You are in a football survivor pool. You have to pick a winner each week, and you can never repeat a choice. Once someone you pick loses, you’re out. It’s down to two players from about 1,000 starting entrants. Note: If you both choose a loser, you tie in the contest.
Note that based on previous picks, you can’t pick New England and your opponent can’t pick Seattle.
Games this week are: Seattle vs. San Francisco and Denver vs. New England. The winners of these games play in the super bowl. Based on all information, we know that Seattle beats San Francisco 64% of the time and Denver beats New England 68% of the time.
In the Super Bowl, there are four potential matchups. Here are the estimated probabilities of each team winning based on the matchup:
Seattle beats New England 65% of the time
Seattle beats Denver 60% of the time
San Francisco beats New England 60% of the time
San Francisco beats Denver about 50% of the time.
Your task: Who should you pick this week and why? Be thorough and show your work