mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2019-12-27 
In tonight's Royal Institution Christmas lecture, Hannah Fry and Matt Parker demonstrated how machine learning works using MENACE.
The copy of MENACE that appeared in the lecture was build and trained by me. During the training, I logged all the moved made by MENACE and the humans playing against them, and using this data I have created some visualisations of the machine's learning.
First up, here's a visualisation of the likelihood of MENACE choosing different moves as they play games. The thickness of each arrow represented the number of beads in the box corresponding to that move, so thicker arrows represent more likely moves.
The likelihood that MENACE will play each move.
There's an awful lot of arrows in this diagram, so it's clearer if we just visualise a few boxes. This animation shows how the number of beads in the first box changes over time.
The beads in the first box.
You can see that MENACE learnt that they should always play in the centre first, an ends up with a large number of green beads and almost none of the other colours. The following animations show the number of beads changing in some other boxes.
MENACE learns that the top left is a good move.
MENACE learns that the middle right is a good move.
MENACE is very likely to draw from this position so learns that almost all the possible moves are good moves.
The numbers in these change less often, as they are not used in every game: they are only used when the game reached the positions shown on the boxes.
We can visualise MENACE's learning progress by plotting how the number of beads in the first box changes over time.
The number of beads in MENACE's first box.
Alternatively, we could plot how the number of wins, loses and draws changes over time or view this as an animated bar chart.
The number of games MENACE wins, loses and draws.
The number of games MENACE has won, lost and drawn.
If you have any ideas for other interesting ways to present this data, let me know in the comments below.
×3      ×2            ×1      
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
@(anonymous): Have you been refreshing the page? Every time you refresh it resets MENACE to before it has learnt anything.

It takes around 80 games for MENACE to learn against the perfect AI. So it could be you've not left it playing for long enough? (Try turning the speed up to watch MENACE get better.)
Matthew
            ×1     Reply
I have played around menace a bit and frankly it doesnt seem to be learning i occasionally play with it and it draws but againt the perfect ai you dont see as many draws, the perfect ai wins alot more
(anonymous)
                 Reply
@Colin: You can set MENACE playing against MENACE2 (MENACE that plays second) on the interactive MENACE. MENACE2's starting numbers of beads and incentives may need some tweaking to give it a chance though; I've been meaning to look into this in more detail at some point...
Matthew
                 Reply
Idle pondering (and something you may have covered elsewhere): what's the evolution as MENACE plays against itself? (Assuming MENACE can play both sides.)
Colin
                 Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "b" then "i" then "s" then "e" then "c" then "t" in the box below (case sensitive):

Archive

Show me a random blog post
 2026 

May 2026

World Cup stickers 2026

Apr 2026

A new puzzle every day
Mixing Wordle with other games

Feb 2026

Christmas (2025) is over
 2025 

Dec 2025

Christmas card 2025

Nov 2025

Christmas (2025) is coming!

Sep 2025

The partridge puzzle

Aug 2025

TMiP 2025 puzzle hunt

Jun 2025

A nonogram alphabet

Mar 2025

How to write a crossnumber

Jan 2025

Christmas (2024) is over
Friendly squares
 2024 

Dec 2024

A regular expression Christmas puzzle
Christmas card 2024

Nov 2024

Christmas (2024) is coming!

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

stickers matrices game of life mathslogicbot runge's phenomenon chebyshev frobel fonts martin gardner people maths mean regular expressions european cup triangles reuleaux polygons pizza cutting inline code platonic solids logo captain scarlet chess game show probability crosswords hats newcastle folding paper world cup final fantasy signorini conditions finite group harriss spiral games cambridge nonograms standard deviation plastic ratio machine learning tennis weak imposition edinburgh sport dataset php sorting convergence nine men's morris christmas quadrilaterals wool geogebra royal baby programming golden spiral boundary element methods pascal's triangle gaussian elimination bluesky databet numbers manchester science festival tetris asteroids ucl rugby statistics golden ratio mathsteroids bubble bobble matrix of cofactors arithmetic live stream arrangement puzzles go propositional calculus curvature bodmas bots pokémon wordle rust oeis video games bempp rhombicuboctahedron ternary sound braiding coventry binary mathsjam squares stirling numbers crossnumber big internet math-off gerry anderson pokémon folding tube maps alphabets fractals hyperbolic surfaces countdown preconditioning flexagons national lottery polynomials turtles latex dinosaurs pi friendly squares crochet correlation cross stitch zines coins wave scattering noughts and crosses thirteen football interpolation craft a gamut of games hannah fry london 24 hour maths weather station partridge puzzle the aperiodical graph theory error bars draughts python data simultaneous equations matrix multiplication misleading statistics wordle pac-man news speed radio 4 chalkdust magazine datasaurus dozen electromagnetic field matrix of minors estimation phd anscombe's quartet christmas card logs errors light pythagoras fence posts numerical analysis sobolev spaces royal institution approximation graphs computational complexity youtube warwick advent calendar menace crossnumbers realhats dates logic determinants reddit puzzles kenilworth exponential growth pi approximation day kings finite element method raspberry pi london underground geometry probability map projections accuracy manchester gather town talking maths in public guest posts tmip dragon curves javascript recursion matt parker trigonometry inverse matrices hexapawn data visualisation books palindromes

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2026