kubikulann
kubikulann
Joined: Jun 28, 2011
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January 23rd, 2014 at 7:19:46 AM permalink
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.
Reperiet qui quaesiverit
odiousgambit
odiousgambit
Joined: Nov 9, 2009
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January 23rd, 2014 at 7:48:37 AM permalink
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
thecesspit
thecesspit
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January 23rd, 2014 at 9:34:53 AM permalink
Quote: kubikulann

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.



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
Buzzard
Buzzard
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January 23rd, 2014 at 9:50:35 AM permalink
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
thecesspit
thecesspit
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January 23rd, 2014 at 10:27:19 AM permalink
Quote: Buzzard

Doesn'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
Buzzard
Buzzard
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January 23rd, 2014 at 10:32:23 AM permalink
Quote: thecesspit

Many 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
paisiello
paisiello
Joined: Oct 30, 2011
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January 23rd, 2014 at 11:10:49 AM permalink
Quote: odiousgambit

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.


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.

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