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Message: <blockquote data-quote="NotAYakk" data-source="post: 8100348" data-attributes="member: 72555">I'm trying to break that asymmetry where the same roll is better with Handicap than Edge.Here is another stab at it:Edge: 2d20, take the higher one unless both are odd; then take the lower one.Handicap: 2d20, take the lower one unless both are even; then take the higher one.Edge is then 75% advantage 25% disadvantage, and vice versa for Handicap.Math:[spoiler]With a base probability of success of P, advantage is 1-(1-P)^2 or 2P-P^2.  Disadvantage is P^2.K advantage and (1-K) disadvantage is then K(2P-P^2) + (1-K)P^2 = 2KP - KP^2 + P^2 - KP^2 = 2KP + (1-2K)P^2.At K=0.5 this is P, aka no advantage or disadvantage.At K=1 this is 2P-P^2, aka advantage.At K=0 this is P^2, aka disadvantage.d/dK is 2P - 2P^2 = 2P(1-P).  This is always positive, and maximal at P=0.5 (where it is 1/2) and zero at P=1 and 0.What this means is that for any case besides certain failure/success, Advantage > Edge > Normal > Handicap > Disadvantage in terms of probability of success.By having double-odd be bad on Edge, it doesn't block crits; your crit chance is doubled.  Your natural 1 chance is halved over a normal roll.With advantage, your natural 1 chance is basically eliminated (1 in 400).Similarly, for Handicap, your natural 1 chance is doubled (just like disadvantage), and your crit chance is halved over a normal roll.With disadvantage, your crit chance is basically eliminated (1 in 400).This assumes crit on a 20; on a 19-20 the math changes a bit.Chance of a 20: 1- .95 * .95 = 9.75%.Chance of a 19 but not a 20: Die 1 lands on an even value that isn't 20 (9/20 chance) times die 2 lands on 19 (1/20), and vice versa (*2), for 18/400, plus double 19 (1/400).Total: 14.5%With real advantage it would be 19%.With a normal roll it would be 10%.Crit on a 18-20 with edge.Same for 20 and 19.For an 18 but not 19 or 20, it is die 1 on an 18, plus die 2 from 1 to 18, plus die 2 on 18 and die 1 from 1 to 17, for 35/400.Total is 23.25%.With real advantage it is 27.75%With a normal roll it is 15%again, about half way in between.[/spoiler]So a neutral roll is 50% advantage/50% disadvantage on this scale.I think I like this one better.  For a given roll, going up the Disadvantage -> Handicap -> (Skip Neutral) -> Edge -> Advantage always makes the roll better (well, no worse).  And unless you land on Neutral, the same roll can be interpreted as any of those.</blockquote>

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