bjnb: Blackjack Notebook

Hugues Hoppe   —    [Open in Colab]   [Open in Kaggle]   [Open in MyBinder]   [GitHub source]

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 (12 parameters including #decks, dealer hit soft17, cut-card, ...)

• Optimal action tables for basic strategy under any rules, reproducing Wikipedia and WizardOfOdds results.

• Six separate composition-dependent strategies based on different levels of attention.

• 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 ~$10^{8}$ 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.

Running this Jupyter notebook:

• The notebook requires Python 3.10 or later.
• We recommend starting a Jupyter server on a local machine with a fast multi-core CPU.
  (The notebook can also be executed on a Colab server, but it runs ~20x slower due to the older, shared processor.)
• Within a Linux environment (e.g., Windows Subsystem for Linux):

    sudo apt install python3-pip
    python3 -m pip install --upgrade pip
    pip install jupyterlab jupytext matplotlib numba tqdm
    jupyter lab --no-browser

• Open the URL (output by jupyter lab) using a web browser (e.g., Google Chrome on Windows).
• Load the notebook (*.ipynb file).
• Evaluate all cells in Code library and then selectively evaluate Results.
• Adjust the EFFORT global variable to trade off speed and accuracy.

References:

• https://en.wikipedia.org/wiki/Blackjack
• https://wizardofodds.com/games/blackjack/basics/#rules
• https://www.casinoguardian.co.uk/blackjack/ -- rich; explore more?
• https://wizardofvegas.com/guides/blackjack-survey/
• https://www.blackjackinfo.com/ -- created by Ken Smith; explore?
• https://www.onlinegambling.com/blackjack/odds/
• https://www.onlineunitedstatescasinos.com/las-vegas/blackjack/
• https://en.wikipedia.org/wiki/Gambling_mathematics
• https://www.gamingtheodds.com/blackjack/house-edge/ -- looks like truncated results of WizardOfOdds assuming no late surrender.
• https://github.com/johntelforduk/blackjack -- Python simulator to evaluate house edge for various strategies.
• First reddit post

(See also references in Tables for basic strategy, Hand calculators, and House edge calculators.)