mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2017-11-14 
A few weeks ago, I took the copy of MENACE that I built to Manchester Science Festival, where it played around 300 games against the public while learning to play Noughts and Crosses. The group of us operating MENACE for the weekend included Matt Parker, who made two videos about it. Special thanks go to Matt, plus Katie Steckles, Alison Clarke, Andrew Taylor, Ashley Frankland, David Williams, Paul Taylor, Sam Headleand, Trent Burton, and Zoe Griffiths for helping to operate MENACE for the weekend.
As my original post about MENACE explains in more detail, MENACE is a machine built from 304 matchboxes that learns to play Noughts and Crosses. Each box displays a possible position that the machine can face and contains coloured beads that correspond to the moves it could make. At the end of each game, beads are added or removed depending on the outcome to teach MENACE to play better.

Saturday

On Saturday, MENACE was set up with 8 beads of each colour in the first move box; 3 of each colour in the second move boxes; 2 of each colour in third move boxes; and 1 of each colour in the fourth move boxes. I had only included one copy of moves that are the same due to symmetry.
The plot below shows the number of beads in MENACE's first box as the day progressed.

Sunday

Originally, we were planning to let MENACE learn over the course of both days, but it learned more quickly than we had expected on Saturday, so we reset is on Sunday, but set it up slightly differently. On Sunday, MENACE was set up with 4 beads of each colour in the first move box; 3 of each colour in the second move boxes; 2 of each colour in third move boxes; and 1 of each colour in the fourth move boxes. This time, we left all the beads in the boxes and didn't remove any due to symmetry.
The plot below shows the number of beads in MENACE's first box as the day progressed.

The data

You can download the full set of data that we collected over the weekend here. This includes the first two moves and outcomes of all the games over the two days, plus the number of beads in each box at the end of each day. If you do something interesting (or non-interesting) with the data, let me know!
                        
(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.
WRT the comment 2017-11-17, and exactly one year later, I had the same thing happen whilst running MENACE in a 'Resign' loop for a few hours, unattended. When I returned, the orange overlay had appeared, making the screen quite difficult to read on an iPad.
g0mrb
                 Reply
On the JavaScript version, MENACE2 (a second version of MENACE which learns in the same way, to play against the original) keeps setting the 6th move as NaN, meaning it cannot function. Is there a fix for this?
Lambert
                 Reply
what would happen if you loaded the boxes slightly differently. if you started with one bead corresponding to each move in each box. if the bead caused the machine to lose you remove only that bead. if the game draws you leave the bead in play if the bead causes a win you put an extra bead in each of the boxes that led to the win. if the box becomes empty you remove the bead that lead to that result from the box before
Ian
                 Reply
Hi, I was playing with MENACE, and after a while the page redrew with a Dragon Curves design over the top. MENACE was still working alright but it was difficult to see what I was doing due to the overlay. I did a screen capture of it if you want to see it.
Russ
                 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 "theorem" in the box below (case sensitive):
 2015-08-27 
In 1961, Donald Michie built MENACE (Machine Educable Noughts And Crosses Engine), a machine capable of learning to be a better player of Noughts and Crosses (or Tic-Tac-Toe if you're American). As computers were less widely available at the time, MENACE was built from from 304 matchboxes.
Taken from Trial and error by Donald Michie [2]
The original MENACE.
To save you from the long task of building a copy of MENACE, I have written a JavaScript version of MENACE, which you can play against here.

How to play against MENACE

To reduce the number of matchboxes required to build it, MENACE always plays first. Each possible game position which MENACE could face is drawn on a matchbox. A range of coloured beads are placed in each box. Each colour corresponds to a possible move which MENACE could make from that position.
To make a move using MENACE, the box with the current board position must be found. The operator then shakes the box and opens it. MENACE plays in the position corresponding to the colour of the bead at the front of the box.
For example, in this game, the first matchbox is opened to reveal a red bead at its front. This means that MENACE (O) plays in the corner. The human player (X) then plays in the centre. To make its next move, MENACE's operator finds the matchbox with the current position on, then opens it. This time it gives a blue bead which means MENACE plays in the bottom middle.
The human player then plays bottom right. Again MENACE's operator finds the box for the current position, it gives an orange bead and MENACE plays in the left middle. Finally the human player wins by playing top right.
MENACE has been beaten, but all is not lost. MENACE can now learn from its mistakes to stop the happening again.

How MENACE learns

MENACE lost the game above, so the beads that were chosen are removed from the boxes. This means that MENACE will be less likely to pick the same colours again and has learned. If MENACE had won, three beads of the chosen colour would have been added to each box, encouraging MENACE to do the same again. If a game is a draw, one bead is added to each box.
Initially, MENACE begins with four beads of each colour in the first move box, three in the third move boxes, two in the fifth move boxes and one in the final move boxes. Removing one bead from each box on losing means that later moves are more heavily discouraged. This helps MENACE learn more quickly, as the later moves are more likely to have led to the loss.
After a few games have been played, it is possible that some boxes may end up empty. If one of these boxes is to be used, then MENACE resigns. When playing against skilled players, it is possible that the first move box runs out of beads. In this case, MENACE should be reset with more beads in the earlier boxes to give it more time to learn before it starts resigning.

How MENACE performs

In Donald Michie's original tournament against MENACE, which lasted 220 games and 16 hours, MENACE drew consistently after 20 games.
Taken from Trial and error by Donald Michie [2]
Graph showing MENACE's performance in the original tournament. Edit: Added the redrawn graph on the left.
After a while, Michie tried playing some more unusual games. For a while he was able to defeat MENACE, but MENACE quickly learnt to stop losing. You can read more about the original MENACE in A matchbox game learning-machine by Martin Gardner [1] and Trial and error by Donald Michie [2].
You may like to experiment with different tactics against MENACE yourself.

Play against MENACE

I have written a JavaScript implemenation of MENACE for you to play against. The source code for this implementation is available on GitHub.
When playing this version of MENACE, the contents of the matchboxes are shown on the right hand side of the page. The numbers shown on the boxes show how many beads corresponding to that move remain in the box. The red numbers show which beads have been picked in the current game.
The initial numbers of beads in the boxes and the incentives can be adjusted by clicking Adjust MENACE's settings above the matchboxes. My version of MENACE starts with more beads in each box than the original MENACE to prevent the early boxes from running out of beads, causing MENACE to resign.
Additionally, next to the board, you can set MENACE to play against random, or a player 2 version of MENACE.
Edit: After hearing me do a lightning talk about MENACE at CCC, Oliver Child built a copy of MENACE. Here are some pictures he sent me:
Edit: Oliver has written about MENACE and the version he built in issue 03 of Chalkdust Magazine.
Edit: Inspired by Oliver, I have built my own MENACE. I took it to the MathsJam Conference 2016. It looks like this:

A matchbox game learning-machine by Martin Gardner. Scientific American, March 1962. [link]
Trial and error by Donald Michie. Penguin Science Survey, 1961.
×26      ×24      ×23      ×18      ×20
(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.
This is very neat. I wonder how long it would take to use that many matches to get all those match boxes.
Duke Nukem
×11   ×10   ×1           Reply
"When playing against skilled players, it is possible that the first move box runs out of beads. In this case, MENACE should be reset with more beads in the earlier boxes to give it more time to learn before it starts resigning."

If someone were doing this, you could do this automatically to avoid the perception or temptation of the operator to help it along. Instead of "oh, it's dead, let's repopulate the boxes", you could just make it part of the inter-game cleanup, like a garbage collection routine. After all the bead deleting/adding whatever, but before the next game starts, look at all the boxes, make sure that each box contains at least one of each color. Now this weakens the learning algorithm moderately, but it guarantees that it will never get stuck.
(anonymous)
   ×4      ×1   ×1     Reply
@(anonymous): Yes, those boxes are for O being MENACE and MENACE playing first
Matthew
×1                 Reply
@Matthew: Thank you for such a quick response. Just to let you know that that link did not work after .../tree/master/output, but I managed to search around for the right files :). In these files MENACE plays the Nought right? and the user plays the Cross?
(anonymous)
                 Reply
@Finlay: You can find them at https://github.com/mscroggs/MENACE-pdf.... The files boxes0.pdf to boxes3.pdf are the boxes for a MENACE that plays first.
Matthew
   ×2   ×1           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 "y-axis" in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

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

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024