An Alternative Illustration to Generalize Sprague-Grundy Theorem

Although game theory is well-established for linear games, where there is no repetition, and games with loops are often disregarded, due to it’s nature of loops being hard to handle, as a player can stay in a loop forever to avoid losing, and thus it is hard to determine whether a the player has a winning strategy efficiently. Due to this lack of exploration of games with loops, modern board games usually have this quality of being complex in terms of the variety of moves, and having some loops. This research proposes an intuitive approach to extend the Sprague-Grundy Theorem from linear games to games that contain cycles to find a computational algorithm to efficiently calculate the wining stragegy.