Leif Hopkins, Team 058 Santa Fe High School: INTERIM REPORT

The Profitability of Games of Chance

Problem Definition:

In a game of chance, the gambler typically risks some in hopes of being on the winning side of a probabalistic wager. Roulette, Blackjack, and various other casino games are examples of this. This project will explore various methods of using probability theory and game theory to the advantage of the gambler, hopefully allowing he/she to ultimately profit in their gambling. It will explore several possible methods of play, eventually making some conclusion regarding those methods.

Plan for Computational Execution of Problem:

Using the C++ computer language, the attempt will first be made to generate a program capable of simulating a given game of chance. After that is completed, the program can be expanded to incorporate players who, programmed to follow different routes given the situations they could potentially encounter, will be models for tracking profit (or lack thereof). Ideally, those players actions would be modeled after principles of probability theory and game theory, or perhaps some pseudo "gamblers logic." Comparisons will ultimately be made between the net profit of each player.

Progress Thus Far

Research has been done on the subjects of probability theory and game theory, though only its most pedestrian topics. I have been refreshing my memory of programming, which is somewhat gapped and failing. Nevertheless, I believe that my competency in both the theoretical and programming aspects of my project are increasing at a rate which is sufficient for adequate completion of my project.

Expected Results

It is expected that those players adhereing to the principles of probability theory and game theory will profit, and those not doing so will not. However, being that probability is a factor within this project itself, it can be expected that anomalies of probability and hence, some differing results, will manifest themselves.

Sources of Research and Study

"Probability Theory- The Laymans Guide...," http://www.peterwebb.co.uk/proabability.htm#intro.

"What is Game Theory?," http://levine.sscnet.ucla.edu/general/whatis.htm

"Professional Gamblers Home Page...," http://www.professionalgambler.com/

"Elementary Probability Theory," http://farside.ph.utexas.edu/teaching/sml/lectures/node10.html

"C++, An Introduction to Computing," Adams et al. 1998 Pretice-Hall, Inc. Upper Saddle River, NJ 07458. Second Edition.