I was asked to formulate a Markov decision problem to determine the optimal strategy of play where, Assume that you play a chess match with a friend. If you play timid your probability of making a draw is $p=0.8$, the probability of winning is $0.1$ and the chance to lose is $0.1$. If you play bold, you either win with a probability $q=0.45$ or lose. Each win brings one point to the score of the winner. The match consists of $5$ games. If the score is a tie after the fifth game, then a "sudden death" rule is adopted; that is, whoever wins the next game is a winner of the match; if it is a draw again, then the game is repeated with the same rule. Can anyone help me to formulate and understand MDP here?
2026-03-31 05:39:51.1774935591
Formulate a Markov Decision Problem for the given strategy
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