Super Bowl Square probabilities

NoahFence · 3rd February 2012, 10:15 AM

OK, so we've all seen the websites that say getting this number + that number = good or bad.

This question is a bit different, and I was wondering if it would be a statistical curiosity. It is at least for me.

Keep in mind this actually happened here at work. Funny stuff:

User A buys 2 squares. She winds up with "4" Patriots, "2" Giants on one square. Ewww.

Her other square? "2" Patriots, "4" Giants.

Yep, she got the same number combination for both teams.

Now, just when you thought it was an interesting outcome, the next day they draw numbers for a totally different set of squares.

The woman who sits next to her got the exact same numbers for her 2 squares. "4" Patriots, "2" Giants on one, "2" Patriots, "4" Giants on the other.

What are the odds?

LarianLeQuella · 3rd February 2012, 10:24 AM

100%. It happened.

GO PATS!

As to predicting this before it happened, and specifically picking these two women out before hand, those are long odds. As to the first coincidence, that has (if I understand it correctly) about a 2% chance of happening if you only buy 2 squares, so not that astronomical. As for some one else getting the exact same distribution with 2 squares, does that become 0.04% (multplicative?)? Not sure how the problem's constraints are set up.

The fact that she sits next to the other woman has nothing to do with it, it's a red herring since both of them are involved in the betting pools.

NoahFence · 3rd February 2012, 10:34 AM

Pretty flippin' bizarre though, eh?

GO PATS!

(I got 11 adults and 5 kids coming over. UGH)

LarianLeQuella · 3rd February 2012, 12:18 PM

I guess bizarre only in that humans suck at determining probabilities on an intuitive level.

I highly recommend The Drunkard's Walk. Very easy and entertaining read on that subject.

Going over to a neighbor's myself. Today at work, everyone wore Patriot's apparel, even though we had a US Senator visiting the plant.

jasonpatterson · 5th February 2012, 10:23 PM

Here's my poke at it:

Since the numbers can't be identical (the reverse wouldn't exist in that case) there should be less than 1/100 chance of picking a pair of scores that are opposites.

Woman A Pick 1: Doesn't matter what numbers as long as they aren't identical. Gets numbers X and Y.
P₁ = 90/100

Woman A Pick 2: Must pick Y and X. There are only 99 squares left to choose from.
P₂ = 1/99

Probability of picking two scores that are opposites:
P₁ x P₂ = 90/9900 = 1/110

Probability of the woman 2 getting the same pairs as woman 1:
It doesn't matter what woman 1 picked, the odds of woman 2 picking the same two pairs out as her are going to be the same no matter the scores.
P₁ = 1/100
P₂ = 1/99
P = 1/9900

Note that in reality the probability of an event like this being noticed is much higher than 1 in a whole bunch. It's not unlikely that someone in the game would get pairs if many people bought two tickets. If someone the next time got the same set of pairs, they'd notice the set of pairs and not comment on all of the other people they hadn't matched with. This probability relies on us stating ahead of time that we are matching woman 2's score to woman 1's, not that at least 1 person in the 30 (just to make up a number) who participated got pairs on day 1 and that on day 2 at least 1 person matched those pairs.

3rd February 2012, 10:15 AM	#1
NoahFence Psycho Kitty Join Date: Mar 2011 Location: Patriot Nation Posts: 9,296	Super Bowl Square probabilities OK, so we've all seen the websites that say getting this number + that number = good or bad. This question is a bit different, and I was wondering if it would be a statistical curiosity. It is at least for me. Keep in mind this actually happened here at work. Funny stuff: User A buys 2 squares. She winds up with "4" Patriots, "2" Giants on one square. Ewww. Her other square? "2" Patriots, "4" Giants. Yep, she got the same number combination for both teams. Now, just when you thought it was an interesting outcome, the next day they draw numbers for a totally different set of squares. The woman who sits next to her got the exact same numbers for her 2 squares. "4" Patriots, "2" Giants on one, "2" Patriots, "4" Giants on the other. What are the odds?
	__________________ Our truest life is when we are in our dreams awake. -Henry David Thoreau

3rd February 2012, 10:24 AM	#2
LarianLeQuella Elf Wino Join Date: Nov 2008 Location: 3rd Rock from the Sun Posts: 1,995	100%. It happened. GO PATS! As to predicting this before it happened, and specifically picking these two women out before hand, those are long odds. As to the first coincidence, that has (if I understand it correctly) about a 2% chance of happening if you only buy 2 squares, so not that astronomical. As for some one else getting the exact same distribution with 2 squares, does that become 0.04% (multplicative?)? Not sure how the problem's constraints are set up. The fact that she sits next to the other woman has nothing to do with it, it's a red herring since both of them are involved in the betting pools.
	__________________ My crappy blog that no one should be forced to read. Ever... But I like traffic and comments, so have at it if you please. Larian LeQuella Armyn ab Treanid Last edited by LarianLeQuella; 3rd February 2012 at 10:30 AM. Reason: Cheering for my favorite team. Less snarky

3rd February 2012, 10:34 AM	#3
NoahFence Psycho Kitty Join Date: Mar 2011 Location: Patriot Nation Posts: 9,296	Pretty flippin' bizarre though, eh? GO PATS! (I got 11 adults and 5 kids coming over. UGH)
	__________________ Our truest life is when we are in our dreams awake. -Henry David Thoreau

3rd February 2012, 12:18 PM	#4
LarianLeQuella Elf Wino Join Date: Nov 2008 Location: 3rd Rock from the Sun Posts: 1,995	I guess bizarre only in that humans suck at determining probabilities on an intuitive level. I highly recommend The Drunkard's Walk. Very easy and entertaining read on that subject. Going over to a neighbor's myself. Today at work, everyone wore Patriot's apparel, even though we had a US Senator visiting the plant.
	__________________ My crappy blog that no one should be forced to read. Ever... But I like traffic and comments, so have at it if you please. Larian LeQuella Armyn ab Treanid

5th February 2012, 10:23 PM	#5
jasonpatterson Philanthropic Misanthrope Join Date: Apr 2009 Location: Space, The Final Frontier Posts: 2,180	Here's my poke at it: Since the numbers can't be identical (the reverse wouldn't exist in that case) there should be less than 1/100 chance of picking a pair of scores that are opposites. Woman A Pick 1: Doesn't matter what numbers as long as they aren't identical. Gets numbers X and Y. P₁ = 90/100 Woman A Pick 2: Must pick Y and X. There are only 99 squares left to choose from. P₂ = 1/99 Probability of picking two scores that are opposites: P₁ x P₂ = 90/9900 = 1/110 Probability of the woman 2 getting the same pairs as woman 1: It doesn't matter what woman 1 picked, the odds of woman 2 picking the same two pairs out as her are going to be the same no matter the scores. P₁ = 1/100 P₂ = 1/99 P = 1/9900 Note that in reality the probability of an event like this being noticed is much higher than 1 in a whole bunch. It's not unlikely that someone in the game would get pairs if many people bought two tickets. If someone the next time got the same set of pairs, they'd notice the set of pairs and not comment on all of the other people they hadn't matched with. This probability relies on us stating ahead of time that we are matching woman 2's score to woman 1's, not that at least 1 person in the 30 (just to make up a number) who participated got pairs on day 1 and that on day 2 at least 1 person matched those pairs.
	__________________ Sandra's seen a leprechaun, Eddie touched a troll, Laurie danced with witches once, Charlie found some goblins' gold. Donald heard a mermaid sing, Susie spied an elf, But all the magic I have known I've had to make myself. - Shel Silverstein