Wednesday, January 22, 2014

answer, please...

Have you ever wanted to ask a math teacher a question?  My students do it all day long.  Here's your chance. For the next 8 hours, I'll answer any and all math questions.  There's no question too silly.  There are questions that are too hard, but if I don't know and can't find out, I'll be happy to tell you that too.  Is there something you've always wondered about?  Is there a puzzle you've always struggled with?  Now's your chance.

And hey, if you know the answer to someone else's question, answer it...  be a math guru, a math nerd...  Now's your chance.  Ask...  or answer...  a question! 

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  1. What are the odds of correctly predicting all game winners in the 64 team NCAA basketball tournament? You may have read Warren Buffet is offering $1 billion to anybody who picks a perfect bracket. Obviously the answer is vanishingly small, yet the WSJ article I read claimed the actual odds are "incalculable." They add that "a previous survey of mathematicians pegged them anywhere from 1 in 150 million to 1 in 9 million trillion."
    Seems to me the same as correctly picking a coin toss 63 times in a row (2 to the 63rd which is I think the 9 million trillion answer.) Please enlighten us!

    1. According to, in a recent post, they stated that the odds are approximately 1 in 9.2 quintillion.

  2. Found this, which discusses how basketball knowledge improves the odds from above, though not how to calculate the odds of the "sophisticated picker."

  3. Found this, which discusses how basketball knowledge improves the odds from above, though not how to calculate the odds of the "sophisticated picker."

  4. So I went and tracked down the WSJ article you mentioned, and I think that their conversation regarding the odds illustrates some of the complexity of the situation. If in each game both teams had an equal chance of winning, the probability would indeed be (.5) raised to the 63rd power or 1 in 9,223,372,036,854,775,808. I think the Wall Street journal was trying to improve the odds by considering the likelihood of a particular team defeating another. For example, no #16 seed has always defeated a #1 seed, (according to the article) and if we also eliminate the #15 seed versus #2 games, we are down to 55 games. This pulls the odds down to about 1 in 36,000,000,000,000,000, making your chances of winning as if you had filled out 256 brackets instead of just one. But the reason that the odds are seemingly incalculable is due to the imprecision of the rating systems that determine the odds of any particular game. The game itself is unpredictable as teams often upset each other under these conditions. Obviously the overall likelihood of winning is extremely low, no matter how knowledgeable you are, at the very best, similar to the odds of winning the lottery, but probably far less likely than even that.

    In class we talk about the lottery all the time, and I ask students how they would feel if they played and ended up just getting their money back. Most think that would be a pretty good thing. So I tell them to give me their numbers and a dollar and guarantee a return of the their dollar. I don't buy a ticket. I just give them the dollar back the next day. Everyone wins... I myself would rather buy a cup of good coffee...