Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

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: 5 days ago
JSON representation

Blackjack Notebook (bjnb): Probabilistic analysis and simulation

Awesome Lists containing this project

README 

        
# bjnb: Blackjack Notebook



[Hugues Hoppe](https://hhoppe.com/)

  — 

  [**[Open in Colab]**](https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb)

  [**[Open in Kaggle]**](https://www.kaggle.com/notebooks/welcome?src=https://github.com/hhoppe/blackjack/blob/main/blackjack.ipynb)

  [**[Open in MyBinder]**](https://mybinder.org/v2/gh/hhoppe/blackjack/main?filepath=blackjack.ipynb)

  [**[GitHub source]**](https://github.com/hhoppe/blackjack)



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.



**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](

   https://colab.research.google.com/github/hhoppe/blackjack/blob/main/blackjack.ipynb),

  but it runs ~20x slower due to the older, shared processor.)

- 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).)