“Chess is an infinitely complex game, which one can play in infinitely numerous and varied ways”—Vladimir Krammik

This and the following two articles in my blog were written with the aim of helping a friend complete his essays for applying somewhere. However, the end results were, at least in my humble opinion, worthy of publication.

A game of chess involves 2 players, if each player has made a move, over 400 possibilities exist for the second move itself. The next move has over 72,000 possible variations ( as can be seen from applying the laws of permutation and combination, but let’s not go into that here); the next move has 9 million options and the fourth move has over 288 billion various versions. At first glance the game of chess certainly seems to have infinite number of ways in which it can be played. However, of these infinite possibilities, only a finite (although large) portion can be said to consist of rational choices. Here rational implies a desire to win the game of chess in question. The individual players concerned may choose to make choices deliberately leading to their defeat in the game, but as long as both parties play with an aim of victory, it can be proven that the number ways the game unfolds is indeed finite. From a more abstract point of view, infinity has no limits; where as the game of chess involves a limited number of pieces moving on a board having a limited number of set positions following a limited set of rules. And the culmination of each such game has to be either an unambiguous win for one of the parties or a draw; wherein each player can play indefinitely without having any hope of a win. The latter course of action can safely be categorised as being irrational. The writer, being an engineer by profession, is not proficient in the ways of intricate logical arguments and knows but two ways in which infinity can be achieved (if such a term as achievement can be applied to the concept) : a division by zero or a recurring function with no upper limit. Take the latter case, an infinite geometric/ arithmetic progression in chess automatically entails a draw. If the parties choose to continue in such a situation, we can safely classify their actions as being irrational and hence the game ceases to be one of chess ( in the classical sense of course) and becomes one of endurance ( the goal being to irritate the other guy into admitting defeat). A division by zero is unlikely to occur where the functions involved are permutation and combination and the limits for the variables involved belong to the set of natural numbers. Now, the humble writer neither claims to be a fervent follower of the game nor a proficient player. However, he hopes it’s not presumptuous of him to assume that a man like Vladimir Kramnik has a rational set of mind at least where the game of chess is concerned. The only conclusion from these assumptions and the rather simplistic arguments he has put forth is that Mr. Kramnik was tending towards the hyperbole when he made the statement and the number of ways in which a game of chess can be played is a finite if gigantic quantity. Some of the other brilliant minds tasked with this assignment may take it upon themselves to elucidate the point the writer has made with mathematical functions and terms that boggle the intellect, however the writer is content with what his humble intellectual faculties have produced.