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Now you’re playing with …

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

💥 Now 100% Bear-ified™! 👌🏾🐻 (Details below.)

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 are:

1. Computing finite discrete probability distributions for:
   • Game designers who want to understand or experiment with various dice mechanics and interactions; and
   • Design tool developers.
2. Generating transparent, weighted random rolls for:
   • Game environment developers who want flexible dice mechanic resolution in, e.g., virtual tabletops (VTTs), chat servers, etc.

Beyond those audiences, dyce 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.

Donors

When one worries that the flickering light of humanity may be snuffed out at any moment, when one’s heart breaks at the perverse celebration of judgment, vengeance, and death and the demonizing of empathy, compassion, and love, sometimes all that is needed is the kindness of a single stranger to reinvigorate one’s faith that—while all may not be right in the world—there is hope for us human beings.

• David Eyk not only inspires others to explore creative writing, but has graciously ceded his PyPI project dedicated to his own prior work under a similar name. As such, dyce is now available as dycelib dyce! Thanks to his generosity, millions dozens of future dyce users will be spared from typing superfluous characters. On behalf of myself, those souls, and our keyboards, we salute you, Mr. Eyk. 🙇‍♂️

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())
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())
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 anydyce, for example, makes use of these to integrate with matplotlib.

Source: plot_2d6_lo_hi.py
Interactive version:

--8<-- "docs/assets/plot_2d6_lo_hi.py"

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.

	dyce Bogosian et al.	icepool Albert Julius Liu	dice_roll.py Karonen	python-dice Robson et al.	AnyDice Flick	d20 Curse LLC	DnDice “LordSembor”	dice Clements et al.	dice-notation Garrido
Latest release	2022	2022	N/A	2021	Unknown	2021	2016	2021	2022
Actively maintained and documented	✅	✅	⚠️4	✅	✅	✅	❌	✅	❌
Combinatorics optimizations	✅	✅	✅	❌	❌	❌	❌	❌	❌
Suitable as a dependency in other projects	✅	✅	⚠️5	✅	❌	✅	⚠️5	✅	❌
Discrete outcome enumeration	✅	✅	✅	✅	✅	❌	✅	❌	❌
Arbitrary expressions	✅	✅	⚠️6	✅	✅	✅	⚠️7	❌	❌
Arbitrary dice definitions	✅	✅	✅	✅	✅	❌	❌	❌	❌
Integrates with other tools	✅	✅	✅	⚠️8	❌	⚠️8	✅	⚠️8	⚠️8
Open source (can inspect)	✅	✅	✅	✅	❌	✅	✅	✅	✅
Permissive licensing (can use and extend)	✅	✅	✅	✅	N/A	✅	✅	✅	✅

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 dyce
...

Alternately, you can download the source and install manually.

% git clone https://github.com/posita/dyce.git
...
% cd dyce
% python -m pip install .  # -or- python -c 'from setuptools import setup ; setup()' install .
...

Requirements

dyce requires a relatively modern version of Python:

• CPython (3.9+)
• PyPy (CPython 3.9+ compatible)

It has the following runtime dependencies:

• numerary for proper best-effort hacking around deficiencies in static and runtime numeric type-checking

• beartype for yummy runtime type-checking goodness (a dependency of numerary)

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

• numpy to supply dyce with an alternate random number generator implementation

If you use beartype for type checking your code, but don’t want dyce or numerary to use it internally, disable it with numerary’s NUMERARY_BEARTYPE environment variable.

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

Customers

• This could be you! 👋

Do you have a project that uses dyce? Let me know, and I’ll promote it here!

And don’t forget to do your part in perpetuating gratuitous badge-ification!

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[dyce-powered]: https://posita.github.io/dyce/ "dyce-powered!"

..
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.. |dyce-powered| image:: https://raw.githubusercontent.com/posita/dyce/latest/docs/dyce-powered.svg
   :align: top
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   :alt: dyce-powered

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Footnotes

1. You won’t find any lexers, parsers, or tokenizers in dyce’s core, other than straight-up Python. That being said, you can always “roll” your own (see what we did there?) and lean on dyce underneath. It doesn’t mind. It actually kind of likes it. ↩

2. Okay, maybe not literally anywhere, but you’d be surprised. Void where prohibited. Certain restrictions apply. Do not taunt Happy Fun Ball. ↩

3. I have attempted to ensure the above is reasonably accurate, but please consider contributing an issue if you observe discrepancies. ↩

4. Sparsely documented. The author has expressed a desire to release a more polished version. ↩

5. Source can be downloaded and incorporated directly, but there is no packaging, versioning, or dependency tracking. ↩ ↩²

6. Callers must perform their own arithmetic and characterize results in terms of a lightweight die primitive, which may be less accessible to the novice. That being said, the library is remarkably powerful, given its size. ↩

7. Limited arithmetic operations are available. The library also provides game-specific functions. ↩

8. Results only. Input is limited to specialized grammar. ↩ ↩² ↩³ ↩⁴