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Transition Matrix for betting game

  1. Nov 8, 2009 #1
    Suppose that a casino introduces a game in which a player bets $1 and can
    either win $2 or lose it, both with equal chances. The game ends when the player runs out
    of money, or when he wins $4.
    (a) Build a transition matrix for the game, and show that it is not a regular transition
    matrix.
    (b) Find the long term expected payoff to the player, and explain why the game is
    pro profitable (or not) for the Casino.

    My Attempt:

    a) P =
    0.5 0.5
    0.5 0.5

    I don't feel this is right because there is a lot of extra information in the question that seems wasted. My attempt to incorporate game ending at $4.

    P =
    0.5 0.5 0
    0.5 0.5 1


    I can't even get to part B as im struggling at the transition matrix, if someone could guide me to a similar example because my textbook lacks here.
     
  2. jcsd
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