## Modified Nim Game Research

#### Mathematics Research

Combinatorial game theory research under the direction of Jordan Ellenberg.

Nim is a two-player game in which each player takes turns removing one or more objects from one of potentially multiple heaps. In misère play, the person who takes the last object loses the game. My research focuses on investigating a modified version of this game: a player has two choices for how many stones he/she can remove from a single pile, and these two choices are given as a percentage of the number of stones in the pile at the start of the game. The results of such games become very interesting when you vary the choice-percentages, the number of stones in the pile at the beginning of the game, the rounding strategies for the two choices, the number of available choices, the number of stone piles, etc.

If you wish to talk about this project, feel free to contact me.