Can I use this for game development mechanics?

Yes, it is perfectly suited for calculating loot drop rates, dice distributions, and complex card game interactions.

How does this skill ensure mathematical accuracy?

It utilizes Python's Fraction class to perform exact rational arithmetic, which prevents the precision loss often associated with floating-point calculations.

What is the 'Norvig Pattern' mentioned in the skill?

It refers to Peter Norvig's approach of defining probability as the ratio of favorable outcomes to the total sample space, emphasizing clear, readable, and functional code.

Does this skill require external Python libraries?

No, it primarily uses standard Python libraries such as itertools and fractions, ensuring high portability and minimal setup.

When should I use Monte Carlo simulations instead of enumeration?

Monte Carlo simulations are recommended when the sample space is astronomically large, making explicit enumeration computationally expensive or impossible.

Probability & Counting Patterns

Name: Probability & Counting Patterns
Author: jimmc414

byjimmc414

•

Data Science & ML

Implements exact probability calculations and combinatorial counting patterns using a functional, Norvig-inspired approach.

This skill provides Claude with standardized patterns for solving complex probability and counting problems. Inspired by Peter Norvig's 'pytudes,' it emphasizes explicit sample space enumeration, exact arithmetic using Python's Fraction class, and efficient outcome counting via itertools. It is particularly useful for modeling card games, dice rolls, and urn problems, or performing Monte Carlo simulations when closed-form solutions are too complex or unavailable.

Key Features

01Exact probability calculations using Python's Fraction class to avoid floating-point errors

02Functional predicates and set operations for defining complex event conditions

03Monte Carlo simulation patterns for approximating outcomes in large-scale probability models

04Explicit sample space enumeration for permutations, combinations, and Cartesian products

051 GitHub stars

06Integration with itertools for memory-efficient generation of mathematical outcomes

Use Cases

01Running brute-force simulations to verify theoretical mathematical models

02Solving complex combinatorial problems like 'Urn' problems or the Birthday Paradox

03Calculating exact odds for card games, board games, and dice roll distributions

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add jimmc414/claude-code-plugin-marketplace count-combinations

For use in Claude.ai and ChatGPT

Download Skill