MATH & DICE
RPG dice probability: d20, 2d6 and advantage
A fair roll does not make every total equally likely. The distribution depends on the number of dice and the modifiers.
One uniform die
For an ideal d20, each face has probability 1/20, or 5%. A result of 15 or higher covers six faces: 6/20, or 30%. The theoretical mean is (1+20)/2 = 10.5.
Adding +5 changes the total, not the chance of each face. To meet difficulty 15 with d20+5, a natural 10 or higher suffices: 11/20, or 55%.
d20+5Try in playground ↗Two dice make a curve
2d6 has 36 equally likely ordered pairs. Six pairs total 7, so P(7) = 6/36 = 16.67%. Only one pair totals 2 and one totals 12: each has probability 1/36 = 2.78%.
That is why 2d6 clusters around the middle while a single d12 spreads its faces evenly.
2d6Try in playground ↗Advantage changes the distribution
Keeping the higher of two d20s gives a 1 − (14/20)² = 51% chance of at least 15. This is different from adding a fixed bonus.
Use the modifier that matches your game rule. Dice Core resolves the expression; mathematics helps interpret its odds.
2d20kh1Try in playground ↗Sources and references
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