icepool 0.12.0

A package for computing dice probabilities

Icepool

A Python package for computing dice probabilities.

GitHub repository.

Features

• Pure Python implementation.
• Exact fractional probabilities using Python ints.
• Dice support all standard operators (+, -, <, >, etc.) as well as an extensive library of functions (rerolling, exploding, etc.)
• Can outperform sequence/multiset-based algorithms on many dice pool problems. In some cases it may be thousands or millions of times faster.

Installing

pip install icepool

The source is pure Python, so making a direct copy can work as well.

Contact

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

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.

Web applications

• Ability score rolling method calculator
• Cortex Prime calculator
• Legends of the Wulin calculator

Inline examples

Advanced Dungeons & Dragons 1st edition ability score methods

Source for these methods.

Method I:

All scores are recorded and arranged in the order the player desires. 4d6 are rolled, and the lowest die (or one of the lower) is discarded.

Method II:

All scores are recorded and arranged as in Method I. 3d6 are rolled 12 times and the highest 6 scores are retained.

Method III:

Scores rolled are according to each ability category, in order, STRENGTH, INTELLIGENCE, WISDOM, DEXTERITY, CONSTITUTION, CHARISMA. 3d6 are rolled 6 times for each ability, and the highest score in each category is retained for that category.

Method IV:

3d6 are rolled sufficient times to generate the 6 ability scores, in order, for 12 characters. The player then selects the single set of scores which he or she finds most desirable and these scores are noted on the character record sheet.

import icepool

"""
The @ operator means "roll the left die, then roll that many of the right die and sum".
Integers are treated as a die that always rolls that number.
Therefore:
* 3 @ icepool.d6 means 3d6.
* icepool.d6 @ 3 means roll a d6 and multiply the result by 3.
"""

method1 = 6 @ icepool.d6.keep_highest(num_dice=4, num_keep=3)
method2 = (3 @ icepool.d6).keep_highest(12, 6)
# num_keep defaults to 1.
method3 = 6 @ (3 @ icepool.d6).keep_highest(6)
method4 = (6 @ (3 @ icepool.d6)).keep_highest(12)

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
ax.plot(method1.outcomes(), method1.pmf(percent=True))
ax.plot(method2.outcomes(), method2.pmf(percent=True))
ax.plot(method3.outcomes(), method3.pmf(percent=True))
ax.plot(method4.outcomes(), method4.pmf(percent=True))
ax.set_title('AD&D 1e ability score methods')
ax.legend(['Method I', 'Method II', 'Method III', 'Method IV'])
ax.set_xlabel('Total of ability scores')
ax.set_xlim(50, 100)
ax.set_ylim(0)
ax.grid(True)
plt.show()