Advantage is a curve trick
Rolling twice and keeping the better result is not a flat bonus — it shifts the curve, and the shift is wildest in the middle.
01The bonus that moves
When a system tells you to roll two dice and take the higher, it feels like a straightforward improvement. It is, but the improvement is not evenly distributed across the die's range.
How the probability shifts
- 01On a d20, advantage gives the largest boost (~25 percentage points) when the target number sits near the middle of the range (around 10–11)
- 02At the extremes (needing a 2 or a 20), the benefit approaches zero — near-certainties and near-impossibilities are almost unchanged
- 03The average equivalent flat bonus is roughly +3 to +4, but that average obscures the uneven distribution
On a d20, rolling with advantage means the probability of hitting any target number follows the formula 1 − (chance of failing both rolls). Near the extremes — needing a 2 or needing a 20 — the effect is almost nothing. You were nearly certain to hit a 2 anyway; you were nearly certain to miss a 20. Advantage cannot rescue you from impossibility or ruin a near-certainty. In the middle of the range, around targets of 10 or 11, the boost is at its largest: roughly twenty-five percentage points (for example 50% rises to 75%) of extra success probability compared to rolling once. That is where the curve has the most room to move.
This has real mechanical consequences. When difficulty numbers are calibrated for a single roll, advantage shifts the effective target down by somewhere between three and four pips on average — but that average hides the fact that a character facing hard tasks gets less benefit than one facing middling ones. Advantage helps most where it matters least and least where it matters most.
A second advantage roll moves the needle far less than the first, because the first already skimmed the best outcomes from the pool.
It also means that stacking advantage adds very little. Most systems sensibly rule that two sources of advantage don't combine, and the math agrees — you can take three dice and keep the best, but the gain over two dice is much smaller. A second advantage roll moves the needle far less than the first, because the first already skimmed the best outcomes from the pool.
What stacking does
- 01A second source of advantage adds almost nothing to the first — the mechanism has already harvested the best outcomes from the pool
- 02This is why most systems correctly rule that multiple advantage sources do not compound
The mirror mechanism, disadvantage, is identical in shape: maximum cost in the middle, near-zero cost at the extremes. A character who needs exactly a 20 is barely punished by disadvantage; a character who usually hits on a 7 or better suddenly feels real pain.
What advantage actually does, then, is compress the useful range of the die toward success — not uniformly, but in a bulge around the midpoint. That is a curve trick, not a flat tax.