Warren Buffett and the owner of the Cleveland Cavaliers are offering one billion dollars to anyone who gets a March Madness (college basketball) bracket perfectly right. This might seem like an outrageously high number, but interestingly enough, they may not even have to pay it! Let's calculate the odds.
1. There are 68 teams that make it into the tournament, and since each team loses once except the winner, there are total games.
2. Let's assume that you have about a 50% chance of guessing each game correctly. [This might even be an understatement, because some really good teams will play really bad teams (especially early on) and will have a more than 50% chance of winning.]
3. After each successful guess, your next guess will also be a 50% chance, so your chance of winning the whole thing is 0.5 x 0.5 x 0.5 x 0.5 ... until you get 67 0.5's, so (0.5)^67.
4. (0.5)^67 = 6.78 x 10^-21, or 0.00000000000000000000678. That's about a one in six sextillion!
Now, most experts think that it is possible to guess the outcome of some games with such certainty that the average percentage of guessing a game right could be closer to about 75%. With this calculation, your odds are still about one in four billion. Buffett is only allowing 10 million entrants, so in all likelihood he won't even have to give the check to anyone!
Works Cited:
http://parade.condenast.com/255536/erinhill/hes-gone-mad-warren-buffett-offers-1-billion-for-perfect-march-madness-bracket/
This is very interesting Joe! It is very interesting that the Cleveland Cavaliers are taking account into very good teams as well. They are very smart for only allowing 10 million entrants which seems like a large number, but in reality is not even close enough for odds.
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