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chalkdust The 304 matchboxes that make up Menace represent all the possible layouts of a noughts and crosses board it might come across while playing. This is reduced from a much larger number by removing winning layouts, only allowing Menace to play first and treating rotations and reflections as the same board.

Each of these layouts would be represented by a single matchbox, as they are all either rotations or reflections of one another.

Each of these matchboxes contains a number of coloured beads, each colour representing a valid move Menace could play for the corresponding board layout. The starting number of beads in each matchbox varies depending on the number of turns that have already been played. In Donald Michie’s original version of Menace, the box representing Menace’s first turn had four beads for each different move. The boxes representing the layouts of the board for Menace’s second turn contained three beads for each different move; there were two beads each for Menace’s third; and one of each in the boxes representing Menace’s fourth go. There are no boxes representing Menace’s fih move as there is only one space remaining and Menace is forced to take it.

Coloured beads representing possible moves.

To speed up the learning process even more, only beads representing unique possible moves are used. So even though all the spaces are free on an empty board, only three need to be represented: centre, side and corner. All other positions are equivalent to one of these three. When Menace makes its move one must find the box representing the current board layout and take a bead at random from that box. The bead represents the space in which Menace wishes to place its counter. This process is repeated every time it is Menace’s go until either somebody wins or the board is filled. The beads shown are the only ones required for each scenario: all other positions on the board are equivalent to one of the positions marked.

Aer having completed a game, Menace is punished or rewarded depending on the outcome. If Menace lost, the beads representing the moves Menace played are removed. If it was a draw, an extra bead of the colour played is added to each relevant matchbox; while if Menace won, three extra beads are added. This means that if Menace played badly, it will have a smaller chance of playing the same game next time. However, if Menace played well, it is more likely to follow the same route the next time and win again. 19

spring 2016

Chalkdust, Issue 03  

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