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Now you’re playing with…

dyce – simple Python tools for exploring dice outcomes and other finite discrete probabilities

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dyce is a pure-Python library for modeling arbitrarily complex dice mechanics. It strives for compact expression and efficient computation, especially for the most common cases. Its primary applications:

1. Computing finite discrete probability distributions for:
   • Game designers who want to understand or experiment with various dice mechanics and interactions;
   • Players (including game masters) who may be curious about in-game probabilities; and
   • Tool authors who serve those game designers or players.
2. Generating transparent, weighted random rolls for:
   • Software developers who want to enable flexible dice mechanic resolution in their gaming environments such as chat servers or virtual tabletops (VTTs).

Beyond those audiences, it may be useful to anyone interested in exploring finite discrete probabilities but not in developing all the low-level math bits from scratch.

dyce is designed to be immediately and broadly useful with minimal additional investment beyond basic knowledge of Python. While not as compact as a dedicated grammar, dyce’s Python-based primitives are quite sufficient, and often more expressive. Those familiar with various game notations should be able to adapt quickly. If you’re looking at something on which to build your own grammar or interface, dyce can serve you well.

dyce should be able to replicate or replace most other dice probability modeling tools. It strives to be fully documented and relies heavily on examples to develop understanding.

dyce is licensed under the MIT License. See the accompanying LICENSE file for details. Non-experimental features should be considered stable (but an unquenchable thirst to increase performance remains). See the release notes for a summary of version-to-version changes. Source code is available on GitHub.

If you find it lacking in any way, please don’t hesitate to bring it to my attention.

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A taste

dyce provides several core primitives. H objects represent histograms for modeling finite discrete outcomes, like individual dice. P objects represent pools (ordered sequences) of histograms. R objects (covered elsewhere) represent nodes in arbitrary roller trees useful for translating from proprietary grammars and generating weighted random rolls that “show their work” without the overhead of enumeration. All support a variety of operations.

>>> from dyce import H
>>> d6 = H(6)  # a standard six-sided die
>>> 2@d6 * 3 - 4  # 2d6 × 3 - 4
H({2: 1, 5: 2, 8: 3, 11: 4, 14: 5, 17: 6, 20: 5, 23: 4, 26: 3, 29: 2, 32: 1})
>>> d6.lt(d6)  # how often a first six-sided die shows a face less than a second
H({False: 21, True: 15})
>>> abs(d6 - d6)  # subtract the least of two six-sided dice from the greatest
H({0: 6, 1: 10, 2: 8, 3: 6, 4: 4, 5: 2})

>>> from dyce import P
>>> p_2d6 = 2@P(d6)  # a pool of two six-sided dice
>>> p_2d6.h()  # pools can be collapsed into histograms
H({2: 1, 3: 2, 4: 3, 5: 4, 6: 5, 7: 6, 8: 5, 9: 4, 10: 3, 11: 2, 12: 1})
>>> p_2d6 == 2@d6  # pools and histograms are comparable
True

By providing an optional argument to the P.h method, one can “take” individual dice from pools, ordered least to greatest. (The H.format method provides rudimentary visualization for convenience.)

>>> p_2d6.h(0)  # take the lowest die of 2d6
H({1: 11, 2: 9, 3: 7, 4: 5, 5: 3, 6: 1})
>>> print(p_2d6.h(0).format(width=65))
avg |    2.53
std |    1.40
var |    1.97
  1 |  30.56% |###############
  2 |  25.00% |############
  3 |  19.44% |#########
  4 |  13.89% |######
  5 |   8.33% |####
  6 |   2.78% |#

>>> p_2d6.h(-1)  # take the highest die of 2d6
H({1: 1, 2: 3, 3: 5, 4: 7, 5: 9, 6: 11})
>>> print(p_2d6.h(-1).format(width=65))
avg |    4.47
std |    1.40
var |    1.97
  1 |   2.78% |#
  2 |   8.33% |####
  3 |  13.89% |######
  4 |  19.44% |#########
  5 |  25.00% |############
  6 |  30.56% |###############

H objects provide a distribution method and a distribution_xy method to ease integration with plotting packages like matplotlib.

>>> import matplotlib  # doctest: +SKIP

>>> outcomes, probabilities = p_2d6.h(0).distribution_xy()
>>> matplotlib.pyplot.bar(
...   [v - 0.125 for v in outcomes],
...   probabilities,
...   alpha=0.75,
...   width=0.5,
...   label="Lowest",
... )  # doctest: +SKIP

>>> outcomes, probabilities = p_2d6.h(-1).distribution_xy()
>>> matplotlib.pyplot.bar(
...   [v + 0.125 for v in outcomes],
...   probabilities,
...   alpha=0.75,
...   width=0.5,
...   label="Highest",
... )  # doctest: +SKIP

>>> matplotlib.pyplot.legend()  # doctest: +SKIP
>>> matplotlib.pyplot.title(r"Taking the lowest or highest die of 2d6")  # doctest: +SKIP
>>> matplotlib.pyplot.show()  # doctest: +SKIP

H objects and P objects can generate random rolls.

>>> d6 = H(6)
>>> d6.roll()  # doctest: +SKIP
4

>>> d10 = H(10) - 1
>>> p_6d10 = 6@P(d10)
>>> p_6d10.roll()  # doctest: +SKIP
(0, 1, 2, 3, 5, 7)

See the tutorials on counting and rolling, as well as the API guide for much more thorough treatments, including detailed examples.

Design philosophy

dyce is fairly low-level by design, prioritizing ergonomics and composability. It explicitly avoids stochastic simulation, but instead determines outcomes through enumeration and discrete computation. That’s a highfalutin way of saying it doesn’t guess. It knows, even if knowing is harder or more limiting. Which, if we possess a modicum of humility, it often is.

!!! quote

“It’s frightening to think that you might not know something, but more frightening to think that, by and large, the world is run by people who have faith that they know exactly what is going on.”

—Amos Tversky

Because dyce exposes Python primitives rather than defining a dedicated grammar and interpreter, one can more easily integrate it with other tools.¹ It can be installed and run anywhere², and modified as desired. On its own, dyce is completely adequate for casual tinkering. However, it really shines when used in larger contexts such as with Matplotlib or Jupyter or embedded in a special-purpose application.

In an intentional departure from RFC 1925, § 2.2, dyce includes some conveniences, such as minor computation optimizations (e.g., the H.lowest_terms method, various other shorthands, etc.) and formatting conveniences (e.g., the H.distribution, H.distribution_xy, and H.format methods).

Comparison to alternatives

The following is a best-effort³ summary of the differences between various available tools in this space. Consider exploring the applications and translations for added color.

License

dyce is licensed under the MIT License. See the included LICENSE file for details. Source code is available on GitHub.

Installation

Installation can be performed via PyPI.

% pip install dycelib
...

Alternately, you can download the source and run setup.py.

% git clone https://github.com/posita/dyce.git
...
% cd dyce
% python setup.py install
...

Requirements

dyce requires a relatively modern version of Python:

• CPython (3.7+)
• PyPy (CPython 3.7+ compatible)

It has the following runtime dependencies:

• typing-extensions (with Python <3.9)

dyce will opportunistically use the following, if available at runtime:

• beartype for yummy runtime type-checking goodness (0.8+)
• graphviz for visualizing rollers and rolls
• matplotlib for visualizing histograms and pools

If you install beartype for type checking your own code, but don’t want dyce to use it (e.g., for performance reasons), you can set the DYCE_BEARTYPE environment variable to a falsy⁹ value before dyce is imported.

See the hacking quick-start for additional development and testing dependencies.