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  1. The main question we want to answer is: “As a Markov chain keeps running, what kind of behavior does each state have?”

  2. This is quite a hard question to answer straight away, so perhaps we should start with a different question.

  3. Introduction One of those things that is easy to understand conceptually but hard to grasp once we look at the math is doing multi-step transition probabilities.

  4. In my last post, I covered the gambler's ruin, where a gambler was trying to win some money on roulette so he could pay child support to his ex-wife.

  5. You are entering a casino to win some money to pay your ex-wife's child support.

  6. Imagine you and your friend are standing on the sidewalk and you suggest a fun game.

  7. Outside my apartment the sidewalks are paved with stone slabs.

  8. When Russian mathematician Pavel Nekrasov looked at "moral statistics," with its yearly rates of crimes, suicides, and marriages, he noticed something unsettling: the data was flat.