---
title: "Dice Probability Calculator: Exact Odds | Dice Parlor"
description: "Exact odds for any dice roll: 3d6+2, advantage (2d20kh1), 4d6 drop lowest, mixed dice. See every total, the average, and compare two rolls side by side."
url: https://diceparlor.me/
---

# Dice probability calculator

Type any roll and see the exact chance of every total: `3d6+2`, `2d20kh1` for advantage, `4d6dl1` for ability scores, or mixed dice like `d8+d6+3`.

## How to write a roll

Write dice the way most rulebooks do: the number of dice, a `d`, then the number of sides. Join parts with + and −; spaces and capitals don't matter. Dice can have 2 to 1,000 sides, with up to 100 in a group.

| You type | It means |
| --- | --- |
| 3d6 | three six-sided dice, added up |
| d20+5 | one twenty-sided die plus 5 |
| 2d20kh1 | roll two d20s and keep the higher (advantage) |
| 2d20kl1 | roll two d20s and keep the lower (disadvantage) |
| 4d6dl1 | roll four d6s and drop the lowest |
| d8+d6−1 | mixed dice and a modifier |
| d% | a percentile die, 1 to 100 |

Put a second roll in **Compare with** to set them side by side and see how often each one rolls higher. **Copy link** makes a link that opens this exact roll for anyone you send it to.

## How the odds are worked out

Nothing here is simulated. Added dice are *convolved*: the chance of each total of two dice is the sum, over every face of the first die, of the chance that the second die makes up the rest, and so on for each further die. For keep and drop rolls the calculator counts, with binomial coefficients, how many ways the dice can land for each kept total. Percentages are rounded only for display; the odds beside them (“1 in 6”) are the same numbers put another way.

## Sources

- Charles M. Grinstead and J. Laurie Snell, *Introduction to Probability*, 2nd edition (American Mathematical Society), §7.1 “Sums of Discrete Random Variables”: convolution, worked through with dice. A free edition under the GNU Free Documentation License is on [Dartmouth's site](https://math.dartmouth.edu/~prob/prob/prob.pdf).
- NIST Digital Library of Mathematical Functions, [§26.3 “Lattice Paths: Binomial Coefficients”](https://dlmf.nist.gov/26.3): the counting behind keep-highest and drop-lowest rolls.

## More tables in the parlour

Five more helpers for game night.

- [Dice pool calculator](https://diceparlor.me/dice-pool-calculator/): Roll a handful of dice and count the hits: the chance of at least so many successes, with exploding dice and rerolled ones.
- [Card draw odds](https://diceparlor.me/card-draw-odds/): The chance of drawing the cards you need, for several groups at once, in the opening hand and turn by turn.
- [Initiative tracker](https://diceparlor.me/initiative-tracker/): Turn order with tiebreaks, hit points and conditions; next and previous turn and a round counter, saved in your browser.
- [Point buy calculator](https://diceparlor.me/point-buy-calculator/): The 27-point buy and standard array from the 5th edition SRD, with ability modifiers and +2/+1 increases.
- [Turn timer & chess clock](https://diceparlor.me/turn-timer/): A turn timer for 2 to 8 players, or a chess clock with increments, with pause, sound and a screen that stays awake.

## Recommended

Two free services for gamers who shop and download online.

Disposable email · no sign-up

### CleanTempMail

Print-and-play files, character sheets and free starter rules often sit behind an email sign-up. CleanTempMail gives you a free temporary inbox at once: no sign-up, a random or custom address on hundreds of domains, and messages deleted automatically after 3 days.

Grab the download link, and keep your real address for the shops and groups you trust.

[Open a temporary inbox](https://cleantempmail.com/)

Disposable cloud browser · free domain lookups

### WebTraceCheck

Spotted a card game or dice set at a surprising price in a shop you've never heard of? WebTraceCheck's free DNS and domain lookup shows the details behind a site's domain, and its disposable cloud browser opens the link on an isolated desktop that is deleted after each session.

Nothing to install, with free time every day.

[Try WebTraceCheck](https://webtracecheck.com/)

## Questions

**What does 2d20kh1 mean?**

Roll two twenty-sided dice and keep the higher one (kh is “keep highest”). Many games call this rolling with advantage. It lifts the average from 10.5 to 13.825, and the chance of 15 or more from 30% to 51%: one minus the chance that both dice show 14 or less, 1 − (14/20)².

**How much better is 4d6 drop the lowest than 3d6?**

About 1.74 points on average: 4d6dl1 averages 15869/1296, or about 12.24, against 10.5 for 3d6. It also makes high totals far more common: 16 or more comes up about 13.0% of the time, against 4.6% with 3d6. Use the 4d6dl1 vs 3d6 example to see both side by side.

**Are these results from a simulation?**

No. Every chance is calculated exactly, by convolution for added dice and by counting for keep and drop rolls, so you get the same numbers every time and there is no sampling error. Very large requests are refused rather than estimated.