Probability

Two players, P1 and P2, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by P1 and P2,respectively. If x>y, then P1 scores 5 points and P2 scores 0 point. If x=y, then each player scores 2 points. If x<y, then P1 scores 0 point and P2 scores 5 points. Let Xi and Yi be the total scores of P1 and P2, respectively, after playing the ith round.