The probabilistic method and positional games

Date: Thursday 11 August 2022

Abstract

My Honours project is focused on two topics: the probabilistic method and positional games. The probabilistic method is a non-constructive existence proof technique, pioneered by Paul Erdős. It is often used in combinatorics to prove the existence of an object with a given property, by defining a probability distribution on some set and proving that the property holds with positive probability. We find that the probabilistic method can be used in the study of positional games and so we begin to explore the topic of positional games. Positional games give a mathematical footing for the analysis of a variety of two-player games played on a finite board including the classical game of tic-tac-toe. In my talk, I will introduce both topics and give some examples.