, they are. So I did quickly notice in this case. If you were my DM and were just spitting out streams of stats, I don't know how long it would take me to catch on for absolute SURE that you weren't using 4d6 drop lowest, but judging from this experiment it appears I would have definite suspicions. The arrays produced are hinky. [/QUOTE]
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