icepool 2.2.1

Dice probability package.

Icepool

Python dice probability package.

GitHub repository.

PyPi page.

Try coding in your browser using Icecup, a simple frontend for scripting and graphing similar to AnyDice, SnakeEyes, and Troll. You can find a series of tutorials here.

Features

• Pure Python implementation using only the Standard Library. Run it almost anywhere Python runs: program locally, share Jupyter notebooks, or build your own client-side web apps using Pyodide.
• Dice support all standard operators (+, -, <, >, etc.) as well as an extensive library of functions (rerolling, exploding, etc.)
• Efficient dice pool algorithm can solve keep-highest, finding sets and/or straights, RISK-like mechanics, and more in milliseconds, even for large pools.
• Exact fractional probabilities using Python ints.
• Some support for decks (aka sampling without replacement).

Installing

pip install icepool

The source is pure Python, so including a direct copy in your project can work as well.

Contact

Feel free to open a discussion or issue on GitHub. You can also find me on Reddit or Twitter.

API documentation

pdoc on GitHub.

JupyterLite notebooks

See this JupyterLite distribution for a collection of interactive, editable examples. These include mechanics from published games, StackExchange, Reddit, and academic papers.

JupyterLite REPL.

As a backup, you can open the notebooks in Google Colab.

Tutorial notebooks

In particular, here is a series of tutorial notebooks.

StackExchange answers

• Call-on traits in Burning Wheel: Success-counting dice pools with explosions and rerolls.
• Vampire the Masquerade V
• Roll multiple ability score arrays and pick the one with the highest total. What is the distribution of each ranked score?
• Year Zero Engine
• Neon City Overdrive
• Broken Compass / Household / Outgunned
• Probability that 0/4 players is dealt Blackjack

Here is a full search of answers in which I mention Icepool.

Web applications

These are all client-side, powered by Pyodide. Perhaps you will find inspiration for your own application.

• Icecup, a simple frontend for scripting and graphing.
• Alex Recarey's Face 2 Face Calculator for Infinity the Game -- including the ability to be installed on Android and iOS and run without an internet connection.
• Ability score rolling method calculator.
• Cortex Prime calculator.
• Legends of the Wulin calculator.
• Year Zero Engine calculator.

Paper on algorithm

Presented at Artificial Intelligence and Interactive Digital Entertainment (AIIDE) 2022.

In the official proceedings.

Preprint in this repository.

BibTeX:

@inproceedings{liu2022icepool,
    title={Icepool: Efficient Computation of Dice Pool Probabilities},
    author={Albert Julius Liu},
    booktitle={Eighteenth AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment},
    volume={18},
    number={1},
    pages={258-265},
    year={2022},
    month={Oct.},
    eventdate={2022-10-24/2022-10-28},
    venue={Pomona, California},
    url={https://ojs.aaai.org/index.php/AIIDE/article/view/21971},
    doi={10.1609/aiide.v18i1.21971}
}

Versioning

Frankly, I haven't made backwards compatibility a top priority. If you need specific behavior, I recommend version pinning. Typing is especially unstable.

Similar projects

In roughly chronological order:

Troll by Torben Ægidius Mogensen

http://hjemmesider.diku.dk/~torbenm/Troll/

The oldest general-purpose dice probability calculator I know of. It has an accompanying peer-reviewed paper.

AnyDice by Jasper Flick

https://anydice.com/

Probably the most popular dice probability calculator in existence, and with good reason---its accessibility and shareability remains unparalleled. I still use it often for prototyping and as a second opinion.

SnakeEyes by Noé Falzon

https://snake-eyes.io/

SnakeEyes demonstrated the viability of browser-based, client-side dice calculation, as well as introducing me to Chart.js.

dice_roll.py by Ilmari Karonen

https://gist.github.com/vyznev/8f5e62c91ce4d8ca7841974c87271e2f

This demonstrated the trick of iterating "vertically" over the outcomes of dice in a dice pool, rather than "horizontally" through the dice---one of the insights into creating a much faster dice pool algorithm.

dyce by Matt Bogosian

https://github.com/posita/dyce

Another Python dice probability package. I've benefited greatly from exchanging our experiences.