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<blockquote data-quote="pemerton" data-source="post: 8792867" data-attributes="member: 42582">I'm not [USER=72555]@NotAYakk[/USER], but I think you've misunderstood the claim.NO ONE in this thread thinks that rolling 3d6 and rolling d20 produces the same likelihood of success against a given target number.Rather, the claim is that there is a simple single-die roll that produces much-the-same likelihood of success against a given target number as 3d6 does. Hence changing the spread of results from a linear distribution (which is what a single-die roll gives) to a curved distribution (which is what 3d6 does) has no real relevance to game play. Because you can get almost identical play with a single die roll.One simple single-die roll that will produce much the same likelihoods as 3d6 is 1d10+5 - in the following list, the values are Target Number, percentage likelihood of meeting or exceeding that target number rolling 3d6, percentage likelihood of meeting or exceeding that target number rolling 1d10+5:[code]3 or lower&nbsp; &nbsp; 100&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1004&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 99.5&nbsp; &nbsp; &nbsp; &nbsp; 1005&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 98.1&nbsp; &nbsp; &nbsp; &nbsp; 1006&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 95.4&nbsp; &nbsp; &nbsp; &nbsp; 1007&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 90.7&nbsp; &nbsp; &nbsp; &nbsp; 908&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 83.8&nbsp; &nbsp; &nbsp; &nbsp; 809&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 74.1&nbsp; &nbsp; &nbsp; &nbsp; 7010&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 62.5&nbsp; &nbsp; &nbsp; &nbsp; 6011&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 50&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 5012&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 37.5&nbsp; &nbsp; &nbsp; &nbsp; 4013&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 25.9&nbsp; &nbsp; &nbsp; &nbsp; 3014&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 16.2&nbsp; &nbsp; &nbsp; &nbsp; 2015&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 9.3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1016&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4.6&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 017&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1.9&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 018&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0.5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0[/code]There is a marked difference only at the extremes, that is the results that are less than 5% likely on 3d6 (ie rolls of 3, 4 5 on 3d6, which fail against target numbers of 4, 5 and 6 respectively; and rolls of 16, 17, and 18 which succeed against those target numbers respectively).As was noted in the OP, and has been reiterated since, these correspond (roughly) to the 1 and 20 results on a d20, which in D&amp;D games are often given special treatment in any event (eg auto-fail or auto-success). You could get much the same result as this in play using some sort of exploding-dice-on-a-10 result.</blockquote>

[QUOTE="pemerton, post: 8792867, member: 42582"] I'm not [USER=72555]@NotAYakk[/USER], but I think you've misunderstood the claim. NO ONE in this thread thinks that rolling 3d6 and rolling d20 produces the same likelihood of success against a given target number. Rather, the claim is that [i]there is a simple single-die roll[/i] that produces much-the-same likelihood of success against a given target number as 3d6 does. Hence changing the spread of results from a linear distribution (which is what a single-die roll gives) to a curved distribution (which is what 3d6 does) has no real relevance to game play. Because you can get almost identical play with a single die roll. One simple single-die roll that will produce much the same likelihoods as 3d6 is 1d10+5 - in the following list, the values are Target Number, percentage likelihood of meeting or exceeding that target number rolling 3d6, percentage likelihood of meeting or exceeding that target number rolling 1d10+5: [code] 3 or lower 100 100 4 99.5 100 5 98.1 100 6 95.4 100 7 90.7 90 8 83.8 80 9 74.1 70 10 62.5 60 11 50 50 12 37.5 40 13 25.9 30 14 16.2 20 15 9.3 10 16 4.6 0 17 1.9 0 18 0.5 0[/code] There is a marked difference only at the extremes, that is the results that are less than 5% likely on 3d6 (ie rolls of 3, 4 5 on 3d6, which fail against target numbers of 4, 5 and 6 respectively; and rolls of 16, 17, and 18 which succeed against those target numbers respectively). As was noted in the OP, and has been reiterated since, these correspond (roughly) to the 1 and 20 results on a d20, which in D&D games are often given special treatment in any event (eg auto-fail or auto-success). You could get much the same result as this in play using some sort of exploding-dice-on-a-10 result. [/QUOTE]

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