The Football Pool

 

I won the football pool a couple times and thought:  “Wouldn’t it be fun to win more?”  It’s a one-dollar pool.  There is no limit to the number of entries.   What if I submitted more than one sheet?  I would have a greater chance of winning.  My one in twenty chance could be a two in twenty-one chance.  What if I really wanted to mess with people one week and guarantee I’d win just for fun; submit enough entries to cover every possible combination?  Fifteen games in a week, excluding Monday night.  How much would it cost to just bet every game?  There are only two possible outcomes on the betting sheet for each game.  There couldn’t be *that* many possibilities altogether.

 

I did the math.  Actually I tried to do the math, but lost the thread.  If there is only one game, there are two possible outcomes (discounting ties); one team wins or the other one does.  If there are two games, there are four possible outcomes.  It gets a little harder after that.  Three games, eight possibilities.  Now I’m confused.  I need a formula.  It’s not simple multiplication; it’s something more sophisticated.  I remember “factorial” from a statistics class a gazillion years ago.  That’s a number times every whole integer number below it in sequence.  That applies to some statistical situations, and almost to this one, but not quite.

 

We turned to our grandson Tony for the math.  He said the answer would be the number of possible outcomes, to the power of the number of games played.  I tested that out on the lower numbers.  One game, two possible outcomes, two to the power of one equals two.  That works.  Two games.  Two to the power of two.  Four.  That works.  Four games, sixteen possibilities.  That’s sixteen dollars to dominate a four game pool.  It’s starting to get a little scary.

 

Okay, so what’ my out-of-pocket cost to guarantee the football pool?  No more bye-weeks at this point in the season, so each pool is fifteen games.  Two to the power of fifteen.  Ooh, that’s a lot of doublings to win a $20 pool.  For a mere $32,768, I can guarantee that no one will beat me; but I can’t guarantee that no-one will tie me!  If one person tied me once, I’d be out $16,000!

 

Not a good bet.