Question

Jim is a gambler who pays his bills by spending weekends in Las Vegas. Lately, he's been playing 21 at a table that returns cards to the deck and reshuffles them all before each hand. As he has a fixed policy in how he plays, his probability of winninga particular hand remains constant, and is independent of all other hands. There is a wrinkle, however, the dealer switches between two decks (deck # 2 is more unfair to Jim than deck # 1), depending on whether or not Jim wins. Jim's wins and losses can be modeled via the transitions of the following Markov chain, whos the particular deck being used (see Figure ) e states correspond to (a) Is this a valid Markov chain? Why or why not? Answer in a short paragraph (b) What is Jim's long term probability of winning? 7 15 (win) loss) 8 C in 4 -(win (loss) 9 Figure 1: Transition diagram for part a & b

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Answer 1

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