4 A card game

You and your friend are playing the following game: you have a three-card deck marked with the numbers 1, 2, and 3, and a spinner with the numbers 1, 2, and 3 on it. The game begins by dealing the cards out so that the dealer (which could be you or your friend) gets one card and the other person gets two. A move in the game consists of a spin of the spinner. The person having the card with the number that comes up on the spinner hands that card to the other person. The game ends when someone has all the cards.

a) Write a Markov chain corresponding to this game.

b) On average, how many moves will this game last?

c) If you are the dealer, what is the probability that your friend wins the game?