
Mike and I heard a trivia contest on the radio. The question was:
In the March Madness games, what are the odds of predicting the entire bracket correctly?
1 in 35,000
1 in 35,000,000 or
1 in 35,000,000,000
Mike and I (nerds that we are) sat and figured out that there are 63 games being played (32 the first round, then 16, then 8, then 4, then 2, then 1). Each game has 2 possible outcomes. So, 2 to the 63rd power should get you close to one of the answers. (We didn't have a calculator on us, so we didn't know exactly which one to pick, but we agreed up to that point.)
However, then Mike said that not all teams are evenly matched, so each game can't be a 50/50 shot. I said that there are still 2 possible outcomes and only 1 will be correct, so you still have a one out of 2 shot for guessing the game correctly. But Mike argues that especially in the first round of games, he thinks the better teams have more than a 1/2 chance of winning.
So, math friends, help us out. Is there a one in two chance of getting the correct outcome for each game, or are some games weighted due to the team's skill?