Wikipedia is a great source of knowledge on the Web. Here is a list of Wikipedia articles that you might consider reading if you want to dig deeper into gambling theory.
Game theory – this is probably the most “classic” piece you need to start with, in any case – following the URLs in this article will lead you down dozens of different paths… but that’s what research is all about, isn’t it? 😉
Gambling and information theory – another fundamental piece to read before you even get started.
Martingale (betting system) – only recommended to gamblers with infinite wealth.
Gambler’s Fallacy – read this before you keep playing roulette obsessively at the Monte Carlo Casino.
Optional stopping theorem – the beauty of mathematics is that it can objectively explain pretty much everything in real life… for example: when to stop!? 🙂
Representativeness heuristic is the term for “making judgments about the probability of an event under uncertainty”, coined by Amos Tversky and Nobel Prize winner Daniel Kahneman.
Von Neumann–Morgenstern utility theorem
A short list of the great men who dedicated their lives to mathematics and contributed to gambling theory in one way or another.
John von Neumann – You can call him one of the most influential mathematician of the 20th century, and definitely THE MOST influential contributor to game theory.