Can a Chess Piece Explain Markov Chains?

The video explores the problem of a knight's random movement on a chessboard, using Markov chains to determine the average number of moves it takes to return to its starting square. It introduces the concept of stationary distribution and applies a theorem to solve the problem. The video also discusses pi in different metrics, highlighting its variability and irrationality.

What is the best counter to the Queen's Gambit?

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How many legal moves does a knight have from its starting position?

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What is the probability of a knight jumping to a specific square when it has multiple options?

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What is a Markov chain and what are its two main components?

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What is the significance of the arrows in the probability transition function of a Markov chain?

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What happens to the stationary distribution if the probability transmission function changes?

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How does the stationary distribution relate to the time it takes for a knight to return to its original square?

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What fraction of time does a knight spend on each square of the chessboard?

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How many random hops does it take on average for a knight to return to its original square?

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If a knight starts in the corner of the chessboard, how would that affect the average number of hops to return?

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