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
                 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 "k" then "i" then "t" then "e" 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

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

Archive

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