The topic we choose for our project are Nim variations, namely, Grundy’s Game and Wythoff's Game. Grundy’s Game is a two-player game that starts with a single heap of objects. Each player take turns splitting a single heap into two heaps of different sizes. The game ends once only heaps of size two and smaller remain, where both cannot be split unequally. Wythoff’'s Game is also a two-player game that consists of two piles of counters or tokens. On each player’s turn, they have the choice of removing any number of counters from one or both of the piles. However, if the player decides to remove from both piles, they must remove the same amount of tokens from each pile. The game comes to an end once one player removes the last counter or counters, giving them the win. Our plan for the three-page report is the following: 1. Introduce Wythoff's Game and show possible winning strategies 2. Introduce Grundy’s Game and show possible winning strategies 3. Comparison between Nim, Wythoff's, and Grundy’s Game and what we learned For our presentation, we are hoping to cover the following: 1. Introduce Wythoff's game (how to play/how to win/winning strategies) 2. and Grundy’s game (how to play/how to win/winning strategies) 3. Explore what we learned References: Nim - Game Theory Textbook (from class) and https://wiki.math.wisc.edu/images/Nim_sol.pdf Wythoff's Game - hitps://math.rice.edu/~michael/teaching/2012Fall/Wythoff.pdf Grundy’s Game - https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/masterschl ebusch.pdf
