# Game Theory

Happy March Madness! (... and maybe next year Illini!)

This year, Warren Buffet and QuickenLoans are partnering around March Madness for a huge marketing campaign. The gist: if you can exactly predict the outcome of all 63 games of the tournament, you'll win \$1 Billion dollars.

That might seem like a losing gamble, but a statistician would disagree. With 63 games, the odds of getting a bracket exactly correct are 1 in 263. (~1 in 9 quintillion!). Sure, you can say it's not totally random, and that educated fans, research, and super-fandom will make the odds a little bit better. But, at the end of the day, you'll still need ~3/4 odds on every game to get near lottery rates. Mr. Buffet has made a pretty sure bet.

But wait! Statisticians don't know everything about sports! What about game theorists?

Game theory is a study of decision making, wherein the players of a game attempt to gaurantee better winnings by working together, rather than competing against eachother. Recently, Arthur Chu caused a rumble in the Jeopardy world by applying game theory to the quiz show.

Applying game theory to the March Madness billion dollar gamble, we need a strategry that will gaurantee a subset of the players more money than they could otherwise earn. In March madness, the "players" are the conferences, schools, coaches and players. On average, every school earns ~6 million dollars in revenue from basketball each year. . With a \$1 billion in the pot, and only 6 million to beat, it's easy to build gauranteed winning strategies.

Let's say the 63 tournament schools worked together to rig the bracket. Gauranteeing the \$1 billion payout, and splitting that payout among the schools/coaches/players. Each school would earn ~16 million dollars. That's almost triple the average yearly revenue for the entire season.

Alternatively, let's say only the players throw the games. At 13 players per team, 63 teams, each player could gaurantee himself over \$1 million dollars in payout.

This is a pretty extreme proposal. The NCAA and courts would undoubtedly apply fines to the coaches, faculty and schools behind such a scandal. But, with a billion dollars at stake, could it be worth it?