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<blockquote data-quote="AaronOfBarbaria" data-source="post: 6804610" data-attributes="member: 6701872">The margin of error can be quite extreme, given that a particular session is a very small sample size and thus not actually very likely to represent the norm - I mean, I just popped over to a batch dice rolling website and had it roll 20d20 for me, which I find to be a believable number of d20 rolls made by a single player in a 4 hour session of D&amp;D (give or take time spent on non-game activities like laughing, sharing tales of life over the last week, and so forth). The results are nearly spot on with the statistically expected average, since the 20 rolls average to 10.55... but the 5th, 9th, and 16th rolls were natural 20s (and the 12th roll was a 19, so I might have scored four critical hits in the session depending on if those particular rolls happened to be attack rolls or not and I was playing a Champion).If you think I comitted the gambler's fallacy, you didn't read me correctly - I didn't say that rolling badly one session gets made up for down the line; I said any particular session could trend low, could trend high, or could manage to trend right along the expected statistical values, and people forget that when they assume trending along the expected values is the only possible outcome.</blockquote>

[QUOTE="AaronOfBarbaria, post: 6804610, member: 6701872"] The margin of error can be quite extreme, given that a particular session is a very small sample size and thus not actually very likely to represent the norm - I mean, I just popped over to a batch dice rolling website and had it roll 20d20 for me, which I find to be a believable number of d20 rolls made by a single player in a 4 hour session of D&D (give or take time spent on non-game activities like laughing, sharing tales of life over the last week, and so forth). The results are nearly spot on with the statistically expected average, since the 20 rolls average to 10.55... but the 5th, 9th, and 16th rolls were natural 20s (and the 12th roll was a 19, so I might have scored four critical hits in the session depending on if those particular rolls happened to be attack rolls or not and I was playing a Champion). If you think I comitted the gambler's fallacy, you didn't read me correctly - I didn't say that rolling badly one session gets made up for down the line; I said any particular session could trend low, could trend high, or could manage to trend right along the expected statistical values, and people forget that when they assume trending along the expected values is the only possible outcome. [/QUOTE]

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