What the mechanic does
An advantage mechanic is simple to state. You roll the same die twice and keep the higher result. Disadvantage is the mirror image: roll twice and keep the lower one. Many tabletop role-playing games use this pair because it replaces a pile of small situational modifiers with one easy rule.
The interesting question is how much a second roll is actually worth. The answer depends on the die, and on what number you need.
The average result
Take a twenty-sided die. A single roll has an average of 10.5. When you roll two and keep the higher, each value from 1 to 20 is no longer equally likely. The chance that the higher die shows exactly k is (2k - 1) / 400, so a 1 has a 1 in 400 chance and a 20 has 39 chances in 400.
Weighting each value by that chance, which is the same expected value calculation used elsewhere, gives an average of about 13.8 (exactly 13.825). Disadvantage is symmetric, so the keep-lower average is about 7.2 (exactly 7.175). The two figures sit on either side of 10.5 by the same distance, roughly 3.3 points.
The same pattern appears on a six-sided die. A single d6 averages 3.5, keeping the higher of two averages about 4.47 and keeping the lower about 2.53. That is a shift of roughly 1 point, which is a larger share of the die’s range than the d20 shift is.
Success chances at different targets
Averages hide the useful detail. Most rolls in a game are a check against a target, so what matters is the chance of meeting it. The two dice are independent events, so with keep-higher you fail only if both dice fail, which keeps the arithmetic straightforward. The same logic gives the probability of at least one success among several tries.
For a check that needs 11 or higher on a d20:
- Single roll: 50%
- Advantage: 1 - 0.5 x 0.5 = 75%
- Disadvantage: 0.5 x 0.5 = 25%
For a target of 15 or higher, a single roll succeeds 30% of the time (6 faces out of 20). Advantage gives 1 - 0.7 x 0.7 = 51%, and disadvantage gives 0.3 x 0.3 = 9%.
For a target of 20, a single roll is 5%. Advantage gives 1 - 0.95 x 0.95, which is 9.75%, and disadvantage gives 0.25%. The absolute gain here is under 5 percentage points, even though the chance almost doubles in relative terms.
Comparing it to a flat bonus
On a d20, each +1 modifier moves a target by 5 percentage points as long as the target is not at an extreme. Advantage turns a 50% check into 75%, a gain of 25 points. That is like a +5 bonus at the middle of the range.
The comparison changes as targets get easier or harder. At a 30% chance, advantage adds 21 points, which is about +4. At 5%, it adds 4.75 points, which is under +1. So advantage is strongest when the outcome is closest to a coin flip and weakest when the check is nearly impossible or nearly certain. A flat bonus, by contrast, keeps the same value across the middle of the range and only runs out at the ends.
The “about +3.3” figure from the averages is the effect on the mean. The “about +5” figure is the effect on a coin-flip check. Both are correct; they answer different questions, and neither should be treated as the single value of advantage.
Rare results and criticals
Advantage also changes how often extremes appear. The chance of at least one natural 20 across two dice is 9.75%, nearly double the single-roll 5%. The chance of rolling a natural 1 with advantage drops to 0.25%, since both dice must show a 1. Systems with critical hits are therefore affected too: advantage makes them more frequent, and disadvantage makes them rarer.
This matters when a rule gives a special effect on a top result. A character who often has advantage will trigger it noticeably more, and that interacts with how the designer intended damage to scale.
Why stacking does not stack
Most advantage systems say that multiple sources of advantage do not add up. That is partly a bookkeeping choice, but the math supports it. Rolling three dice and keeping the highest gives a d20 average of about 15.5 (exactly 15.4875), only about 1.7 above the two-dice figure. Returns shrink with each extra die, so a cap at two dice avoids runaway results.
Many games also let advantage and disadvantage cancel out, regardless of how many of each apply. This keeps play fast, though it is a simplification: two sources of one against a single source of the other would net out to one in a purely additive model, but the rule collapses it to a plain roll.
What to take from the numbers
- Advantage is worth the most when your chance is near 50% and the least when it is near 0% or 100%.
- The shift in the average on a d20 is about 3.3 either way.
- Extremes become noticeably more or less common, so any rule tied to a top or bottom result changes in value.
- Results from one session will not match these figures neatly, because short-run results wander well away from the averages.
For a quick check of your own table, you can build a dice spreadsheet by listing all 400 pairs of d20 results. That makes the distribution easy to see and confirms the numbers above.