Invited Paper Session Abstracts - The Mathematics of Games

Thursday, August 4, 2:00 PM - 3:50 PM, Harrison

Games, how to win them and how to design them, often lead to mathematical questions. Generally intractable games, such as poker, have ‘toy’ variants that yield to explicit mathematical analysis, while some simple ‘solved’ games such as tic-tac-toe become very challenging when moves are auctioned to the highest bidder. The talks in this session discuss the design considerations of games and the determination of optimal play in both games of chance and no-chance.

Organizer:
Michael Catalano-Johnson, Susquehanna International Group

Recent Advances in Game Design

2:00 p.m. - 2:20 p.m.
David Pettey, Susquehanna International Group
Over the past 20 years there have been noticeable advancements made in game design that have led to significantly more enjoyable games. We will highlight several of the general principles employed to improve design, and why we believe they lead to better games.

Solving Poker-Like Games

2:30 p.m. - 2:50 p.m.
Bill Chen, Susquehanna International Group
We will look at how to solve 'toy' poker games, using examples from the book 'The Mathematics of Poker' by Chen and Ankenman, and what the solutions mean for real poker games.

Richman Games

3:00 p.m. - 3:20 p.m.
Daniel Loeb, Susquehanna International Group
In Richman games (aka bidding games), rather than alternating moves, the two players bid for the privilege of making the next move. Players may or may not know the bankroll of their opponents. We discuss optimal strategies for players.

Misère Russian Roulette (with Multiple Revolvers)

3:30 p.m. - 3:50 p.m.
Michael Catalano-Johnson, Susquehanna International Group
Two players take turns removing (without replacement) a random stone from a player selected urn, each containing known mixtures of black and white stones. A player wins as soon as he or she draws a white stone. How to play? sometimes the correct play is counterintuitive. We establish simple to calculate rules for optimal play.