Predicting the Winner in the Game of Nim

Abstract

Game Theory is defined as a means of mathematical analysis when interests collide with each other to reach the best possible decision-making options taking into consideration the given circumstances to get the desired results. Even though Game Theory is related to well-known games such as checkers, XO, and poker. In fact, it is associated with more serious problems pertaining to sociology, economics, politics, military sciences. Game Theory includes several sorts of games like Combinatorial Games.

This Paper gives the reader a detailed outlook of a special Combinatorial game called Nim Game. Before the start of the game we will develop a strategy to determine the winner in advance with the help of some basic mathematical concepts like Minimum Excluded (MEX), Grundy Numbers and The XOR Number.