- #1
ha9981
- 32
- 0
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 I am struggling at the transition matrix, if someone could guide me to a similar example because my textbook lacks here.
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 I am struggling at the transition matrix, if someone could guide me to a similar example because my textbook lacks here.