Tanya Khovanova

P-positions in Modular Extensions to Nim

2015 · arXiv (Cornell University)

In this paper, we consider a modular extension to the game of Nim, which we call $m$-Modular Nim, and explore its optimal strategy. In $m$-Modular Nim, a player can either make a standard Nim move …

From Unequal Chance to a Coin Game Dance: Variants of Penney’s Game

2021 · Recreational mathematics magazine

Abstract We start by exploring and analyzing the various aspects of Penney’s game, examining its possible outcomes as well as its fairness (or lack thereof). In search of a fairer game, we create many variations …