In Dungeons and Dragons, players roll dice to resolve actions. The iconic d20 determines whether an attack hits, a skill check succeeds, or a saving throw holds.
Most of the time a single d20 is rolled against a target number. The dungeon master sets the difficulty: a creature’s armor class for attacks, a skill check DC for abilities. If the roll meets or exceeds the target, the player succeeds.
But sometimes the player gets an advantage. Instead of rolling one d20, they roll two and take the higher result. This is supposed to model favorable circumstances — attacking a prone enemy, sneaking while unseen, having the high ground.
How much does advantage actually help? Let’s simulate it.
A single d20
A d20 is a uniform distribution from 1 to 20. Each outcome is equally likely. The expected value is 10.5.
The histogram is flat — every number from 1 to 20 appears about 5% of the time. The mean is 10.5, the median is 10.5, the min is 1, the max is 20. Nothing surprising.
Rolling with advantage
Now roll two dice and take the higher number.
The shape is completely different. Low results are nearly impossible — rolling a 1 with advantage requires both dice to land on 1, which happens 1 in 400 times. High results are much more likely. The average jumps from 10.5 to about 13.8.
About 50% of advantage rolls are 14 or higher. The median is somewhere around 15.
Understanding advantage through weapon modifiers
As a DM, when you offer advantage, what is it like doing?
I would say its somewhat like giving the character a +3 magic weapon or other piece of equipment.
We can understand this by modeling out 3 scenarios:
- A basic d20 roll against a variety of AC
- A d20 roll with a +3 magic weapon modifier
- An advantage roll without a modifier
For most target numbers, advantage wins. The +3.3 average bump is better than a flat +3 modifier, and the reduced chance of a low roll is a nice bonus.
But advantage does appear to be weaker on boundary conditions. The maximum roll with advantage is still 20. You can’t exceed the die’s natural range. Against very high AC, a flat modifier can outperform advantage around the boundary.
I say around the boundary because once the AC has eclipsed the reachable area of the modified roll, advantage takes over again due to the double chance of rolling a natural 20, which always hits.
Here’s the simulated probabilities of hitting across different ACs and strategies: