Alice, Bob, Charlie, and David are all playing a basketball tournament such that they are randomly paired up and the winners of each pair best out of 1 for the title. When Alice plays Bob, she has a chance of 1/3 of winning. When Alice plays Charlie or David, she has a 2/3 chance of winning. When Bob plays Charlie or David, he has a 3/4 chance of winning. What is the probability that Alice wins the tournament?