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Research Paper | Management | India | Volume 6 Issue 1, January 2017

Checkmate or Not-: Validation and Application of Zermelo's Theorem in Chess

Dr. D.C. Agrawal ^[3] | Ankur Kukreti ^[4]

Abstract: In this paper author, has tried to prove Zermelos theorem by using mathematical induction and by using Zermelos theorem author has proved that Chess has a solution. This would be done by analysing few games played between two opponents (Viswanathan Anand from India and Garry Kasprov from Russia) and then analysing the defects made by each of the player per move and would try to prove that a person inducing more defects losses the game and if both the person induces equal defects or no defects then the game eventually ends in a draw. In first 3 matches, first match was won by a player playing with white pieces (Anand), one match was won by a player playing with black pieces (Garry) and one match was drawn between both the opponents, By the use of fraction defectives [1] author have shown that the first two matches (match won by white and match won by black) were won by the player playing less defective moves compared to his opponent while one match which was drawn between two players have moves exhibiting more or less equal defects or no defects (s) and the fourth match is a dummy match which will serve as a proving of the 3rd match between Anand and Garry. Through this it is concluded that all player loses a game if they themselves induces defects in games otherwise the match would end in a draw. Moreover, author has also rectified the defects and provided correct moves in place of defective moves thereby proving that match would end in a draw.

Keywords: Chess, dummy, fraction defectives, Zermelos theorem

Edition: Volume 6 Issue 1, January 2017,

Pages: 1324 - 1328