Dice math – Advantage

I thought a little about Advantage in DnD5e and here’s a very short post about it. Advantage is quite simple. If a roll is made with advantage, the player rolls two d20s and takes the higher number as the result. Disadvantage reverses the situation and the player rolls two d20s and takes the lower number.

Having an advantage increases the expected result by about 3.3 and disadvantage decreases the expected result by 3.3. This isn’t too surprising, since probabilities of a disadvantage roll are just mirrored from advantage – i.e. probability of getting 1 with advantage is the same as probability of getting 20 with disadvantage. This mirroring is quite nicely illustrated by the probability distributions.

Another consequence of this is that opposed tests of advantage vs normal and normal vs disadvantage are also identical.

Finally, if both parties have advantage (or disadvantage), the difference of the rolls is likely to be smaller than when both parties would roll normally. Thus, the situation where both parties have advantage or disadvantage is very much different from a ‘normal’ confrontation!

I hope these were illustrative. In the end, the behavior makes sense, but at least I hadn’t really thought about this.



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