I recently got interested in some game theory applications to poker. I want to try some of them out programmatically, but a lot of the math is a bit confusing. I learn math on my own fairly quick and I was wondering what topics I should study to be able to fully grasp what they are discussing. What are some good recommendations?
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There are different resources for reading on game theory
1) There are online lectures: Game theory 101 which is fairly popular.
2) There is a book: Non Cooperative Game Theory by Tamer Basar, which covers the topic like a subject.
3) There is a nice blog called : www.mindyourdecisions.com
Overall to start with you should study the following:
1) Normal form or strategic form of a game. This is a matrix formulation of a game, rows representing one player's payoff function and the columns representing the other player's payoff function
2) Saddle Point Equilibrium
3) Pure Strategies and mixed strategies
4) Nash Equilibrium
5) Extended form of a game: This is a tree based formulation of a game
These should be enough to understand whatever is being talked about game theory
With the jargons of game theory, poker games are finite sequential games with perfect but incomplete information . To understand the formulation of sequential games, you may want to understand the concept of "tree" which can be found in some standard descriptive set theory textbook. To undertand related concepts like mixed strategy, behavioural strategy, formulation of incomplete information, some knowledge of probability theory seems to be indispensable, especially those related to conditional probability, random variable et al.
I vaguely remembered that it is mentioned somewhere that J.P ponssard's earlier works involves applications of game theory to poker, which you might take an interest in .
My recommendation is to take a look at the study plan of the subject in any college, there usually is a section about "previous requisites". As for my college, the previous requisites they have for the 4th year course of game theory is:
A first course in all of those should be enough, but I haven't done that subject yet, so I can't tell any further.
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Game Theory is not a first year course, so I believe that you will need to devote a considerable amount of time preparing with general reading in mathematics. Otherwise, you are unlikely to be able to understand and apply the concepts involved.
So my recommendation is to start by reading an introductory text in pure mathematics.