An abstract strategy game is a game like chess or Go in which no luck is involved (like there is in poker, where you're dealt a hand of cards at random) and there's no real-world theme (like there is in Monopoly, where your goal is to earn money by buying property). These games are therefore games of pure skill.

 

However, there are often so many potential moves at any given point in the game that less experienced players may play essentially at random at some points. This leads to questions like the following: What would happen if two people who could each see two moves ahead played against each other? What would happen if a person who could see two moves ahead played against a person who could only see one move ahead? What is the probability of ending in a certain board configuration in each case? How long would you expect each game to last?

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We'll address these questions for the traditional games of Tapatan and Picaria and, hopefully, our own variants on them as well. We can frame them in terms of Markov chains: mathematical models for studying the behavior of systems that progress to different states according to predetermined probabilities. 

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This approach will require us to use both probability and linear algebra, and we'll have to blend theoretical work with some calculations to solve them. These calculations will be carried out in R.