Playing D&D, I became interested in the probability distributions of rolling dice. For example, 2d6+3 means 'roll 2 6-sided dice, sum them, and add 3'.
The repo defines a library and simple site for evaluating expressions like this and computing the complete probability distribution. It's implemented in Rust and exposed as a WebAssembly library. You can try it out at dice.alexkennedy.dev (though the UI is currently super basic).
Dice of n sides are represented by the expression dn. For example, d20 represents a single 20-sided dice.
Rolling m such dice and taking the sum of all of them is represented by mdn. For example, if you cast a Fireball, you can represent that as usual by 8d6.
You can also represent advantage and disadvantage by using a or d respectively after the dice term. For example, d20a and d20d represent rolling two 20-sided dice and taking the best or worst, respectively.
You can also do more arbitrary best or worst groupings. To represent throwing k n-sided dice, and taking the sum of the m best or worst, use mdnak or mdndk, respectively.
For example, to throw 10 6-sided dice and take the sum of the best 5, you can do 5d6a10. The number you are adding comes first, and the size of pool comes last.
You can add and subtract dice or constants however you like.
d20a + d4: Roll ad20with advantage (best of two throws) and add a d4.2(d6d10-7): Roll 10 6-sided dice, take the worst, subtract 7 and then double the result.
Multiplying two dice (e.g. d6*d6) is not currently supported.
This repo contains a CLI for demonstration.
$ cargo run calculate "d20a+2d4"You can also run simulate to simulate rolling many dice according to your expression.
$ cargo run simulate --runs=1000000 "d20a+2d4"- Liu, A. J. (2022). Icepool: Efficient Computation of Dice Pool Probabilities. Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, 18(1), 258–265. https://doi.org/10.1609/aiide.v18i1.21971