The Strategic Games Foundation funds Honours, Masters and PhD students on research in the mathematics of sport, gambling and conflicts. Please contact Tristan if you would like to be a sponsor of the foundation. All funding goes to the research candidates. There are no administration costs.
Dr Tristan Barnett (The Baron)
Associate Professor Tim Byrnes (CV)
Emeritus Professor Stewart Ethier (CV)
The Strategic Games Foundation constitution can be found here (pdf)
1. Developing a mobile app for casino games as a decision support tool
Calculations on casino games are obtained for the probabilities of winning for the various outcomes, average loss and the distribution of payouts. Strategies are obtained where they exist such as blackjack and pontoon. All of this information is developed on a mobile phone app. Analysis is given for poker machines, roulette, craps, two-up, baccarat, caribbean stud poker, sic bo, casino war, big wheel, blackjack, pontoon and pai gow; thus covering the majority of casino games offered in Australia.
2. Automating a predictive tennis calculator
The probabilities of winning and match duration are programmed from any score line during a match in progress. A flow chart is represented on a point-by-point basis on the probabilities of winning. Tournament predidctions are given for a player to reach a specific round and for player A to meet player B. The information could be used by tennis commentary to give additional information for spectator interest.
PROPOSED PHD PROJECTS
1. Automating online tennis betting for profit
By analyzing point-by-point data a dependency Markov Chain prediction model is developed in Excel using forward and backward recursion to calculate the chances of winning as well as the first four moments of the number of points remaining in a match conditional on the scoreboard. A simulation prediction model is also developed where the Markov Chain dependency assumption does not hold. A Bayesian updating rule is formulated for the match in progress. The whole system is automated in Betfair to demonstrate a player advantage.
2. The mathematics of volleyball and pickleball
The probabilities of winning a match and the first four moments of the number of points remaining in a match from any score line for tennis can be obtained using recursion formulas in spreadsheets. This enables calculations for other racket sports such as table tennis. However, volleyball and pickleball are more complex to analyze than tennis due to the rotation of serve. This project calculates the probabilities of winning a match and the first four moments of the number of points remaining in a match from any score line for volleyball and pickleball.
3. Applying risk theory to game theory
The 'minimax theorem' is the most recognized theorem for determining strategies in a two-person zero-sum game. Other common strategies exist such as the 'maximax principle' and 'minimize the maximum regret principle'. All these strategies follow the Von Neumann and Morgenstern linearity axiom which states that numbers in the game matrix must be cardinal utilities and can be transformed by any positive linear function f(x)=ax+b, a>0, without changing the information they convey. This project describes risk-averse strategies for a two-person nonzero-sum game where the linearity axiom may not hold. This may appear inappropriate when there is a negative payout and a player may want to reduce the probability of ending up with the maximum possible loss by reducing the expected payout under the Nash Equilibrium. Analysis is also obtained in quantum game theory where the quantum Kelly equilibrium is established for a two-person zero-sum game.