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<blockquote data-quote="Guest 6801328" data-source="post: 7483740">@<a href="http://www.enworld.org/forum/member.php?u=50987" target="_blank">CleverNickName</a>First, you don't need 10,000 columns, you need exactly 400: one for each of the 400 possible combinations, which have a perfectly even probability distribution.Second, the math (or logic) error you made was to assume the benefit is equal to the delta between the two values.&nbsp; 50% of the time the higher value would have been the result even without Advantage, and thus there's no benefit.Imagine two rolls with Advantage:The first produces an 8 and a 16The second produces a 10 and a 4You might say, &quot;That's an average of 7 (8 + 6 / 2) better!&quot;&nbsp; But if we take the first number to be the result of the &quot;first die&quot;, that is, the one you would have rolled if you didn't have Advantage, then it didn't help you on the second roll.&nbsp; So Advantage gave you a bonus of +8 in the first case and 0 in the second case, for an average bonus of 4 not 7.If you integrate this across all 400 possible combinations, it's the same as just dividing your result in half.&nbsp; EDIT: Yeah, this is effectively what Dausuul did.</blockquote>

[QUOTE="Guest 6801328, post: 7483740"] @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=50987"]CleverNickName[/URL][/U][/B][/I] First, you don't need 10,000 columns, you need exactly 400: one for each of the 400 possible combinations, which have a perfectly even probability distribution. Second, the math (or logic) error you made was to assume the benefit is equal to the delta between the two values. 50% of the time the higher value would have been the result even without Advantage, and thus there's no benefit. Imagine two rolls with Advantage: The first produces an 8 and a 16 The second produces a 10 and a 4 You might say, "That's an average of 7 (8 + 6 / 2) better!" But if we take the first number to be the result of the "first die", that is, the one you would have rolled if you didn't have Advantage, then it didn't help you on the second roll. So Advantage gave you a bonus of +8 in the first case and 0 in the second case, for an average bonus of 4 not 7. If you integrate this across all 400 possible combinations, it's the same as just dividing your result in half. EDIT: Yeah, this is effectively what Dausuul did. [/QUOTE]

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