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average result from an open ended dice roll
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<blockquote data-quote="Nifft" data-source="post: 4361052" data-attributes="member: 6562"><p>Did this answer your question? It seems light on details.</p><p></p><p>Basically, when you roll two dice and take the maximum value, you're allowing large values to <u>cover</u> small values, which slants the distribution towards the high end.</p><p></p><p>Consider the case of max(2d20). You have 400 possible results, but if either die is a 20, the other die won't matter -- a roll of 20 "covers" all nineteen lesser values. This means there are 39/400 cases where the end result is 20, as opposed to 1/20 cases normally -- in percentage terms, you can expect max(2d20) to yield a 20 result 9.75% of the time, as opposed to 5% of the time.</p><p></p><p>Now, 4d6 drop lowest is more complicated to visualize because there are more thingies to track, but the slanting works similarly.</p><p></p><p>Cheers, -- N</p></blockquote><p></p>
[QUOTE="Nifft, post: 4361052, member: 6562"] Did this answer your question? It seems light on details. Basically, when you roll two dice and take the maximum value, you're allowing large values to [u]cover[/u] small values, which slants the distribution towards the high end. Consider the case of max(2d20). You have 400 possible results, but if either die is a 20, the other die won't matter -- a roll of 20 "covers" all nineteen lesser values. This means there are 39/400 cases where the end result is 20, as opposed to 1/20 cases normally -- in percentage terms, you can expect max(2d20) to yield a 20 result 9.75% of the time, as opposed to 5% of the time. Now, 4d6 drop lowest is more complicated to visualize because there are more thingies to track, but the slanting works similarly. Cheers, -- N [/QUOTE]
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