Dice Probability Calculator
Type any dice notation and see the exact odds of every total — worked out, not sampled. Handles advantage, keep-highest and modifiers.
Every total, and how likely it is
What the shape tells you
- These are exact probabilities, worked out rather than sampled. A simulated 5% and a real 5% are not the same claim.
- Advantage is worth about +3.3 on a d20 on average, but that average hides the shape: it is worth about a single point when you need a 2 or a 20, and a full +5 when you need an 11.
- A flat die makes every modifier worth the same amount. On a bell curve — 2d6, 3d6 — a +1 is worth far more in the middle of the range than at either end.
- Adding a modifier moves the whole curve and changes nothing about its shape. Adding a die changes the shape.
- Dropping the lowest of four dice raises the average from 10.5 to 12.24, and it also cuts the bottom off: a 3 becomes about 1 in 1,300 rather than 1 in 216.
- Notation:
3d6,d20+5,4d6kh3for keep-highest-three,2d20kl1for keep-lowest, or just the wordsadvantageanddisadvantage.
How to use
- Type notation like 3d6, d20+5, 4d6kh3, or the word advantage.
- Set a target number to see your chance of hitting it.
- Press Roll it for an actual roll, with dropped dice shown struck through.
Frequently asked questions
Are these odds simulated?
No — they are worked out exactly. A simulated 5% and a real 5% are not the same claim, and the difference matters when you are deciding whether a build works. Where an exact answer would take too long to compute, the tool says so and stops rather than quietly switching to a sample.
How much is advantage actually worth?
On average, exactly 3.325 on a d20 — but the average hides the useful part. It is worth almost nothing when you need a 2 or a 20, and a full 25 percentage points when you need an 11. That is why advantage matters most on the rolls that were already close.
Why does 4d6 drop lowest average 12.24?
Because throwing away the worst die pulls the whole distribution up, and it cuts the bottom off hard: rolling a 3 goes from 1 in 216 to 1 in 1,296. The exact average is 12.2446, against 10.5 for three straight dice.
Does a +1 always help the same amount?
On a d20, yes — every modifier is worth exactly 5%, because the die is flat. On a curve like 2d6 or 3d6 it is not: a +1 is worth far more in the middle of the range than at either end, because there are more outcomes there to move across the line.
What is the difference between adding a die and adding a modifier?
A modifier slides the whole curve sideways and changes nothing about its shape — the spread stays identical. Adding a die changes the shape, making the middle relatively more likely and the extremes rarer.
What notation is understood?
NdM with an optional modifier — 3d6, d20+5, 1d8-1 — plus kh and kl for keeping the highest or lowest dice, as in 4d6kh3 or 2d20kl1. The words advantage and disadvantage work too, since that is what people actually say.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.