Examining a Non-Standard Turn Order in Impartial Games
James Winfield Welsh
Iona College
Benjamin Gaines
Iona College
Abstract
A combinatorial game is a two player game that has a well-defined ruleset and no element of chance. This means that assuming optimal play, the winner can be determined before the first turn is taken. In many well-known games, this gives the first player an advantage. In an effort to address this, we observe how both players’ strategies would change when the second player is given an extra turn at the start to compensate for having to go second. We focus on examples of impartial games under this change, and how it affects the strategic play of the games.
Author Biography
Benjamin Gaines, Iona College
Dr. Benjamin Gaines is an Assistant Professor of Mathematics at Iona College. He teaches courses in mathematical thinking, calculus, introduction to proof, differential equations, linear algebra, discrete mathematics, and number theory. His research interests include algebraic geometry, with a focus on toric geometry and mathematical physics; and math education, particularly on questions involving writing in mathematics.
