Dice Probability Explained: 2d6, 4d6 Drop Lowest, Advantage and More

Whether you're playing a tabletop RPG or balancing your own game, the shape of a dice distribution matters as much as its average.

One die vs several

A single d20 is flat: every number from 1 to 20 has a 5% chance. Add several dice and the results bunch in the middle. 3d6 also ranges from 3 to 18, but 10 and 11 come up 12.5% of the time each, while 3 and 18 come up less than 0.5% of the time. Designers use this: one big die means swingy results; several small dice mean predictable ones.

4d6, drop the lowest

The classic way to roll ability scores: roll four d6 and keep the highest three (4d6kh3). It averages 12.24 instead of 10.5 for 3d6, and 18s become about 1.6% likely instead of 0.5%.

Advantage and disadvantage

Roll 2d20 and keep the higher (2d20kh1) or the lower (2d20kl1). Advantage raises the average from 10.5 to about 13.8. Its real effect depends on the target: needing 15 or more, a single d20 succeeds 30% of the time; with advantage, 1 − 0.7² = 51%. Near the middle of the range, advantage is worth roughly +5; at the extremes much less.

Calculating it yourself

Type any expression into the dice probability calculator: 2d6, 1d20+5, 1d8+1d6+3, 4d6kh3, d%. It computes the exact distribution (not a simulation), the average and standard deviation, and highlights the chance of meeting a target.

For game designers

• Use the standard deviation to compare swinginess between options.
• Check the chance of the worst outcomes, not only the average — players remember failures.
• For random drops rather than rolls, the drop rate calculator answers "how many tries until it appears?".