bjnb: Blackjack Notebook

Blackjack — "the most widely played casino banking game in the world".

Goals:

Solution methods for both:
1. Probabilistic analysis of blackjack actions and outcomes under many strategies, and
2. Monte Carlo simulation for cut-card effects and precise split-hand rewards.
Support for many rule variations (13 parameters including number of decks, dealer hits soft 17, cut-card, ...).
Optimal action tables for basic strategy under any rules, reproducing Wikipedia and WizardOfOdds results.
Six strategies with progressively greater attention, from basic strategy to full composition dependence.
Computation of house edge under any rules, with either basic or composition-dependent strategies.
Comparisons with online hand calculator and house edge calculator results.
Novel analysis and visualization of the cut-card effect and its surprising oscillations.
Open-source Python, sped up with jitting (~30x) and multiprocessing (~10x), simulating $\sim 10^{8}$ hands/s.
GPU implementation using numba.cuda, simulating $\sim 10^{10}$ hands/s.

Versions:

1.0 (March 2022): use probabilistic analysis for basic strategy tables and approximate house edge.
2.0 (July 2022): add Monte Carlo simulation, hand analysis, and cut-card analysis.
3.0 (January 2025): add CUDA implementation of simulation.
3.1 (October 2026): fix bugs in simulating split hands and shoe ends; regenerate all results.

Running this Jupyter notebook:

The notebook requires Python 3.10 or later.
We recommend a Jupyter server on a local machine with a fast multi-core CPU and ideally an NVIDIA GPU.
(The notebook can also be executed on a Colab server, where it greatly benefits from a CUDA GPU.)
Install JupyterLab on Linux or macOS, or on Windows within Windows Subsystem for Linux, because the multiprocessing uses fork.
Open the notebook (blackjack.ipynb file); its first cells install the required packages.
Evaluate all cells in Code library and then selectively evaluate Results.
Adjust the EFFORT global variable (or set the EFFORT environment variable) to trade off speed and accuracy.
Alternatively, after installing the packages listed in its first code cell, run the paired script directly, e.g., EFFORT=1 python blackjack.py.

References:

Name		Name	Last commit message	Last commit date
data		data
.gitignore		.gitignore
LICENSE		LICENSE
README.md		README.md
blackjack.ipynb		blackjack.ipynb
blackjack.py		blackjack.py
house_edge_from_cut_card_1_decks.pdf		house_edge_from_cut_card_1_decks.pdf
house_edge_from_cut_card_2_decks.pdf		house_edge_from_cut_card_2_decks.pdf
house_edge_from_cut_card_4_decks.pdf		house_edge_from_cut_card_4_decks.pdf
house_edge_from_cut_card_6_decks.pdf		house_edge_from_cut_card_6_decks.pdf
house_edge_from_cut_card_8_decks.pdf		house_edge_from_cut_card_8_decks.pdf
pyproject.toml		pyproject.toml
random32.py		random32.py

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