Yasmin and Zheng play a game called Target 13 where they each have a fair cubical dice with faces numbered in the usual way with the integers from 1 to 6, and where one turn of the game consists of them throwing their dice simultaneously.

After each turn, the person whose die shows the higher score gets a number of points equal to the total of both dice, and the other person gets no points. If both dice show the same score, then each player gets the same number of points as the score on their die. The winner is the first person to get 13 or more points. If this happens for both players simultaneously, the game is tied.

What is the probability that someone has won the game after the second turn?

What is the smallest number of turns needed to guarantee that the game has finished?