Football squares

00000

These three links, among others, may prove interesting to you:

http://caseyshead.com/2013-super-bowl-squares-odds/
http://www.printyourbrackets.com/best-super-bowl-squares-odds-probabilities.html
http://simononsports.blogspot.com/2011/02/super-bowl-box-history.html

Quote: Transcend

We do not know what the numbers will be for the Superbowl yet but the numbers were drawn for the NFC and AFC games, 3 home 0 away. Is there any math I could do to figure out probability of winning either half or final...or it just be a crap shoot like the picking of numbers was?

You got some great numbers. See chart at -- https://wizardofodds.com/ask-the-wizard/156/

My late uncle George was incredibly lucky. On the day he got promoted to Lieutenant he was sitting in the Captain's office in the Fire house. In walked another Captain and offered 2 for $1 lottery tickets to the Captain. He was a tight Pollock and turned to George and said, I will take one and you want the other, right George ? What could he do ? He won a 1957 Plymouth.

Many years later after he retired a guy in Zizzimo's bar asking George to split a $100 square. Paid $2500 a quarter. George walk home and got money from Aunt Eve. By time he got back the guy had another partner. He went back and got $50 more. He and Aunt Eve went to Hawaii that year. 0 and 0 won 2 quarters and final score.

Mot sure what year Maryland started daily number, but I know it was July 29. Cause Uncle George bet it for 3 and 1/2 years, Even had my sister bet it for him when he was on vacation. Saw Uncle George on bus near right after Thanksgiving one year. That's when I found out about it. Told Joise I was gonna bet it for a month. Had $3 each day with a book and $1 with the state. Last day of December it came in. $2300 total.

Quote: EdCollins

These three links, among others, may prove interesting to you:

http://caseyshead.com/2013-super-bowl-squares-odds/
http://www.printyourbrackets.com/best-super-bowl-squares-odds-probabilities.html
http://simononsports.blogspot.com/2011/02/super-bowl-box-history.html

Thank you for these, I hope to get good numbers for the Superbowl, those links were useful none the less.

Quote: sodawater

You got some great numbers. See chart at -- https://wizardofodds.com/ask-the-wizard/156/

Perfect, thanks soda. I had looked through some of the ask the wizard sections I guess not enough though.


Thanks again everyone.

There is a lot of information summarized at footballsquares.blogspot.com (maybe too much). You can use that site to see strategy for selecting squares and the probability for winning real big and taking two or more squares. There are also a set of tables like some of the links above that show how likely 3-0 comes up for each of the quarters. There are details as your situation involves two games and half-time scores and final scores are correlated.

It wasn't that hard for me and I went ahead a calculated your situation exactly. Using 5209 games from 1994-end of 2013 reg season, 220 have ending digits of home 3 visitors 0 winning the half, 134 winning the final score, and 26 have 3-0 winning both the half and final score. Now with two games, 85.94% of the time 3-0 wins neither. The remaining 14.06% of the time, the expected return is $217.32. Congrats, so far you are worth more than was wagered and there is still the Super Bowl to come. Hope that something other than 86% chance comes yours way. (corrected)

	Payout	Probabilty	Expectation
win nothing	$0	85.94%	$0
final score for 1 game	$2000	4.77%	$95.39
half for 1 game	$1000	7.83%	$78.31
half+final for 1 game	$3000	0.93%	$27.76
each game is a winner	$2-6K	0.53%	$15.85
Total		100%	$217.32

Back in the 60's, when Colts were extremely popular in Baltimore, my Mom worked at a factory. She told my Dad they could never sell all the squares on the pool despite there being over 300 employees. Might have had something with the fact they drew the numbers before selling the squares. REALLY !

My wife once had four squares on a $50 board and won all four quarters, One square one twice and two of her others also won.

Quote: DRich

My wife once had four squares on a $50 board and won all four quarters, One square one twice and two of her others also won.

Depending on how she picked the four squares, winning four squares would happen between 0.01% and 0.06% of the time. On average, once in 3200 games.

Quote: FanofX

There is a lot of information summarized at footballsquares.blogspot.com (maybe too much). You can use that site to see strategy for selecting squares and the probability for winning real big and taking two or more squares. There are also a set of tables like some of the links above that show how likely 3-0 comes up for each of the quarters. There are details as your situation involves two games and half-time scores and final scores are correlated.

It wasn't that hard for me and I went ahead a calculated your situation exactly. Using 5209 games from 1994-end of 2013 reg season, 184 have ending digits of home 3 visitors 0 winning a half, 134 winning the final score, and 62 have 3-0 winning both the half and final score. Now with two games, 85.94% of the time 3-0 wins neither. The remaining 14.06% of the time, the expected return is $244.96. Congrats, so far you are worth more than was wagered and there is still the Super Bowl to come. Hope that something other than 86% chance comes yours way.

	Payout	Probabilty	Expectation
win nothing	$0	85.94%	$0
final score for 1 game	$2000	4.77%	$95.39
half+final for 1 game	$3000	2.21%	$66.21
half for 1 game	$1000	6.65%	$65.49
each game is a winner	$2-6K	0.53%	$17.87
Total		100%	$244.96

Thanks for all the information, the expectation was almost spot on, won the half of one game for $1000 split four ways. Where did you get the numbers for the table you made? I checked that blog you posted and didn't see anything on data besides if buying multiple squares where to place them. Still need to find out what the Superbowl numbers are, hopefully they will be half way decent.

Quote: FanofX

Depending on how she picked the four squares, winning four squares would happen between 0.01% and 0.06% of the time. On average, once in 3200 games.

How did you come up with that number? I would think they would be a lot more correlated. If a square wins once, I would think it is a lot more likely to win again over a random square. Obviously if you have the 0,3, or 7's your chances are a lot better.

Quote: Transcend

Thanks for all the information, the expectation was almost spot on, won the half of one game for $1000 split four ways. Where did you get the numbers for the table you made? I checked that blog you posted and didn't see anything on data besides if buying multiple squares where to place them. Still need to find out what the Superbowl numbers are, hopefully they will be half way decent.

The numbers for the tables come from 5209 pro football scores from 1994-2012 (all games) + 2013 (regular season). I made a mistake that's now corrected on the previous post. 26 games (not 62) games have home-visitor ending digits 3-0 at both the half and the final score. With that mistake, your expectation was $217.32 not $244.96 ... but since you actually won $1000, I hope you are not too unhappy.

To make the table, once I had the how many of the historical 5209 games gave you a winner at the half, at the final score, or for both, I then propagated those probabilities to all possibilities as your winnings were for two playoff games treating each game independently.

The tables (Oct 2013 blog post) have the probabilities of winning in each quarter, but do not convey the correlated probilities (i.e. winning both at the half and the final score) which is needed for your expectation value. When you get your Super Bowl numbers, I can make the same sort of calculation ... it will be easier as it involves only one game.

Quote: DRich

How did you come up with that number? I would think they would be a lot more correlated. If a square wins once, I would think it is a lot more likely to win again over a random square. Obviously if you have the 0,3, or 7's your chances are a lot better.

You are absolutely correct about squares being correlated with increased chances especially with 0, 7, 3, and 4's.

To get the number, I simulated over 1 billion squares games, randomizing the digits on the rows and columns, sampling all 5209 historical football box scores. I did this for all possible ways to select between 1-5 squares. For selecting four squares, like your wife, it's rare that you will win all four squares. When you do win all four squares, usually it's like your wife's case ... one of her squares won twice and two of the other squares each one once. If she picked all the squares in a column corresponding to the underdog team, winning four squares would happen 0.064% of the time - and she probably had one of the good numbers for that column. If she happened to pick four squares all on unique rows and columns, there's less likelihood that she would get all good numbers, and only 0.0136% of the time would she be expected to win four squares. There are a total of 16 different ways you can pick four squares in a 10 x 10 grid where the rows and columns get randomized. The average of those 16 different ways gives about 1 chance out of 3200 for picking four squares and winning all four times in a squares game.

My blog on all of this shows that there are strategies. You can't increase or decrease your expectation value ... squares is a fair game. But you can change how likely you are to win 0, 1, 2, 3, or 4 squares depending on how you pick squares. In the example above, picking all of them in a column turns out to win something 12.39% of the time (but gives you the largest chance for winning all four squares). Picking them all with unique rows and columns wins something 13.47% of the time (but gives the least chance for winning all four squares). What you can do is trade away a small probability difference for winning something for a much larger probability of winning two or more (and sometimes even all four) squares.

Thanks for all the information fanofx, any chance you could figure out the probabilities and expected return of the numbers 4 home, 0 away. Thanks.

Quote: Transcend

Thanks for all the information fanofx, any chance you could figure out the probabilities and expected return of the numbers 4 home, 0 away. Thanks.

Wow - Great numbers again! Expectation is $421.67 but remember that more than 88% of the time, you'll go home empty (which is why winning the 1st $1000 is so cool). My numbers are based on the 5209 historical games that I have from 1994. An analysis of the Bronco's and Seahawk's scoring tendencies suggest your expectation is about $550/$300 (not exact as correlations aren't accounted) if the home team (4) is Denver/Seattle. Denver scores a lot of TDs relative to FGs whereas Seattle scores with a more even mixture. See this link.

	Payout	Probabilty	Expectation
win nothing	$0	88.35%	$0
final score	$8000	1.59%	$127.47
half or (1st and 3rd)	$3000	3.21%	$96.18
1st or 3rd	$1500	5.14%	$77.17
half and (1st or 3rd)	$4500	0.94%	$42.33
final and (1st or 3rd)	$9500	0.44%	$41.95
final, half and (1st or 3rd)	$12500	0.13%	$16.80
final, half or (1st and 3rd)	$11000	0.13%	$14.78
party time	$14000	0.02%	$2.69
1st, half, and 3rd	$6000	0.04%	$2.30
Total		100%	$421.67

Hope the Super Bowl is like 2012 Week 12 Bengals vs Raiders! It's happened once before with 4-0 winning all four squares.
Raiders 0 0 10 0 10
Bengals 14 10 0 10 34

I hope I added to the enjoyment of you and your buddies' squares game this year.

So squares is basically bingo? Lol

Quote: zhoutangclan

So squares is basically bingo? Lol

Basically... There seems to be some thing to how you pick multiple squares to slightly increase your odds, but one square... That is just blind luck.

Quote: FanofX

Wow - Great numbers again! Expectation is $421.67 but remember that more than 88% of the time, you'll go home empty (which is why winning the 1st $1000 is so cool). My numbers are based on the 5209 historical games that I have from 1994. An analysis of the Bronco's and Seahawk's scoring tendencies suggest your expectation is about $550/$300 (not exact as correlations aren't accounted) if the home team (4) is Denver/Seattle. Denver scores a lot of TDs relative to FGs whereas Seattle scores with a more even mixture. See this link.

	Payout	Probabilty	Expectation
win nothing	$0	88.35%	$0
final score	$8000	1.59%	$127.47
half or (1st and 3rd)	$3000	3.21%	$96.18
1st or 3rd	$1500	5.14%	$77.17
half and (1st or 3rd)	$4500	0.94%	$42.33
final and (1st or 3rd)	$9500	0.44%	$41.95
final, half and (1st or 3rd)	$12500	0.13%	$16.80
final, half or (1st and 3rd)	$11000	0.13%	$14.78
party time	$14000	0.02%	$2.69
1st, half, and 3rd	$6000	0.04%	$2.30
Total		100%	$421.67

Hope the Super Bowl is like 2012 Week 12 Bengals vs Raiders! It's happened once before with 4-0 winning all four squares.
Raiders 0 0 10 0 10
Bengals 14 10 0 10 34

I hope I added to the enjoyment of you and your buddies' squares game this year.

Thank you for all the information and you most certainly have added quite a bit of fun to our squares for this year. Thanks for all the work you did figuring it out.

Quote: Transcend

Basically... There seems to be some thing to how you pick multiple squares to slightly increase your odds, but one square... That is just blind luck.

No! If the expectation for any square is the same (say, x), then the expectation for any set of n squares is just n*x. The variance may be different depending on which squares you pick (since the squares are not independent), but your EV is the same.

This is just like saying that no betting system can overcome a negative expectation game, or that you can't add up a sequence of negative numbers and get a positive number. Expectation is additive!!

Quote: AxiomOfChoice

No! If the expectation for any square is the same (say, x), then the expectation for any set of n squares is just n*x. The variance may be different depending on which squares you pick (since the squares are not independent), but your EV is the same.

This is just like saying that no betting system can overcome a negative expectation game, or that you can't add up a sequence of negative numbers and get a positive number. Expectation is additive!!

And that is why I leave the math to other people...I was just going by the blog that fan posted which at the end showed expectations based on square location.

Quote: AxiomOfChoice

No! If the expectation for any square is the same (say, x), then the expectation for any set of n squares is just n*x. The variance may be different depending on which squares you pick (since the squares are not independent), but your EV is the same.

This is correct ... the expectation value for any square selected before the numbers are chosen is the same. The footballsquares.blogspot.com goes into detail exactly on the differences in variance that depend on which squares are selected. Since it's rare to win a square, that variance is tabulated as the probability to win two or more squares.

The expectation is always the same, but if you can pick multiple squares, you can trade a small probability for winning something (mostly a single square) for sometimes a much larger (relative) probability for winning multiple squares.

On the expectation value once you have your numbers, there are many tables on the internet, but they don't take into account the correlations that can occur. My tabulations for Transcend try to emphasize that those correlations are important. Over 1/4 of his current expectation value comes from the likelihood that his square wins multiple times. You can't get that from tables on the internet.

I didn't play this year, but様ike the game itself葉he resulting squares were boring:

0,0
3,0
3,3
3,3

Quote: smoothgrh

I didn't play this year, but様ike the game itself葉he resulting squares were boring:

0,0
3,0
3,3
3,3

I agree. My four squares lost. This has been said before, but I think this was the more boring Super Bowl I can remember. However, boring is usually good for sharp props.

Quote: smoothgrh

I didn't play this year, but様ike the game itself葉he resulting squares were boring:

0,0
3,0
3,3
3,3

Interestingly enough, 0,0 looks a Lot like the "I can't believe this!" face- O.O Which I'm sure that MANY SB Fans from BOTH Teams were doing throughout the SB game. Pretty shocking when normal Pre Season games are BETTER than the Big Daddy of all games, the SB! O.O