The NFL season is almost here, and with it there will be a lot of gambling. Two years ago, the estimate was that Americans wager over $12 billion on the NFL and online gambling sites have proliferated since then. One fun - and potentially inexpensive - way to gamble is with a survivor pool.
In an NFL survivor pool game, you pick one winner each week. If your team wins, you “survive”. If not, you lose and are out of the game. You also can choose each team only once.
The fact that you can choose each team only once adds a ton of strategy and backward induction to these contests - and that is where game theory analysis can become valuable. For example, there are often times a player should not pick the team most likely to win in a week if it allows a more favorable situation in future weeks.
Here is a real example from the 2014 NFL Playoffs that I give to my game theory class as a homework assignment. Can you figure out who to bet on and why? If you want to know the answer, watch the video at the bottom.
NFL Survivor Pool Problem Assignment
You are in a football survivor pool. You have to pick one NFL game each week. If the team you pick wins, you keep playing. If you ever pick a losing team, you are eliminated. Note – you can never repeat a choice, so you may only pick a team one time throughout the season.
The contest is 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.
The conference championship games are:
· Seattle vs. San Francisco
· Denver vs. New England.
The winners of these games play in the Super Bowl. Based on all information known at the time, 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. Once you want to see the answer, you can watch the video below: