Two dice are not a random number from 2 to 12
This is the thing worth taking away, and almost everybody who reaches for dice to pick something has it wrong.
There is exactly one way to roll a 2: both dice show one. There are six ways to roll a 7: 1 and 6, 2 and 5, 3 and 4, and each of those the other way round. So seven turns up six times as often as two.
Anybody who has played a board game knows this in their bones and then forgets it the moment they need to choose between eleven options. If you want each option equally likely, roll one die with that many faces, or use a number generator. Two dice will always favour the middle.
The chart is exact, not sampled
Most dice tools that show you odds get them by rolling ten thousand times and counting. That gives a figure that is close, wobbles every time you reload, and cannot tell you the difference between a one in a thousand and a one in twelve hundred.
For plain dice and modifiers this works out every combination properly, by convolution: start with nothing, add one die at a time, and spread each running total across the faces. It is a small amount of arithmetic and it is right to the last decimal.
Keep and drop rules are the exception. Working out "keep the highest three of four" exactly is genuinely difficult, so those are simulated over twenty thousand rolls, and the page tells you that is what you are looking at rather than presenting both the same way.
Keep the highest is more generous than it looks
The traditional way to roll a character is four six-sided dice, drop the lowest. It feels like rolling 3d6 with a bit of luck attached.
Straight 3d6 averages 10.5. Four dice keeping the best three averages about 12.24, and it very nearly removes the chance of a genuinely poor score. That is not a small adjustment, it is a different distribution wearing the same clothes.
Disadvantage is worse than it feels
Rolling two twenty-sided dice and taking the lower one sounds like a mild inconvenience.
A single d20 averages 10.5. Take the lower of two and the average falls to about 7.2, and the chance of rolling a twenty goes from one in twenty to one in four hundred. Advantage moves everything the same distance in the other direction, which is why both are handed out sparingly.
The seed is there so you can prove it
Every roll here comes from a seeded generator and the seed is printed under the dice. Put the same seed in and you get the same dice, every time.
That is the difference between a result somebody has to take on trust and one they can check. If you are using dice to settle something, being able to reproduce the roll afterwards is worth more than the roll itself.
It is a pseudorandom generator, which is exactly right for a game and exactly wrong for anything where somebody has money on the outcome and an incentive to work out what comes next. This does not pretend otherwise.
Common questions
Is rolling 2d6 a fair way to pick a number from 2 to 12?
No. There is one way to roll a 2 and six ways to roll a 7, so seven comes up six times as often, and it is the most useful thing on this page. If you want every option equally likely you need one die with that many sides, or a random number generator. Two dice cluster in the middle and always will.
What notation does it understand?
3d6 for three six-sided dice. 1d20+5 with a modifier. 2d6+1d4 for mixed dice. 4d6kh3 keeps the highest three of four. 2d20kl1 keeps the lowest of two, which is disadvantage. 4d6dl1 drops the lowest, which is the same thing as 4d6kh3. Spaces and capitals are ignored.
Are the probabilities exact or simulated?
Exact wherever the maths allows, and it says which you are looking at. For plain dice and modifiers it works out every combination by convolution, so the figures do not wobble when you press the button again. Keep and drop rules are genuinely awkward to compute exactly, so those are simulated over twenty thousand rolls and labelled as simulated rather than dressed up as exact.
Why is 4d6 keep highest 3 the traditional character roll?
Because it is quietly generous. Straight 3d6 averages 10.5. Rolling four and dropping the worst averages about 12.24, and it also shrinks the chance of a really low score to almost nothing. It feels like the same roll and it is not.
How harsh is disadvantage really?
Harsher than it looks. A single d20 averages 10.5. Rolling two and taking the lower averages about 7.2, and your chance of a 20 drops from one in twenty to one in four hundred. Advantage moves it the same distance the other way.
Can I show somebody the roll?
Yes. Every roll is seeded, and the seed is shown. The same seed always produces the same dice, so a result can be reproduced rather than taken on trust. That matters if you are using it to settle something.
Is it actually random?
It is a seeded pseudorandom generator, which is deliberate: it makes results reproducible and testable. That is the right trade for games and decisions. It is not the right thing for anything where somebody has an incentive to predict the result, such as a prize draw of real value, and it does not claim to be.