Combinatorial Game Theory
Nowakowski, Richard J. 1952-, Landman, Bruce M. 1951-, Luca, Florian 1969-, Nathanson, Melvyn B. 1944-, Nešetřil, Jaroslav 1946-, Robertson, Aaron 1971-, Berlekamp, Elwyn R. 1940-2019, Conway, John Horton 1937-2020, Guy, Richard K. 1916-2020, Walter de Gruyter GmbH & Co. KG
Abstract
Given a combinatorial game, can we determine if there exists a strategy for a player to win the game, and can we pinpoint what this strategy is? The answer to these questions varies from game to game, and even the most trivial games can become a burden to solve if we change a few rules, such as playing the game under the misere play rule. In this paper, we learn some fundamental techniques that are useful to solving many games. We will analyze the game of Nim and its many variations, and learn about the Sprague-Grundy function and how to create a single game out of many. Using the techniques we learned, we analyze and completely solve the Green Hackenbush game.