How often does the first team to win a game win the World Series if they lose the second game?

After last night's loss of the Phillies to the Yankees the World Series is tied one game to one game. I thought that I could update the information from yesterday on the probability that the team that wins the first game of the World Series wins the whole series.

Now the question is "What is the probability that the team that wins the first game of the series and loses the second wins the World Series?" A review of 100 years or so of World series data (plus looking at each series on wikipedia) shows that 50% of the time the teams in the World Series split the first two games. This provides our data set. 50% of the teams that won the first game and lose the second win the World Series.

That makes perfect sense, now the teams are one and one and each team has to win three games to win the whole thing. It becomes a best of five series. Simulations with 10,000 trials and assuming that the teams win 50% of the time confirm the historical trend. In 50% of the cases when the teams split the first two games, the winner of the first game goes on to win the World Series 50% of the time.