Warren Buffett: $1 billion to whoever calls winners of all March Madness games
January 22nd, 2014 at 3:03:05 PM
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An article in the Daily News says Warren Buffet is offer one billion dollars to anyone who can correctly predict all 63 games in the 2014 March Madness bracket. It claims that the probability of winning is 1 in 4,294,967,296. In case that number looks familiar (JB) it equals 2^32.
That isn't what I get. Let's assume one were to pick the higher ranked seed in every game. The following table shows the probability of winning each game, based on historical experience.
With the last three games all 1- vs. 1-seed I'm assuming a 50% chance of getting each one right.
That said, if you take the product of everything in the "Prob. All Wins" column the answer is 1 in 46,940,073,802. That looks pretty far off from the 1 in 4,294,967,296 quoted in the Daily News. If all 63 games had the same chance of being a winner, then my figure would suggest a probability of success of 67.7% per game, and 70.3% for the Daily News.
Does anyone see a flaw in my math? How about a logical argument for the 1 in 2^32 used by the Daily News? Granted that the higher ranked seed (lower number) is not always the favorite, but that can't be the only reason for this disparity. Thoughts?
That isn't what I get. Let's assume one were to pick the higher ranked seed in every game. The following table shows the probability of winning each game, based on historical experience.
| Game | Count | Wins | Prob. Win | Games | Prob. All Wins |
|---|---|---|---|---|---|
| 1 vs 16 | 116 | 116 | 1.000000 | 4 | 1.000000 |
| 8 vs 9 | 116 | 58 | 0.500000 | 4 | 0.062500 |
| 5 vs 12 | 116 | 75 | 0.646552 | 4 | 0.174748 |
| 4 vs 13 | 116 | 91 | 0.784483 | 4 | 0.378733 |
| 6 vs 11 | 116 | 78 | 0.672414 | 4 | 0.204431 |
| 3 vs 14 | 116 | 99 | 0.853448 | 4 | 0.530529 |
| 7 vs 10 | 116 | 70 | 0.603448 | 4 | 0.132605 |
| 2 vs 15 | 116 | 108 | 0.931034 | 4 | 0.751386 |
| 1 vs 8 | 60 | 49 | 0.816667 | 4 | 0.444815 |
| 4 vs 5 | 62 | 34 | 0.548387 | 4 | 0.090438 |
| 3 vs 6 | 64 | 36 | 0.562500 | 4 | 0.100113 |
| 2 vs 7 | 66 | 50 | 0.757576 | 4 | 0.329385 |
| 1 vs 4 | 52 | 36 | 0.692308 | 4 | 0.229719 |
| 2 vs 3 | 48 | 29 | 0.604167 | 4 | 0.133238 |
| 1 vs 2 | 56 | 31 | 0.553571 | 4 | 0.093906 |
| 1 vs 1 | 0.500000 | 3 | 0.125000 |
With the last three games all 1- vs. 1-seed I'm assuming a 50% chance of getting each one right.
That said, if you take the product of everything in the "Prob. All Wins" column the answer is 1 in 46,940,073,802. That looks pretty far off from the 1 in 4,294,967,296 quoted in the Daily News. If all 63 games had the same chance of being a winner, then my figure would suggest a probability of success of 67.7% per game, and 70.3% for the Daily News.
Does anyone see a flaw in my math? How about a logical argument for the 1 in 2^32 used by the Daily News? Granted that the higher ranked seed (lower number) is not always the favorite, but that can't be the only reason for this disparity. Thoughts?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 22nd, 2014 at 3:24:52 PM
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I assume he bought insurance for this. How much do you think he is paying for the insurance? It has to be astronomical.
Expect the worst and you will never be disappointed.
I AM NOT PART OF GWAE RADIO SHOW
January 22nd, 2014 at 3:28:51 PM
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Quote: GWAEI assume he bought insurance for this. How much do you think he is paying for the insurance? It has to be astronomical.
If anyone can scrape up a billion dollars it is Warren Buffet.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 22nd, 2014 at 3:31:05 PM
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Buffet sells insurance, he doesn't buy it :)
If he is making this offer from his personal stash, he would be crazy to insure it.
If it's one of his companies (wasn't Quicken Loans involved somehow?) that might be different.
If he is making this offer from his personal stash, he would be crazy to insure it.
If it's one of his companies (wasn't Quicken Loans involved somehow?) that might be different.
January 22nd, 2014 at 3:39:14 PM
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Quote: GWAEI assume he bought insurance for this. How much do you think he is paying for the insurance? It has to be astronomical.
Buffet said that one of his own insurance companies is writing the policy so it is somewhat self insured. I guess other holders of Berkshire Hathaway are sharing the risk.
"Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things."
-- Isaac Newton
January 22nd, 2014 at 3:52:42 PM
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I though a company is offering this, and Buffet is underwrting it.
Like espn or whatever company is promoting it.....and they pay buffet x amount to insure it for 1 billion.
I mean what does buffet himself care if someone can pick the right brackets. He is a businessman. What does he make from this deal?
I guess if I understand this right...he makes the cost of the insurance policy. He limits it to 10 million entries.
am i understanding this wrong?
Like espn or whatever company is promoting it.....and they pay buffet x amount to insure it for 1 billion.
I mean what does buffet himself care if someone can pick the right brackets. He is a businessman. What does he make from this deal?
I guess if I understand this right...he makes the cost of the insurance policy. He limits it to 10 million entries.
am i understanding this wrong?
January 22nd, 2014 at 4:03:42 PM
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Quote: LarrySI though a company is offering this, and Buffet is underwrting it.
Like espn or whatever company is promoting it.....and they pay buffet x amount to insure it for 1 billion.
I mean what does buffet himself care if someone can pick the right brackets. He is a businessman. What does he make from this deal?
I guess if I understand this right...he makes the cost of the insurance policy. He limits it to 10 million entries.
am i understanding this wrong?
It sounds like quicken loans is getting a lot of advertising from this.
January 22nd, 2014 at 4:13:59 PM
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What an odd proposition from The Orifice of Omaha.
Each day is better than the next
January 22nd, 2014 at 4:14:09 PM
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Isn't there 68 teams and 67 games now in the tournament?
At my age, a "Life In Prison" sentence is not much of a deterrent.
January 22nd, 2014 at 4:21:33 PM
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lol
January 22nd, 2014 at 4:22:00 PM
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Quote: DRichIsn't there 68 teams and 67 games now in the tournament?
Standard March Madness pools ignore the opening games, and this contest is the same.
From: https://www.facebook.com/notes/quicken-loans/quicken-loans-billion-dollar-bracket-challenge-short-form-rules/10152185833560489
Odds: Grand Prize – 1:9,223,372,036,854,775,808, which may vary depending upon the knowledge and skill of entrant
That's 2^63, so they are ignoring the opening games.
January 22nd, 2014 at 4:42:44 PM
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Quote: Wizard
Does anyone see a flaw in my math? How about a logical argument for the 1 in 2^32 used by the Daily News? Granted that the higher ranked seed (lower number) is not always the favorite, but that can't be the only reason for this disparity. Thoughts?
1. No, assuming there are no mistakes in the historical records.
2. They are the NY Daily News, that's why!
3. I think your method is a pretty good estimate for a "skilled player". If you can find data from a large pool that would repick after every round, that could give a better estimate of "win percentage per game". However, I can't think of a public bracket that actually does that.
January 22nd, 2014 at 4:57:29 PM
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How much does it cost to enter this contest? How many times can you enter? What is the deadline to enter and is it before or after the first round? With $1billion being such a large number, there may be a way to use an "educated guess" system to narrow down the possibilities to increase the chances of winning to considerably less than what random numbers imply. Also, what happens if more than one person wins, is the prize split among the winners or not?
January 22nd, 2014 at 6:08:09 PM
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Quote: tringlomaneStandard March Madness pools ignore the opening games, and this contest is the same.
From: https://www.facebook.com/notes/quicken-loans/quicken-loans-billion-dollar-bracket-challenge-short-form-rules/10152185833560489
Odds: Grand Prize – 1:9,223,372,036,854,775,808, which may vary depending upon the knowledge and skill of entrant
That's 2^63, so they are ignoring the opening games.
i see, according to their dates the contest doesn't start until the second round.
At my age, a "Life In Prison" sentence is not much of a deterrent.
January 22nd, 2014 at 6:11:27 PM
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This is misleading. The first round is really the "play in" games where the final 8 teams play in 4 games to advance to round 2. Round 2 is when the field of 64 starts
January 22nd, 2014 at 6:12:25 PM
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Quote: WizardI don't think so. See this page for the brackets.
The NCAA considers there to now be 68 teams. The other four games used to be called "play in" games but they changed that last year and called those games round one of the tournament.
Link
At my age, a "Life In Prison" sentence is not much of a deterrent.
January 22nd, 2014 at 8:14:54 PM
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Quote: DRichQuote: WizardI don't think so. See this page for the brackets.
The NCAA considers there to now be 68 teams. The other four games used to be called "play in" games but they changed that last year and called those games round one of the tournament.
Link
If you want to get pedantic, the Dayton game was never a "play-in" game (unless you're Jim Rome), as both teams were considered to be "in the tournament," especially for tournament money purposes. The only actual play-in games I remember (where the NCAA did not consider the losers to be in the tournament) were in the first year or two of the 64-team bracket; the worst eight or so conferences historically were paired against each other the week before the bracket was announced, and only the winners were included.
January 22nd, 2014 at 8:57:44 PM
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Buffet isn't worried. Apparently it's easier to hit 4 holes-in-one in a single round of golf than predicting this thing perfectly.
From The Atlantic magazine:
"You might consider the odds of filling out a perfect March Madness bracket to be, well, small. You would be wrong. Flipping a coin and getting 10 straight heads; predicting the Super Bowl MVP before the NFL season begins; finding exact change in your pocket—the odds of these marvels occurring are, indeed, small. But the chances of correctly guessing all 63 games in the NCAA tournament are so vanishingly minuscule, they exist in the realm of Bigfoot, the Loch Ness Monster, and "President Alec Baldwin"
Those odds are 1 in 128 billion, according to DePaul math professor Jeff Bergen. (Some outlets are quoting 1 in 9.2 quintillion, but that assumes that all 63 games are 50-50 toss-ups, which they're not. For example, Number 1 seeds just about always advance to the second round.) If everyone in the United States filled out a bracket, Chris Chase calculated, we'd get a $1 billion winner every 400 years."
From The Atlantic magazine:
"You might consider the odds of filling out a perfect March Madness bracket to be, well, small. You would be wrong. Flipping a coin and getting 10 straight heads; predicting the Super Bowl MVP before the NFL season begins; finding exact change in your pocket—the odds of these marvels occurring are, indeed, small. But the chances of correctly guessing all 63 games in the NCAA tournament are so vanishingly minuscule, they exist in the realm of Bigfoot, the Loch Ness Monster, and "President Alec Baldwin"
Those odds are 1 in 128 billion, according to DePaul math professor Jeff Bergen. (Some outlets are quoting 1 in 9.2 quintillion, but that assumes that all 63 games are 50-50 toss-ups, which they're not. For example, Number 1 seeds just about always advance to the second round.) If everyone in the United States filled out a bracket, Chris Chase calculated, we'd get a $1 billion winner every 400 years."
January 22nd, 2014 at 9:12:26 PM
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Quote: WizardQuote: renoCheck out the YouTube video on this page.
I'd be interested to know how he calculated the 1 in 128 billion figure.
1 in 128 billion is (1999/3000)^63
My guess is he just estimated 2/3 chance of winning each game based on basketball knowledge -- for picking the winner of 63 games.
January 22nd, 2014 at 10:47:32 PM
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Quote: sodawaterQuote: WizardQuote: renoCheck out the YouTube video on this page.
I'd be interested to know how he calculated the 1 in 128 billion figure.
1 in 128 billion is (1999/3000)^63
My guess is he just estimated 2/3 chance of winning each game based on basketball knowledge -- for picking the winner of 63 games.
Roughly, I assume. Your guess is basically the same thing I wrote in the other thread about this:
https://wizardofvegas.com/forum/off-topic/general/16679-buffett-offers-1-billion-for-perfect-ncaa-bracket/#post316127
But you would have to ask him to be sure, the makers of the video probably told him to cut out the details just like the Phoenix TV station cut out Wiz's details on good video poker.
Jeffrey Bergen: jbergen@depaul.edu
If you wrote him Wiz, I would hopefully expect him to respond. Personally I don't think either your or his estimate is bad unless you have a lot more data to crunch.
January 23rd, 2014 at 12:53:59 AM
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So what happens when the final 4 are known, and somebody's still in it? With a billion dollars on the line? It would make the Black Sox look like peanuts.
If the House lost every hand, they wouldn't deal the game.
January 23rd, 2014 at 12:56:13 AM
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Quote: beachbumbabsSo what happens when the final 4 are known, and somebody's still in it? With a billion dollars on the line? It would make the Black Sox look like peanuts.
Considering that would be about 37 billion to 1, I don't think we have to worry about it.
January 23rd, 2014 at 12:57:44 AM
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Quote: sodawaterConsidering that would be about 37 billion to 1, I don't think we have to worry about it.
Ye of little faith :)
“There is something about the outside of a horse that is good for the inside of a man.” - Winston Churchill
January 23rd, 2014 at 3:37:25 AM
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Quote: WizardQuote: renoCheck out the YouTube video on this page.
I'd be interested to know how he calculated the 1 in 128 billion figure.
I wonder if he bought insurance, and how much it cost.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
January 23rd, 2014 at 4:06:33 AM
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Quote: odiousgambitQuote: WizardQuote: renoCheck out the YouTube video on this page.
I'd be interested to know how he calculated the 1 in 128 billion figure.
I wonder if he bought insurance, and how much it cost.
that was discussed on the 1st page of this thread.
Expect the worst and you will never be disappointed.
I AM NOT PART OF GWAE RADIO SHOW
January 23rd, 2014 at 4:30:40 AM
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BTW, I believe that I read that they are giving away $100K in prizes to the top 20 pickers so give it a go.
DO NOT blindly accept what has been spoken.
DO NOT blindly accept what has been written.
Think. Assess. Lead. DO NOT blindly follow.
January 23rd, 2014 at 7:07:31 AM
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Quote: GWAEthat was discussed on the 1st page of this thread.
No one came up with a figure, though. Unless my vision has gotten even more pathetic.
From "ask the wizard" on another issue, https://wizardofodds.com/ask-the-wizard/284/
Quote:Probability of [the event] = 2.71%. To be exact, 0.0271275.
Given that the dealership would have had to pay [X amount] in the event of [this event], the fair cost of the policy would have been [X amount] × 0.0271275
1 in 128 billion = 0.0000000000078125
1 000 000 000 * 0.0000000000078125 = 0.0078125
So the answer seems to be that the risk is so minimal, insurance is laughable. However, bear in mind I often screw these things up.
PS: it occurs to me that 128 billion submissions would change everything, or even submissions in the millions too. So, I guess it was smart to limit it to one per household.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
January 23rd, 2014 at 7:19:46 AM
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I don't get all.
They say there is no price to pay for betting. So, why wouldn't you introduce a huge number of different bets? Cost = zero ; prob of winning increasing.
There's some information missing, I suppose.
They say there is no price to pay for betting. So, why wouldn't you introduce a huge number of different bets? Cost = zero ; prob of winning increasing.
There's some information missing, I suppose.
Reperiet qui quaesiverit
January 23rd, 2014 at 7:48:37 AM
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seems to me we need to know WWTWD
good for "ask the W?" What Would the Wizard Do if he was the guy with this challenge? For example, would he allow a lot more submissions? What would the math show, as far as how many submissions start to create concern?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
January 23rd, 2014 at 9:34:53 AM
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Quote: kubikulannI don't get all.
They say there is no price to pay for betting. So, why wouldn't you introduce a huge number of different bets? Cost = zero ; prob of winning increasing.
There's some information missing, I suppose.
One entry per household.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
January 23rd, 2014 at 9:50:35 AM
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Doesn't seem fair to the homeless.
Shed not for her
the bitter tear
Nor give the heart
to vain regret
Tis but the casket
that lies here,
The gem that filled it
Sparkles yet
January 23rd, 2014 at 10:27:19 AM
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Quote: BuzzardDoesn't seem fair to the homeless.
Many things aren't.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
January 23rd, 2014 at 10:32:23 AM
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Quote: thecesspitMany things aren't.
And yet so many people think the homeless have chosen to be so.
Shed not for her
the bitter tear
Nor give the heart
to vain regret
Tis but the casket
that lies here,
The gem that filled it
Sparkles yet
January 23rd, 2014 at 11:10:49 AM
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Quote: odiousgambitPS: it occurs to me that 128 billion submissions would change everything, or even submissions in the millions too. So, I guess it was smart to limit it to one per household.
Of course, so conservatively assuming 100 million households entering:
n =100,000,000
p = 0.0000000000078125 (as before)
The probability that you will get no winners is:
P(N=0) = (1 - p)^n
= 0.999219052256535
And the probability that you'll get at least one winner is:
P(N>0) = 1 - P(N=0)
= 0.000780947743464933
Therefore, the cost of the insurance policy should actually be:
C = ($1,000,000,000)(0.000780947743464933)
= $780,947.74
Of course you are only going to get a small fraction of that number of households actually entering but that would require another estimate based on previous contests of similar magnitude. So if n = (5%)(100,000,000) = 5,000,000 then C = $39,061.88 only.
