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General Tabletop Discussion
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The math of Advantage and Disadvantage
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<blockquote data-quote="WhosDaDungeonMaster" data-source="post: 7524165"><p>Actually, this error the OP made was in interpreting the % Diff. In his table (which is very nice and thorough), it seems he is simply subtracting the probabilities and assumes dividing the difference by 5% yields the effective +/- adjustment that advantage and disadvantage would give.</p><p></p><p>That was his error and oversimplification, but it really is a minor point as the result is close enough. The proper interpretation is in comparing the probability of success for a single roll without the advantaged probability.</p><p></p><p>For example, if the target number is 11, the normal probability is 50%. With advantage, it is 75%. So, what number for a single die roll would give you at least a 75% chance for success? A 6.</p><p></p><p>What does that mean? If you had the choice between rolling for an 11 with Advantage or a single roll for 11 with a +5 modifier (i.e. a 6), your chances for success would be the same.</p><p></p><p>Look at another example. The OP's table shows a target number of 8 has a 65% of success. With advantage, it is 87.75%. What target number has AT LEAST an 87.75% chance? A 3. So a single roll of 3 has at least as good a chance of success as an 8 with advantage. Or, another +5. Note: a single roll of 4 will not be as good as having advantage in this case, so the minimum modifier that would represent the benefit of advantage as +5 in this case.</p><p></p><p>At the other end of the spectrum, consider a target number of 18 with a 15% chance for success. With advantage, that increases to 27.75%. What number as a single roll has at least a 27.75% chance of success? A 15. A single roll with an additional +3 that targets 18 is slightly better than rolling for 18 with advantage.</p><p></p><p>Now, in all these examples, the division of the % Diff by 5% (the OP's approach) yields roughly the same numbers, especially when one considers rounding due to discrete results. But, understanding how these numbers should really be compared is a bit more complex.</p></blockquote><p></p>
[QUOTE="WhosDaDungeonMaster, post: 7524165"] Actually, this error the OP made was in interpreting the % Diff. In his table (which is very nice and thorough), it seems he is simply subtracting the probabilities and assumes dividing the difference by 5% yields the effective +/- adjustment that advantage and disadvantage would give. That was his error and oversimplification, but it really is a minor point as the result is close enough. The proper interpretation is in comparing the probability of success for a single roll without the advantaged probability. For example, if the target number is 11, the normal probability is 50%. With advantage, it is 75%. So, what number for a single die roll would give you at least a 75% chance for success? A 6. What does that mean? If you had the choice between rolling for an 11 with Advantage or a single roll for 11 with a +5 modifier (i.e. a 6), your chances for success would be the same. Look at another example. The OP's table shows a target number of 8 has a 65% of success. With advantage, it is 87.75%. What target number has AT LEAST an 87.75% chance? A 3. So a single roll of 3 has at least as good a chance of success as an 8 with advantage. Or, another +5. Note: a single roll of 4 will not be as good as having advantage in this case, so the minimum modifier that would represent the benefit of advantage as +5 in this case. At the other end of the spectrum, consider a target number of 18 with a 15% chance for success. With advantage, that increases to 27.75%. What number as a single roll has at least a 27.75% chance of success? A 15. A single roll with an additional +3 that targets 18 is slightly better than rolling for 18 with advantage. Now, in all these examples, the division of the % Diff by 5% (the OP's approach) yields roughly the same numbers, especially when one considers rounding due to discrete results. But, understanding how these numbers should really be compared is a bit more complex. [/QUOTE]
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