# Transition Matrix for a betting game

#### ha9981

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.

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#### fresh_42

Mentor
2018 Award
This should be a Markov process, but we could as well list all possible paths. It is always a good idea to draw a graph.

Homework Helper
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 proprofitable (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.
How much does the player start with? Nothing? Two dollars? Once you know that list out as the states the amounts of money the person could have after each bet, whether win or lose, then assign probabilities.

"Transition Matrix for a betting game"

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