Chess & Football: a computational comparison

ChessChess is played in a defined physical area which is broken into 64 discrete spaces. Pieces move within this area following a number of specified rules: for example, rooks can move horizontally and vertically, bishops move diagonally.

As a result of prescribed rules being followed within a defined area, chess is amenable to computational principles. This is also why it is possible to calculate the total number of possible moves in a game of chess, 10120. This is a reasonably massive number; for comparison, it is conjectured that there are about 1075 atoms in the entire universe.

It may not appear that the same principles of computation could be applied to football. However, football is also played within a defined physical space and is performed with reference to a specific set of rules. Football players may have much more freedom than chess pieces, but the scope of their mobility is circumscribed by both the rules of the game and their anthropomorphic limitations. Despite greater state-space complexity, it should still be possible to compute the format of every game of football that could ever be played.

There are some key differences between football and chess to take into account when devising a holistic computational model of the former. For example, there are more subtle variations of action in football, with complex intersections of speed, strength and cognitive ability impacting upon the movements available to each player. The probabilistic prediction of all possible moves is also less defined, as football is predicated on continuous play rather than discrete positional changes.

Despite these added features of game complexity, the difference between chess and football is fundamentally one of degree rather than substance. A computational rendering of football simply has to take into account factors such as: playing area; rules of the game; the scope of player movement; the scope of ball movement; player motivation; refereeing fallibility; the weather; crowd responses etc. Scientists will then be able to map the entire range of possible football matches. Top mathematical minds at WCC currently consider that the approximate maximum number of different matches that could be played is 400 squadrillion (400 followed by enough zeroes to fill a medium-sized black hole).

Mathematician Pierre-Simon Laplace postulated the existence of an entity that, knowing the complete state of universal conditions at a specific point in time, could accordingly envisage all past and future occurrences. (This entity subsequently became known as Laplace’s demon.) This view suggests that all events were determined from the genesis of the universe; therefore, complete knowledge of the state of spacetime at a particular juncture could enable complete predictive powers. It’s not yet possible to establish the state of the universe in its totality, but a holistic computational model of football can derive predictions from a more localised level. Once the exact initial conditions of a certain game are known, it will be possible to predict every kick, jump, shout, shrug of the shoulders and feigned injury with total accuracy.

As chess is subject to computational principles, a computer, Deep Blue, was able to beat the human grandmaster Gary Kasparov in 1997. As a similar computational representation could calculate all of the possible moves in any football match, WCC believes the first non-biological team will triumph in a World Cup circa the year 2410.

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