“Nontraditional Positional Games: New methods and boards for playing Tic-Tac-Toe”

Document Type

Presentation Abstract

Presentation Date

5-9-2012

Abstract

Positional games are played by two players who alternately attempt to gain control of winning configurations. In traditional positional games, the players alternately place pieces in open positions on a game board. In this defense we explore a variation on this game where players alternately make a hop move instead. During a hop a player moves one of his own pieces and replaces it with one of his opponent’s. We explore the Hop-Positional game played on two classes of boards: $AG(2,q)$ and $PG(2,q)$. In particular we explore how a counter-intuitive strategy leads to an optimal result for the second player on many boards. Once we have establish our results on these two classes of boards we define a new type of board called a nested board, in which the points of a board are replace with copies of another board. We will discuss two types of games on the class of nested boards. First the traditional positional game in which players alternately place pieces in open positions, and second the Hop-positional game where players alternately hop on the nested board. We divide the nested boards of interest into four classes based on the structure of the component boards. We will demonstrate threshold values for the size of the nested board in each class in order to guarantee the second player has a drawing strategy in each game.

Additional Details

Doctoral Dissertation Defense. Link to the presenter's dissertation.

Dissertation Committee:
Jenny McNulty, Chair (Mathematical Sciences),
Mark Kayll (Mathematical Sciences),
George McRae (Mathematical Sciences),
Mike Rosulek (Computer Science),
Nikolaus Vonessen (Mathematical Sciences)

Wednesday, May 9, 2012
10:10 am in Math 108

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