# 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 2^{63}. (~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?