Sunday, March 30, 2014

I Do Not Feel So Bad About My Bracket Picks

The One Billion Dollar Prize Pay Out Was A Safe Bet

Last night Evelyn and I watched FL "whup up on" DAYTON but did not stay up late enough to see Wisconsin upset Arizona.  

Today it could work out that University of Michigan and Michigan State University both make it into the final four.  

I heard yesterday that the 1 BILLION DOLLAR contest to make a perfect NCAA bracket pick is now officially over, absolutely no one who entered a bracket has it all right so far.  

Which is not surprising since the odds against a completely perfect bracket are 1:18,446,744,073,709,551,616 against or in english:

The odds against picking a perfect are:

one to 
eighteen quintillion
four hundred forty six quadrillion 
seven hundred forty four trillion 
seventy three billion 
seven hundred nine million 
five hundred fifty one thousand 
six hundred sixteen 
against.

These are pretty small odds and the folks that put up one billion dollars against this event occurring were pretty sure their money was safe.  

Even after eliminating all the possible ways that four number 16 seeds could wind up in the final four are eliminated their money is safe.  

And even just accounting for the fact that the last eight teams were all ranked their money was safe.

And most importantly even accounting for all the different ways two number one seeds, two number two seeds, a seven seed, an eight seed, and an eleven seed could make to the final eight (which is what actually happened) then their money was safe.  

This is because the number different of ways at 1,1,2,2,7,8,11 seed can arrive in the final eight is so large the money is safe.

The final 8 brackets were: (1,11) (4,7) (1,2) and (8,2)

Great8  Final4  Final2  Champ  Final2 Final4   Great8
1 ------+ (1)                          (2)  +------ 1
        +------+        -----        +------+
11 -----+      |          |          |      +------ 2
               +--------- v ---------+
4 ------+      |                     |      +------ 8
        +------+                     +------+
7 ------+                                   +------ 2

So there is just ONE way that the above 'Great-8' bracket could be but to GET-THERE there are lots and lots of ways.  Just considering the #1 Seed in the upper left hand corner (University Of Florida) it was only ONE of SIXTEEN teams that could have been there.  So assuming it made it then in the previous round there were EIGHT DIFFERENT OPPONENTS it could have had.  And in the previous round there were FOUR and in the previous TWO so that is 8*4*2 or 64 different ways it could arrive at where it was. This is true for all eight teams so there are 64*64*64*64*64*64*64*64 = 64^8 = 281,474,976,710,656 which in english is: 

two hundred eighty-one trillion 
four hundred seventy-four billion 
nine hundred seventy-six million 
seven hundred ten thousand 
six hundred fifty-sixth

So even though lots and lots of people picked (Florida vs Dayton AND Michigan St vs UCON AND Arizona vs Wisconsin AND Kentucky vs Michigan) NO BODY PICKED exactly HOW they got where they got. since the actual path those eight teams was one way out of 281,474,976,710,656 different ways.