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Old 2014-03-13, 22:58   #1
NBtarheel_33
 
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Default Quick! Guess what the next LL residue will be!

If you're good at that kind of thing, Warren Buffett is offering a $1 billion prize for doing something only half as difficult: completing a perfect NCAA Tournament bracket. There are a total of 63 games, for each of which there is a 1/2 probability that you'll guess the winner. The odds of winning are hence \frac{1}{2^{63}}, or 1 in 9.22 quintillion.

To put this in perspective, this task is equivalent to my telling you the first bit of an LL residue, and you correctly guessing the next 63 bits!

The expected value of an entry into Buffett's stunt competition? $0.000000000108420217. If someone happens to win this thing, they would likely be the subject of an FBI inquiry into how they did it, long before they'd be able to even think about the prize!

Last fiddled with by NBtarheel_33 on 2014-03-13 at 22:59
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Old 2014-03-13, 23:07   #2
CRGreathouse
 
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Quote:
Originally Posted by NBtarheel_33 View Post
There are a total of 63 games, for each of which there is a 1/2 probability that you'll guess the winner. The odds of winning are hence \frac{1}{2^{63}}, or 1 in 9.22 quintillion.

To put this in perspective, this task is equivalent to my telling you the first bit of an LL residue, and you correctly guessing the next 63 bits!

The expected value of an entry into Buffett's stunt competition? $0.000000000108420217.
Surely not that bad. I would expect that the best-ranked team would beat the bottom-ranked team with probability > 50.1%.
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Old 2014-03-14, 00:37   #3
ewmayer
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Surely there are lots of data from previous online NCAA tournament contests which could be meta-studied to

a) see what the resulting odds of a perfecto are, if >= 1 has occurred;

b) [if !a] get a more precise estimate of the actual odds, by comparing the frequency of "near misses" with that predicted by a naive coin-flip-style model. If such a model were still reasonable but one could bias the odds of each "flip" to (say) 0.6 using relative rankings and other common heuristics, the odds of a perfecto jump by nearly 100000.
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Old 2014-03-14, 00:37   #4
Spherical Cow
 
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Quote:
Originally Posted by CRGreathouse View Post
Surely not that bad. I would expect that the best-ranked team would beat the bottom-ranked team with probability > 50.1%.
True- I'll look for the source, but I've read that a Duke mathematician has estimated that the odds of a person with information about all of the teams' records would actually have about a 1-in-a-billion chance of picking all the winners, rather than the 1-in-9 quintillion. But since only 15 million entries are allowed, Mr. Buffett's money is still fairly safe.

Norm
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Old 2014-03-14, 03:48   #5
ixfd64
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This could be used to search for evidence of ESP, particularly precognition.
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Old 2014-03-14, 04:30   #6
Xyzzy
 
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Quote:
This could be used to search for evidence of ESP, particularly precognition.
Or, it might be a trap for time travelers.
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Old 2014-03-14, 06:22   #7
retina
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Quote:
Originally Posted by Spherical Cow View Post
Mr. Buffett's money is still fairly safe.
Indeed. One would image that his advisers have suitably advised him of the odds. Plus he has probably insured against the prize being won and won't be out of pocket for any more than the excess if someone does win it. In short: reasonably cheap advertising for only the price of an insurance policy.
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Old 2014-03-14, 08:45   #8
LaurV
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Default Quick! Guess what the next LL residue will be!

Easy! The next interesting residue will be zero. All the other are non interesting.
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Old 2014-03-14, 10:27   #9
fivemack
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Quote:
Originally Posted by retina View Post
Indeed. One would image that his advisers have suitably advised him of the odds. Plus he has probably insured against the prize being won and won't be out of pocket for any more than the excess if someone does win it. In short: reasonably cheap advertising for only the price of an insurance policy.
The amusing bit here is that Warren Buffet has got more advertising for providing the insurance policy than the original company has for making the offer!

Warren Buffet runs one of the richest reinsurance companies in the world: the buck stops there. In the remarkably unlikely event that someone wins, it would be about 1.4% of Berkshire Hathaway's spare money paid out; no insurance company likes to make large payouts, but it wouldn't be a problem.
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Old 2014-03-14, 19:01   #10
LaurV
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I have an easier guess for you to do, and more interesting too: you have to pick right only ~30 bits, which is infinite easier, and tell me the exponent of the first mersenne prime which takes the EFF's money... Who needs buffet's billions?
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Old 2014-03-14, 19:14   #11
R.D. Silverman
 
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Quote:
Originally Posted by CRGreathouse View Post
Surely not that bad. I would expect that the best-ranked team would beat the bottom-ranked team with probability > 50.1%.
It's so nice to see and read common sense!

Indeed. One would expect a high probability for the 1st 4 seeds in each region to win their 1st game and a better than 50% probability to win
the next as well.
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