https://github.com/hhoppe/blackjack
Blackjack Notebook (bjnb): Probabilistic analysis and simulation
https://github.com/hhoppe/blackjack
blackjack blackjack-game monte-carlo-simulation probabilistic-modeling
Last synced: 2 months ago
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Blackjack Notebook (bjnb): Probabilistic analysis and simulation
- Host: GitHub
- URL: https://github.com/hhoppe/blackjack
- Owner: hhoppe
- License: mit
- Created: 2022-03-09T03:15:25.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2025-05-08T04:47:21.000Z (5 months ago)
- Last Synced: 2025-05-08T05:28:58.058Z (5 months ago)
- Topics: blackjack, blackjack-game, monte-carlo-simulation, probabilistic-modeling
- Language: Jupyter Notebook
- Homepage:
- Size: 9.74 MB
- Stars: 9
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# bjnb: Blackjack Notebook
[Hugues Hoppe](https://hhoppe.com/)
—
[**[Open in Colab]**](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb)
[**[in Kaggle]**](https://www.kaggle.com/notebooks/welcome?src=https://github.com/hhoppe/blackjack/blob/main/blackjack.ipynb)
[**[in MyBinder]**](https://mybinder.org/v2/gh/hhoppe/blackjack/main?filepath=blackjack.ipynb)
[**[in Deepnote]**](https://deepnote.com/launch?url=https%3A%2F%2Fgithub.com%2Fhhoppe%2Fblackjack%2Fblob%2Fmain%2Fblackjack.ipynb)
[**[GitHub source]**](https://github.com/hhoppe/blackjack/blob/main/blackjack.ipynb)
Blackjack — *"the most widely played casino banking game in the world"*.
**Goals**:
- Solution methods for both:
1. [Probabilistic analysis](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Probabilistic-analysis)
of blackjack actions and outcomes under many strategies, and
2. [Monte Carlo simulation](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Monte-Carlo-simulation)
for cut-card effects and precise split-hand rewards.
- Support for many [rule variations](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Define-Rules)
(12 parameters including #decks, dealer hit soft17, cut-card, ...)
- Optimal [action tables](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Tables-for-basic-strategy) for
[basic strategy](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Define-Actions-and-Strategy)
under any rules, reproducing
[Wikipedia](https://en.wikipedia.org/wiki/Blackjack#Basic_strategy) and
[WizardOfOdds](https://wizardofodds.com/games/blackjack/strategy/calculator/) results.
- Six separate [composition-dependent strategies](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Define-Actions-and-Strategy)
based on different levels of *attention*.
- Computation of
[house edge](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#House-edge-results)
under any rules, with either basic or composition-dependent strategies.
- Comparisons with online
[hand calculator](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Hand-calculator-results) and
[house edge calculator](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#House-edge-results) results.
- Novel analysis and visualization of the
[*cut-card effect*](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Effect-of-using-a-cut-card)
and its [surprising oscillations](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#cut-card-graph).
- Open-source Python, sped up with jitting (\~30x) and multiprocessing (\~10x),
simulating \~$10^{8}$ hands/s.
- GPU implementation using `numba.cuda`, simulating \~$10^{10}$ 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.
**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](
https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb),
where it greatly benefits from a CUDA GPU.)
- Within a Linux environment (e.g.,
[Windows Subsystem for Linux](https://docs.microsoft.com/en-us/windows/wsl/install)):
```bash
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](
https://www.reddit.com/r/blackjack/comments/t9ygkm/python_notebook_to_analyze_blackjack_optimal/)
(See also references in
[Tables for basic strategy](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Tables-for-basic-strategy),
[Hand calculators](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#Hand-calculators), and
[House edge calculators](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb#House-edge-calculators).)