https://github.com/drvinceknight/sal

Generate the transition matrix for snakes 🐍 and ladders
https://github.com/drvinceknight/sal

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Generate the transition matrix for snakes 🐍 and ladders

• Host: GitHub
• URL: https://github.com/drvinceknight/sal
• Owner: drvinceknight
• License: cc0-1.0
• Created: 2020-11-03T14:07:43.000Z (about 4 years ago)
• Default Branch: main
• Last Pushed: 2020-11-03T16:59:42.000Z (about 4 years ago)
• Last Synced: 2024-06-20T00:44:48.838Z (7 months ago)
• Language: Python
• Size: 15.6 KB
• Stars: 1
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.4236276.svg)](https://doi.org/10.5281/zenodo.4236276)

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# Snakes and ladders

This repository contains a script to generate [`main.csv`](./main.csv) which

contains the transition matrix for a Markov chain representation of the popular

board game Snakes and Ladders.

## Assumptions

The official rules are used: a player must land exactly on 100, if they do not

they stay where they are. This is reflected in the final rows of the matrix.

## Usage

### Generate the data

To generate the data:

    $ python main.py

### Use the dataa

To load the data as a numpy array:

    >>> import numpy as np

    >>> P = np.loadtxt(fname="main.csv", delimiter=",")

We can see we have a 101 by 101 array:

    >>> P.shape

    (101, 101)

The last row corresponds to the absorbing state of ending the game:

    >>> P[-1]

    array([0., 0., ... 0., 1.])

The penultimate row corresponding to the 99th square shows that 1/6 of the time

the game ends but 5/6th of the time the player stays where they are:

    >>> P[-2]

    array([0. ... 0.833333, 0.166667])

Similarly the row that corresponds to the 98th square captures that:

- 1/6 of the time they roll leads us to square 99 where there is a snake to square 70.

- 1/6 of the time the game ends

- 2/3 of the time the player stays where they are.

We can see check this:

    >>> P[-3]

    array([0. ... 0.166667, ... 0.666667, 0.      , 0.166667])

    >>> P[-3, 70]

    0.166667

## To test that the results listed in this README are as expected

    $ python -m pytest --doctest-glob=README.md