Background

A friend and I were looking into the avrae/d20 package. We noticed some concerning code flow with regards to how Random is being used. The package being used (random.py) is the old version of the MT algorithm which tends towards statistically lower outcomes (as compared to the 2002 or newer versions). It's also hit or miss given the lack of seeding which means we'd expect the randomness to basically end up being subsets of older rolls. (Deterministic for the purpose of statistical modeling.) Also, it's one of the slowest random algorithms.

There's lots of alternatives that are easy to use and provide more randomness and quicker throughput.

Suggested Improvement

Upgrade to a new random package to be used on lines 405 and 407 of expression.py. A package in the PCG family would likely be optimal for Avrae's usage.

Quote from the page on comparison to other algorithms:

PCG was developed by applying TestU01 to reduced-size variants,[7] and determining the minimum number of internal state bits required to pass BigCrush. BigCrush examines enough data to detect a period of 235, so even an ideal generator requires 36 bits of state to pass it. Some very poor generators can pass if given a large enough state;[8] passing despite a small state is a measure of an algorithm's quality, and shows how large a safety margin exists between that lower limit and the state size used in practical applications.

PCG-RXS-M-XS (with 32-bit output) passes BigCrush with 36 bits of state (the minimum possible), PCG-XSH-RR (pcg32() above) requires 39, and PCG-XSH-RS (pcg32_fast() above) requires 49 bits of state. For comparison, xorshift*, one of the best of the alternatives, requires 40 bits of state,[5]: 19  and Mersenne twister fails despite 19937 bits of state.[9]

This could avoid the known issues of many-zero state recovery in pre-2002 MT algorithms of which random.py uses. The best outcome for Avrae would be faster generation.