chalkdust therefore reinforcing the sequence of moves that had been played. These moves, however, might not necessarily have been good ones: Menace might just have got lucky. I also wrote a program for a perfect strategy for noughts and crosses to train Menace against. This strategy only lets another player draw or lose against it. What struck me when training Menace against this program was the number of times it ran out of beads in certain boxes, having lost so many times that all of the beads from a particular box were removed. If there are no beads le in the box representing the current scenario, Menace is said to “resign” as it doesn’t “think” it can win in its current situation. This is OK if it’s a box representing a move that you rarely come across, but when it’s the box representing the empty board, the box that Menace always starts oﬀ with, there’s a problem! To fix this, all I needed to do was to add more beads to this box, although this had the consequence that it takes Menace longer to learn.

Graphs showing Menace against a perfect strategy. The y-axis shows the number of games Menace has drawn minus the number it has lost. On the right, we can see that aer having added beads to the starting state of Michie’s original Menace, it takes longer to draw the same number of games as it has lost (cross the x-axis).

Machine learning is being used in many fields today including in the work of technology giants such as Facebook and Google, whom we have already mentioned have made breakthroughs in the more complex game of Go. The AI programs learning to play Go are not saving all the possible layouts of the game as we have done with noughts and crosses, as there are more of these than there are atoms in the universe. Instead, these programs detect similar paerns and use them as a starting point for their learning. However, the programs are then taught in a similar way to the way we taught Menace to play against diﬀerent strategies, although the programs learning Go play against themselves repeatedly. So ideas that emerged from simple machines in the past are still being used today for much more complicated tasks. Oliver Child is a high school student living in Brussels who is interested in all kinds of maths and computing. Oliver was first introduced to Menace by Mahew Scroggs, who has made a version of Menace that you can play against at mscroggs.co.uk/menace chalkdustmagazine.com

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Chalkdust, Issue 03

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