It is a very simple question.
I would like to learn Game Theory but I am not that good at Probability Theory.
I would like to know it is necessary to be good at probability theory in order to learn game theory? If yes, how they are related to each others? What is the best strategy for someone to be good in Game Theory?
Please give a good reference to start learning both.
I appreciate your help.
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Some years ago I had this kind of situation. I took a class with the name "Probability" I thought that was ok, I am fine with general probability, nothing more than that. Turned out this course was going to be more with game theory "a la Las Vegas" style then just conventional probability. And so I passed with a B. The reason for missing my A was because I did not fully comprehend the nature of the games, like card games, roulette, bridge, black jack, things like that. I never really played those games and so compared to my fellow students, I was at a disadvantage. So if you want to be good at game theory, learn how to play the games first and foremost before even going into probability. Once you know the "tricks" of the game, for the most part you do not need to know heavy probability at all. The major probability distributions even taught in a college credit high school course will suffice.
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I personally love game theory and probability theory. I have always played different card games like craps, roulette, and poker but never knew that it was included in game theory. I completely overlooked game theory, and did not realize how much it went with probability theory. There is a probability every time that you lay a card down that you will not win for that round. Once you understand the game, you realize that the probability gets lower as you get higher in your risk. I would suggest learning probability before you try to learn game theory. Once you learn probability, your odds are higher for success in game theory.
Because we call it a "game" does not it make a game in the sense that is studied by Game Theory. Roulette, slot machines, and other games of chance are not strategic games.
Game Theory studies games where what is the best for you (usually) depends on what the other players are doing are doing.
For Game Theory, you will need basic probability: Bayes rule, discrete and continuous random variables, and computing expectations are the basic tools of the trade but advanced probability is not required.
Osborne: An Introduction to Game Theory is the textbook I use (undergrad level), it has a section on the Appendix on probability with everything you may need. I'm not sure if I'd recommend it for self study but the section on the appendix will show you that you need very little of probability.