"It was the best of times, it was the blurst of times" is the kind of output you get if you sit an infinite number of monkeys in front of an infinite number of typewriters. This of course a well known thought experiment about whether such a scheme could produce the works of Shakespeare.
An analogous question is whether such a system could produce the worlds best ever game of chess. These days such an experiment does not even require monkey's, as a computer can just as easily come up with random moves. I've stumbled across a few such programs, including one that is used a demo for chessboard.js If you go to http://chessboardjs.com/examples/5002 you can watch a game where the moves are chosen at random from the set of legal moves in any position.
Having watched a couple of games I can make the following observations
(1) It is frustrating to watch
(2) The games go on forever
(3) I suspect any hidden masterpieces are a long way off being revealed
As the code for this is open source I may try and experiment with the settings. For example, always play mates in 1 might be worth trying, as is capture the biggest piece. While it moves the games away from being totally random, it may move them towards a simplistic 'human like' style
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