The Mathematics of Snakes and Ladders

A fun and beautifully pointless investigation into the mathematical properties of the board game 'Snakes and Ladders'. It turns out to contain some quite interesting mathematical and computational problems. For example did you know that the first player to act has a 0.9% winning advantage, that you have about a 50% probability of going up the ladder on square 80, that it takes on average 35.5 throws to reach the finish or that the fairest starting positions for 2 players in on squares 39 and 22. Set as a series of challenges so you can play along too.

To the blog article...

Written by Calum Grant 2016.

Source code and building

The source code is written in C++11, and can be downloaded here.

The code builds on OSX/Windows/Linux. Just install a C++ compiler and run build.sh or build.bat. A newish C++ compiler is needed (e.g. Visual Studio 2015) to compile C++11.