Analytics Magazine Analytics Magazine, May/June 2014 | Page 86

FIVE- M IN U T E A N A LYST If a similar wager cost $1 to play, it would depend on what else you would do with the money. Foregoing a late afternoon soda to buy a ticket for this game, if you enjoy talking about it, would be OK. Dumping out your life savings in order to play games is a terrible idea (we’ve written about this before, see July 2013 [5]). The point is that we all do lots of things where the odds of winning are practically zero. This is not necessarily a bad thing. If you derive “pleasure” out of daydreaming about winning a billion dollars or have fun arguing basketball scores with your friends, go for it! Just do so with eyes open, knowing that it is incredibly unlikely that you will win. And don’t forget, there are also 20 first-prize winners, regardless of whether the grand prize is given or not, valued at $100,000. While no billion, this is no small amount of money, and most importantly, does not require you to be perfect, simply better than the other players who enter. If you think you are good at filling out your bracket, then perhaps you should enter with the hopes that you win the first prize. Here, the odds are no worse than 1:750,000, which is a number that you can start to comprehend! A note on calculation. I used R to do the large calculations in this article. 76 | A N A LY T I C S - M A G A Z I N E . O R G Professionals always need to be concerned about numerical stability and floating point precision, which may be the subject of a subsequent article. If I did not have a good computational platform or was doing this 50 years ago, I would resort to Sterling’s Approximation, It’s amazing to think about all of the computation that we simply take for granted. Finally, knowing that is very handy. (If you need a proof, start writing out numbers in binary) Harrison Schramm (harrison.schramm@gmail. com) is an operations research professional in the Washington, D.C., area. He is a member of INFORMS and a Certified Analytics Professional (CAP). NOTES & REFERENCES 1. http://www.slate.com/articles/sports/sports_ nut/2014/03/billion_dollar_bracket_challenge_why_ it_s_a_bad_idea_to_enter_warren_buffett.html 2. https://tournament.fantasysports.yahoo.com/ quickenloansbracket/challenge/?qls=BDB_B14qlb03. qlredirect 3. When your exponents have exponents, the numbers are really huge! 4. Comment: If you want real understanding in mathematics, there is no substitute for expanding by hand. This is how the mathematicians of 50 years ago did things, and there is goodness in it, even today. 5. http://www.analytics-magazine.org/july-august2013/838-five-minute-analyst-carnival-game W W W. I N F O R M S . O R G