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.
Running simulation (10,000 trials)...
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.
Running simulation (10,000 trials)...
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. Click the toggle below the histogram to switch between frequency and cumulative views.
About 50% of advantage rolls are 14 or higher. The median is somewhere around 15.
The boundary case
If the DM offered a choice between rolling with advantage and reducing the target number by 3, which is better?
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 there’s a catch. The maximum roll with advantage is still 20. You can’t exceed the die’s natural range. If the creature’s AC is 21, even a perfect advantage roll misses. Reducing the target by 3 gives you a chance — however small — that you simply don’t have with advantage.
And in D&D, a natural 20 always hits regardless of AC, and it doubles the damage dice. Advantage doubles the chance of a natural 20 (from 5% to 9.75%), which shifts the calculus for very high AC targets.
The right call depends on the specific numbers. But the general rule: advantage is almost always better against reachable targets, and a flat modifier is better when the target is out of range entirely.