Re: [math-fun] Game Theory/Chess strategy question
All chess positions are intrinsically won, drawn or lost for the side to move [Zermelo (?), von Neumann] There may be more than one move which retains the value of the position and this seems to be usually the case. The set of moves SM that progress mate by only one ply may have more than one move in it but usually (so far, about 85% of the time) this appears not to be the case. The set of moves that progress mate to some other objective ('conversion' or 'end of phase') may be different from SM. The set of moves (probably one) that, in a draw situation, maximises the probability of a win against a fallible player may depend on the nature/degree of the opponent's fallibility. I would suggest that 'a strategy' is an algorithm for (successively) filtering down to the chosen move. Papers including the word 'fallible', 'skill', 'skilloscopy' in http://centaur.reading.ac.uk/view/creators/90000763.html may be relevant. A reasonably authority advises me that Lasker was the first to play the opponent as opposed to the ever-present Goddess of Chess, Kaissa. Today, with databases characterising the play of the top players, this is increasingly the case. Tal and Kasparov seem to be examples of players who particularly created 'opportunities to win against fallible players' by not necessarily choosing the best theoretical move. Guy
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Guy Haworth