Sam and Pat are playing foosball. When they begin, the score is 0-0. To make things interesting, if the score ever becomes tied, it is instantly reset to 0-0. Starting from any score, the probability that Sam gets the next point is 1/3. The game stops when one player’s score reaches 2.
Answer:-
Denote by (x, y) the score of Sam and Pat respectively, a Markov chain that describes the game is :
The probability that Pat wins is the probability that we get absorbed to the state (0, 2).
Now, how can I Setting up the equations?, and solve for a(1,0), a(0,0) and a(0,1)
How it needs to be solved next?
found this question on MIT
Let $a,b,c$ be the probability that Pat wins from $(1,0), (0,0), (0,1)$ respectively. Looking at $(0,1)$ you have $c=\frac 23 + \frac 13b$. Write the equations that come from the other two states and you have three equations in three unknowns.