Dice Roller Calculator

The notation reads left to right as count, sides, modifier. N is the number of dice, d separates the count from the sides, M is the number of sides per die, and +K (or -K) is a flat number added to or subtracted from the total. So 2d6+3 means roll two six-sided dice, sum the faces, and add 3. 1d20 means roll one twenty-sided die with no modifier. A bare dM with no leading number is treated as 1dM, so d20 and 1d20 give the same result. Modifiers are clamped to a maximum magnitude of 1000, dice counts to 100 per expression, and sides to 1000.

4d6kh3 means roll four six-sided dice and keep the highest three. The lowest die is dropped, which pushes the average per ability score from 10.5 (the plain 3d6 mean) up to about 12.24. It is the rolling method recommended in the D&D 5e Player's Handbook for generating a heroic character, and it produces a noticeably higher score distribution than 3d6 without the runaway results of point-buy maximums. The calculator handles kh and kl (keep lowest) for any number from 1 up to the dice count, so 2d20kl1 gives you a 5e disadvantage roll and 2d20kh1 gives you advantage.

The expected value of one fair die is (sides plus 1) divided by 2. A d6 averages 3.5, a d20 averages 10.5, a d100 averages 50.5. For a multi-die roll like NdM you multiply that per-die expected value by N, then add the modifier: 3d6 averages 10.5, 3d6+5 averages 15.5, 8d6 averages 28. The calculator shows the expected value, the minimum possible total, and the maximum possible total alongside the actual roll, so you can see how lucky or unlucky a given result is relative to the underlying probability distribution.

A standard tabletop polyhedral set has seven dice: d4 (tetrahedron), d6 (cube), d8 (octahedron), d10 (pentagonal trapezohedron), d12 (dodecahedron), d20 (icosahedron), and a percentile d10 used with the regular d10 to roll d100. D&D, Pathfinder, Call of Cthulhu, and most modern RPGs use this set. The calculator accepts any of these standard dice plus arbitrary sides up to dM where M is 1000, which covers exotic formats like d30 used for some random tables, d50 for old-school sci-fi systems, and the d1000 used in a few percentile-heavy hobby games.

Mulberry32 is a small, fast, seedable pseudo-random number generator. The seed is passed in explicitly, so the same seed always produces the same dice sequence, which is exactly what unit tests need to verify the math. In the browser, the calculator seeds Mulberry32 with Date.now at the moment you click Roll, so consecutive rolls produce different results in practice while staying fully testable in code. For non-cryptographic uses like tabletop dice the distribution is more than fair enough, the speed is irrelevant on any modern device, and the determinism is the load-bearing feature.