PHOTO BY STEPHEN SLADE. COURTESY OF UNIVERSITY OF CONNECTICUT
Shabazz Napier (13) leads UConn to
victory over Kentucky in the 2014 NCAA
Championship game.
I was bemused to read this article [1]
in Slate magazine detailing the odds of
Warren Buffet’s basketball challenge,
which may be found here [2]. [Buffet
offered a billion dollars to anyone who
submitted a perfect bracket (i.e., correctly predicting the winner of all 63
games) of “March Madness,” otherwise
known as the NCAA Men’s Basketball
Championship Tournament.] A billion
dollars – even with taxes – is a lot of
money. How hard is it to come up with
a perfect bracket? There is only one
perfect bracket in a world with many
potential brackets, so we first need to
find out how many possible brackets
there are.
The NCAA is a single elimination
tournament, which means that each
team plays until they lose. In a single
elimination tournament, each round is
made up of n teams, with n / 2 games
n /2
played. Therefore, there are 2
possible outcomes in the first round. Knowing that the tournament starts with 64
teams, there are
possible
outcomes for the first round. Using similar calculations at each round, there are
possible outcomes, only one of which
is correct.
For comparison’s sake, 1 billion is
a thousand million, or 109 so the odds
of winning the basketball challenge
9 2
are around 1: (10 ) or one in a billion
billion 3 . So, it appears your odds of
winning are not very good at all.
Frequently, one can get a feel for the
value of a gambling game by the “fair
price” that one would be willing to pay
to play the game; specifically, the value
that would make one indifferent between
playing the game and just keeping their
money. For this game, a “fair” price would
be nine million attempts per penny!
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