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Bob O'H

Posts: 2309
Joined: Oct. 2005

Quote (stevestory @ Oct. 21 2018,13:02)
Quote (Jkrebs @ Oct. 21 2018,13:33)
Quote (stevestory @ Oct. 20 2018,15:49)
BarryMath:

 Quote Saturday Fun: When the Lottery Bet Has a Positive Expected ValueOctober 20, 2018 Posted by Barry Arrington under Intelligent Design No CommentsThis is one of those very rare times when the lottery bet has a positive mathematical expected value. Expected value is calculated as: (Amount possibly won * probability of winning) minus (Amount of bet * probability of losing).The probability of winning Mega Millions is 1 in 302,575,350. The next jackpot is \$904 million (cash value of \$1.6 billion annuity). The expected value is (\$904,000,000 * 1/302,575,350) minus (\$2.00 * .9999999999999999999) = \$0.98.This means on average in the long run, for every \$2.00 ticket you buy, you would expect to win \$2.98 if the jackpot were always \$904 million.  Of course, you still lose the whole \$2.00 every time you lose, which is almost always.  Still, on average, over the long run, the expected value is positive (\$2.98 – \$2.00 = \$0.98).In the long run, it is a good bet. Of course, the problem is there is no long run. You only have a single shot at it. To achieve the long run average expectation, you would have to play several hundred million times.

he's not doing the math right.

Hmmm. What's wrong with Barry's math. Is not the expected value for a ticket \$0.98???

his analysis is missing a few terms. Taxes reduce the EV, and he's got no terms for winning a lower pot cuz multiple winners.

Plus, he then writes
 Quote This means on average in the long run, for every \$2.00 ticket you buy, you would expect to win \$2.98 if the jackpot were always \$904 million.

Oolong mentions multiple winners (at least I think that's what they are getting at). And, from a quick approximation, you would need about 200m tickets sold to have a 50% chance of someone else having the same number as you.

(I'm assuming everyone chooses their numbers randomly, which is of course wrong)

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It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

DiEb

Posts: 286
Joined: May 2008

Quote (Bob O'H @ Oct. 22 2018,09:28)

Quote (stevestory @ Oct. 21 2018,13:02)

Quote (Jkrebs @ Oct. 21 2018,13:33)

Quote (stevestory @ Oct. 20 2018,15:49)
BarryMath:

 Quote Saturday Fun: When the Lottery Bet Has a Positive Expected ValueOctober 20, 2018 Posted by Barry Arrington under Intelligent Design No CommentsThis is one of those very rare times when the lottery bet has a positive mathematical expected value. Expected value is calculated as: (Amount possibly won * probability of winning) minus (Amount of bet * probability of losing).The probability of winning Mega Millions is 1 in 302,575,350. The next jackpot is \$904 million (cash value of \$1.6 billion annuity). The expected value is (\$904,000,000 * 1/302,575,350) minus (\$2.00 * .9999999999999999999) = \$0.98.This means on average in the long run, for every \$2.00 ticket you buy, you would expect to win \$2.98 if the jackpot were always \$904 million.  Of course, you still lose the whole \$2.00 every time you lose, which is almost always.  Still, on average, over the long run, the expected value is positive (\$2.98 – \$2.00 = \$0.98).In the long run, it is a good bet. Of course, the problem is there is no long run. You only have a single shot at it. To achieve the long run average expectation, you would have to play several hundred million times.

he's not doing the math right.

Hmmm. What's wrong with Barry's math. Is not the expected value for a ticket \$0.98???

his analysis is missing a few terms. Taxes reduce the EV, and he's got no terms for winning a lower pot cuz multiple winners.

Plus, he then writes

 Quote This means on average in the long run, for every \$2.00 ticket you buy, you would expect to win \$2.98 if the jackpot were always \$904 million.

Oolong mentions multiple winners (at least I think that's what they are getting at). And, from a quick approximation, you would need about 200m tickets sold to have a 50% chance of someone else having the same number as you.

(I'm assuming everyone chooses their numbers randomly, which is of course wrong)

First, there is a glaring mistake which just shows a lack of understanding - though it does not change the result:
 Quote The expected value is (\$904,000,000 * 1/302,575,350) minus (\$2.00 * .9999999999999999999) = \$0.98.
No, you have to pay for the ticket even if you are winning, so it should be
 Quote The expected value is (\$904,000,000 * 1/302,575,350) minus \$2.00  = \$0.98.

Then, there are a lot of important details which are omitted:

1) You can win fixed prices of \$2 up to \$1,000,000 ( http://www.megamillions.com/how-to-....to-play ) Those add up to an expected win of \$0.255

2) The size JP of the jackpot depends on the number N of tickets sold: according to wikipedia "Approximately 60% of Mega Millions sales is returned to players as prizes;", so each ticket should add an expected .6*\$2 - \$0.255 = \$0.945

The "expected jackpot" is now at \$1,600,000,000, up from \$868,000,000. But that is misleading - it's the annuity version. According the mega millions, the cash-option represents "A one-time, lump-sum payment that is equal to the cash in the Mega Millions jackpot prize pool." It seems that this is 56.5% of the numbers above, so the cash went up from  \$490,000,000 to \$904,000,000 - indicating 438,000,000 tickets sold. Sounds plausible

3) The probability that you have to share the jackpot depends on N, too: the number of winners of the jackpot follows the binominial law, but in this case it can be modeled by the Poisson distribution. If your chance of getting all numbers right is 1/302,575,350 = 1/Q, the the probability that you are the only winner is  exp(- N/Q) That's 23.5% with N=438,000,000.

4) Your expected share of the jackpot is JP/N * (1 - exp(- N/Q)) With N=1, that's \$2.99, with N=438,000,000, that's \$1.58

5) The expected outcome of buying a single ticket for \$2 is thus \$1.58 + \$ 0.26 - \$2 = -\$0.16

6) This result is more realistic than Barry's, though it still ignores taxes - and assumes that there is only the standard ticket.

7) I don't think that this is a good example for gambler's ruin: the probabilities involved are so small. A more interesting question is: would it be a good investment of \$601,150,700 to buy every single combination?

a) The cash-value of the jackpot should increase by \$286,000,000 to \$1,190,000,000

b) You are certain to regain \$77,175,499 in direct wins

c) You are certain to take part in the jackpot, but your expected part is "only" \$629,000,000 (assuming 438,000,000 other tickets out there)

So, you would get back \$706,000,000, that's 17.4%  on your capital. Unfortunately, there will be taxes.

Edited by stevestory on Oct. 24 2018,07:28

Dr.GH

Posts: 2173
Joined: May 2002

This looked like a good lottery discussion of odds, and payoffs.

https://finance.yahoo.com/news.......53.html

Edited by Dr.GH on Oct. 23 2018,05:25

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"Science is the horse that pulls the cart of philosophy."

L. Susskind, 2004 "SMOLIN VS. SUSSKIND: THE ANTHROPIC PRINCIPLE"

Richardthughes

Posts: 11130
Joined: Jan. 2006

Arrington, queen of the dungheap, seems fixated on trying to goad Bob and peddling apologetics. Where are the design inferences?

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"You magnificent bastard! " : Louis
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fnxtr

Posts: 3007
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 Quote (Richardthughes @ Oct. 23 2018,10:39) Arrington, queen of the dungheap, seems fixated on trying to goad Bob and peddling apologetics. Where are the design inferences?

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"[A] book said there were 5 trillion witnesses. Who am I supposed to believe, 5 trillion witnesses or you? That shit's, like, ironclad. " -- stevestory

"Wow, you must be retarded. I said that CO2 does not trap heat. If it did then it would not cool down at night."  Joe G

Bob O'H

Posts: 2309
Joined: Oct. 2005

 Quote (Richardthughes @ Oct. 23 2018,12:39) Arrington, queen of the dungheap, seems fixated on trying to goad Bob and peddling apologetics. Where are the design inferences?

I inferred that the "Bob Argues With a Saudi About Whether it is Good to Execute Homosexuals" post was designed for Barry to get back to his usual talking points about morality being objective. It's the same ol', same ol'

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It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

Acartia_Bogart

Posts: 2123
Joined: Sep. 2014

Quote (Bob O'H @ Oct. 23 2018,16:01)
 Quote (Richardthughes @ Oct. 23 2018,12:39) Arrington, queen of the dungheap, seems fixated on trying to goad Bob and peddling apologetics. Where are the design inferences?

I inferred that the "Bob Argues With a Saudi About Whether it is Good to Execute Homosexuals" post was designed for Barry to get back to his usual talking points about morality being objective. It's the same ol', same ol'

I repeated back Barry’s words, replacing “executing homosexuals” with “preventing a homosexual valedictorian from giving the valedictory address”.

I was shocked to see my comment quickly removed and me being banned.

Edited by stevestory on Oct. 24 2018,07:27

Ptaylor

Posts: 1102
Joined: Aug. 2006

 Quote (Acartia_Bogart @ Oct. 24 2018,13:35) I was shocked to see my comment quickly removed and me being banned.

Well, as Bob O'H said "It's the same ol', same ol'"!

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We no longer say: “Another day; another bad day for Darwinism.” We now say: “Another day since the time Darwinism was disproved.”
-PaV, Uncommon Descent, 19 June 2016

Bob O'H

Posts: 2309
Joined: Oct. 2005

StephenB writes something sensible:
Quote
jdk:

 Quote In 21, Stephen, you explained what you would tell the Saudi. The Saudi would you tell you were wrong about the objective standard.Then what?

I would ask him *why* he thought I was wrong about the objective standard and form a response based on his answer. It hardly makes sense to answer an empty and mindless objection such as “you are wrong.”

Try to have a polite conversation? This will never catch on.

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It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

Jkrebs

Posts: 445
Joined: Sep. 2004

Mimus adds the last word (and maybe his last words.)

 Quote What I believe is neither hear nor there. Barry’s bluster and general dick-ish-ness in this thread are all based on the idea that subjective morality provides no way to argue against murdering gay people. In his own words, there is only “personal preference” for not murdering people for their sexual orientation.Barry has now disappeared from the thread. You are the only person left arguing for moral objectivism, but the only argument you could offer to the Saudi amounts to your “personal preference” for one philosophy over another. Perhaps you can make an argument that you think makes your philosophy better than another. But then so can a moral subjectivist. So we are back to choosing a moral system that fits your personal preference. All of Barry’s bluster adds up to nothing.

Texas Teach

Posts: 1783
Joined: April 2007

Quote (Jkrebs @ Oct. 24 2018,17:04)
Mimus adds the last word (and maybe his last words.)

 Quote What I believe is neither hear nor there. Barry’s bluster and general dick-ish-ness in this thread are all based on the idea that subjective morality provides no way to argue against murdering gay people. In his own words, there is only “personal preference” for not murdering people for their sexual orientation.Barry has now disappeared from the thread. You are the only person left arguing for moral objectivism, but the only argument you could offer to the Saudi amounts to your “personal preference” for one philosophy over another. Perhaps you can make an argument that you think makes your philosophy better than another. But then so can a moral subjectivist. So we are back to choosing a moral system that fits your personal preference. All of Barry’s bluster adds up to nothing.

That is, objectively, a smack down.

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Henry J

Posts: 5201
Joined: Mar. 2005

If it were objective, then there would be no point arguing about it, since it would be established...

Bob O'H

Posts: 2309
Joined: Oct. 2005

Quote (Texas Teach @ Oct. 24 2018,17:29)
Quote (Jkrebs @ Oct. 24 2018,17:04)
Mimus adds the last word (and maybe his last words.)

 Quote What I believe is neither hear nor there. Barry’s bluster and general dick-ish-ness in this thread are all based on the idea that subjective morality provides no way to argue against murdering gay people. In his own words, there is only “personal preference” for not murdering people for their sexual orientation.Barry has now disappeared from the thread. You are the only person left arguing for moral objectivism, but the only argument you could offer to the Saudi amounts to your “personal preference” for one philosophy over another. Perhaps you can make an argument that you think makes your philosophy better than another. But then so can a moral subjectivist. So we are back to choosing a moral system that fits your personal preference. All of Barry’s bluster adds up to nothing.

That is, objectively, a smack down.

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It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

k.e..

Posts: 4922
Joined: May 2007

Quote (Bob O'H @ Oct. 25 2018,14:55)
Quote (Texas Teach @ Oct. 24 2018,17:29)

Quote (Jkrebs @ Oct. 24 2018,17:04)
Mimus adds the last word (and maybe his last words.)

 Quote What I believe is neither hear nor there. Barry’s bluster and general dick-ish-ness in this thread are all based on the idea that subjective morality provides no way to argue against murdering gay people. In his own words, there is only “personal preference” for not murdering people for their sexual orientation.Barry has now disappeared from the thread. You are the only person left arguing for moral objectivism, but the only argument you could offer to the Saudi amounts to your “personal preference” for one philosophy over another. Perhaps you can make an argument that you think makes your philosophy better than another. But then so can a moral subjectivist. So we are back to choosing a moral system that fits your personal preference. All of Barry’s bluster adds up to nothing.

That is, objectively, a smack down.

Relatively speaking.

And it's goodnight from me...

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"I get a strong breeze from my monitor every time k.e. puts on his clown DaveTard suit" dogdidit
"ID is deader than Lenny Flanks granmaws dildo batteries" Erasmus
"I'm busy studying scientist level science papers" Galloping Gary Gaulin

fnxtr

Posts: 3007
Joined: June 2006

Quote (k.e.. @ Oct. 25 2018,07:08)
Quote (Bob O'H @ Oct. 25 2018,14:55)

Quote (Texas Teach @ Oct. 24 2018,17:29)

Quote (Jkrebs @ Oct. 24 2018,17:04)
Mimus adds the last word (and maybe his last words.)

 Quote What I believe is neither hear nor there. Barry’s bluster and general dick-ish-ness in this thread are all based on the idea that subjective morality provides no way to argue against murdering gay people. In his own words, there is only “personal preference” for not murdering people for their sexual orientation.Barry has now disappeared from the thread. You are the only person left arguing for moral objectivism, but the only argument you could offer to the Saudi amounts to your “personal preference” for one philosophy over another. Perhaps you can make an argument that you think makes your philosophy better than another. But then so can a moral subjectivist. So we are back to choosing a moral system that fits your personal preference. All of Barry’s bluster adds up to nothing.

That is, objectively, a smack down.

Relatively speaking.

And it's goodnight from me...

Oo 'eck. Down the rabbit hole we go...

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"[A] book said there were 5 trillion witnesses. Who am I supposed to believe, 5 trillion witnesses or you? That shit's, like, ironclad. " -- stevestory

"Wow, you must be retarded. I said that CO2 does not trap heat. If it did then it would not cool down at night."  Joe G

steve_h

Posts: 537
Joined: Jan. 2006

EricMH
 Quote @Nonlin.org, I agree with why you say NS doesn’t exist. Only Lamarckianism exists. Great point. There is no reproducing digital code in nature apart from living organisms, and all living organisms are purposeful. Therefore, only purposeful selection ever takes place. I believe that is a categorical disproof of Darwinian evolution.

Reminds me of Gil's  post about mutating the computer doing the emulation for some reason.

fnxtr

Posts: 3007
Joined: June 2006

Quote (steve_h @ Oct. 30 2018,16:11)
EricMH

 Quote @Nonlin.org, I agree with why you say NS doesn’t exist. Only Lamarckianism exists. Great point. There is no reproducing digital code in nature apart from living organisms, and all living organisms are purposeful. Therefore, only purposeful selection ever takes place. I believe that is a categorical disproof of Darwinian evolution.

Reminds me of Gil's  post about mutating the computer doing the emulation for some reason.

If she weighs the same as a duck, then she's made of wood...

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"[A] book said there were 5 trillion witnesses. Who am I supposed to believe, 5 trillion witnesses or you? That shit's, like, ironclad. " -- stevestory

"Wow, you must be retarded. I said that CO2 does not trap heat. If it did then it would not cool down at night."  Joe G

k.e..

Posts: 4922
Joined: May 2007

Quote (fnxtr @ Oct. 31 2018,03:26)
Quote (steve_h @ Oct. 30 2018,16:11)
EricMH

 Quote @Nonlin.org, I agree with why you say NS doesn’t exist. Only Lamarckianism exists. Great point. There is no reproducing digital code in nature apart from living organisms, and all living organisms are purposeful. Therefore, only purposeful selection ever takes place. I believe that is a categorical disproof of Darwinian evolution.

Reminds me of Gil's  post about mutating the computer doing the emulation for some reason.

If she weighs the same as a duck, then she's made of wood...

Tell us all about using sheep's intestines for predicting earth quakes.

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"I get a strong breeze from my monitor every time k.e. puts on his clown DaveTard suit" dogdidit
"ID is deader than Lenny Flanks granmaws dildo batteries" Erasmus
"I'm busy studying scientist level science papers" Galloping Gary Gaulin

Bob O'H

Posts: 2309
Joined: Oct. 2005

Quote (steve_h @ Oct. 30 2018,18:11)
EricMH

 Quote @Nonlin.org, I agree with why you say NS doesn’t exist. Only Lamarckianism exists. Great point. There is no reproducing digital code in nature apart from living organisms, and all living organisms are purposeful. Therefore, only purposeful selection ever takes place. I believe that is a categorical disproof of Darwinian evolution.

Reminds me of Gil's  post about mutating the computer doing the emulation for some reason.

I think Upright BiPed (of all people) summarises things nicely
 Quote 110Upright BiPedOctober 29, 2018 at 8:58 pmThere is so much wrong on this thread. It’s depressing.

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It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

Ptaylor

Posts: 1102
Joined: Aug. 2006

Mention of both Eric Holloway and Gil prompts this: a few weeks ago the presence of Eric Holloway at UD and the respect afforded him there caused me to look him up, and I wasn’t really surprised to find that Google sent me to the People page of Dembski’s Evolutionary Informatics site, where he is featured. Something else, though, caught my attention:

Gil is still mentioned on the staff roster, although acknowledged as deceased - fair enough IMO -  but  they have kept his email address there! I can imagine a phone call:
”Good morning, this is the Evolutionary Informatics Lab - how may I help you? …do we have a Gil Dodgen here? - let me check our staff directory…yes, Mr Dodgen is one of our senior members…sorry, no, I can’t put you through to him, I’m afraid he’s deceased. You can contact him by email however - his address is G I L D…”
Ineptitude - it seems to follow ID around.

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We no longer say: “Another day; another bad day for Darwinism.” We now say: “Another day since the time Darwinism was disproved.”
-PaV, Uncommon Descent, 19 June 2016

k.e..

Posts: 4922
Joined: May 2007

 Quote (Ptaylor @ Oct. 31 2018,12:37) Mention of both Eric Holloway and Gil prompts this: a few weeks ago the presence of Eric Holloway at UD and the respect afforded him there caused me to look him up, and I wasn’t really surprised to find that Google sent me to the People page of Dembski’s Evolutionary Informatics site, where he is featured. Something else, though, caught my attention:Gil is still mentioned on the staff roster, although acknowledged as deceased - fair enough IMO -  but  they have kept his email address there! I can imagine a phone call: ”Good morning, this is the Evolutionary Informatics Lab - how may I help you? …do we have a Gil Dodgen here? - let me check our staff directory…yes, Mr Dodgen is one of our senior members…sorry, no, I can’t put you through to him, I’m afraid he’s deceased. You can contact him by email however - his address is G I L D…”Ineptitude - it seems to follow ID around.

Yeah, they probably just need to wait a bit for his new smtp server account to be set up. Gil should be emailing any day now via jesusmail.

After all it's what the whole ID project is all about, denying death and fantasizing about imaginary beings.

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"I get a strong breeze from my monitor every time k.e. puts on his clown DaveTard suit" dogdidit
"ID is deader than Lenny Flanks granmaws dildo batteries" Erasmus
"I'm busy studying scientist level science papers" Galloping Gary Gaulin

stevestory

Posts: 11211
Joined: Oct. 2005

 Quote Probability of a single protein forming by chanceOctober 31, 2018 Posted by News under Cell biology, Origin Of Life, Probability No CommentsHat tip: Philip Cunningham April 7, 2017

derp derp derp

stevestory

Posts: 11211
Joined: Oct. 2005

 Quote 1FourFacesOctober 28, 2018 at 2:45 pmKraus is yet another atheist Jew in science with a serious chip on his shoulder. They seem to be the majority. Where are the God-believing Jews of science? I would love to hear their point of view.

 Quote 6Tom RobbinsOctober 29, 2018 at 7:15 am“Krause is yet another atheist JEW’??? What forum am I on? the new reich or The new Social Darwinist? What does his ethnic background matter? Just trying to somewhat gently, but firmly point out how horrible throwing the word JEW about at individuals sounds. And then, the response, “hey, some of my friends are God fearing Jews” those “kind” are ok… Come on people, you are better than that are you not? We need to stop throwing labels at people, sounds terribly racists and is a substitute for pointing out the real issue here, which is not whether he is a Jew or not, its scientism that so ignorantly tries to mock people of faith by hiding behind this idea that science makes God superfluous, when actually, science only gives rational evidence for a God, and uncovers his glory – right? A POSITIVE message we Christians are called to carry, not segregating entire groups of people with labels, and there is no room whatsoever to judge others – judge the ideas not the person – whether we like it or not, God loves Krause as much as he does you or I. But please, lets top with the this JEW or that JEW comments – I am not a snowflake or a thought sensor kind of person, but for decency and for those of Jewish heritage that frequent this site. Can we please be just a bit more careful with the language we sling about.
careful TR

k.e..

Posts: 4922
Joined: May 2007

Quote (stevestory @ Nov. 01 2018,01:50)
 Quote 1FourFacesOctober 28, 2018 at 2:45 pmKraus is yet another atheist Jew in science with a serious chip on his shoulder. They seem to be the majority. Where are the God-believing Jews of science? I would love to hear their point of view.

 Quote 6Tom RobbinsOctober 29, 2018 at 7:15 am“Krause is yet another atheist JEW’??? What forum am I on? the new reich or The new Social Darwinist? What does his ethnic background matter? Just trying to somewhat gently, but firmly point out how horrible throwing the word JEW about at individuals sounds. And then, the response, “hey, some of my friends are God fearing Jews” those “kind” are ok… Come on people, you are better than that are you not? We need to stop throwing labels at people, sounds terribly racists and is a substitute for pointing out the real issue here, which is not whether he is a Jew or not, its scientism that so ignorantly tries to mock people of faith by hiding behind this idea that science makes God superfluous, when actually, science only gives rational evidence for a God, and uncovers his glory – right? A POSITIVE message we Christians are called to carry, not segregating entire groups of people with labels, and there is no room whatsoever to judge others – judge the ideas not the person – whether we like it or not, God loves Krause as much as he does you or I. But please, lets top with the this JEW or that JEW comments – I am not a snowflake or a thought sensor kind of person, but for decency and for those of Jewish heritage that frequent this site. Can we please be just a bit more careful with the language we sling about.
careful TR

Damn Reich right don't tell everyone we're a bunch of alt right lite fanatics all hail the Great Old Dictator.

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"I get a strong breeze from my monitor every time k.e. puts on his clown DaveTard suit" dogdidit
"ID is deader than Lenny Flanks granmaws dildo batteries" Erasmus
"I'm busy studying scientist level science papers" Galloping Gary Gaulin

DiEb

Posts: 286
Joined: May 2008

Quote (DiEb @ Oct. 22 2018,13:55)
Quote (Bob O'H @ Oct. 22 2018,09:28)

Quote (stevestory @ Oct. 21 2018,13:02)

Quote (Jkrebs @ Oct. 21 2018,13:33)

Quote (stevestory @ Oct. 20 2018,15:49)
BarryMath:

 Quote Saturday Fun: When the Lottery Bet Has a Positive Expected ValueOctober 20, 2018 Posted by Barry Arrington under Intelligent Design No CommentsThis is one of those very rare times when the lottery bet has a positive mathematical expected value. Expected value is calculated as: (Amount possibly won * probability of winning) minus (Amount of bet * probability of losing).The probability of winning Mega Millions is 1 in 302,575,350. The next jackpot is \$904 million (cash value of \$1.6 billion annuity). The expected value is (\$904,000,000 * 1/302,575,350) minus (\$2.00 * .9999999999999999999) = \$0.98.This means on average in the long run, for every \$2.00 ticket you buy, you would expect to win \$2.98 if the jackpot were always \$904 million.  Of course, you still lose the whole \$2.00 every time you lose, which is almost always.  Still, on average, over the long run, the expected value is positive (\$2.98 – \$2.00 = \$0.98).In the long run, it is a good bet. Of course, the problem is there is no long run. You only have a single shot at it. To achieve the long run average expectation, you would have to play several hundred million times.

he's not doing the math right.

Hmmm. What's wrong with Barry's math. Is not the expected value for a ticket \$0.98???

his analysis is missing a few terms. Taxes reduce the EV, and he's got no terms for winning a lower pot cuz multiple winners.

Plus, he then writes

 Quote This means on average in the long run, for every \$2.00 ticket you buy, you would expect to win \$2.98 if the jackpot were always \$904 million.

Oolong mentions multiple winners (at least I think that's what they are getting at). And, from a quick approximation, you would need about 200m tickets sold to have a 50% chance of someone else having the same number as you.

(I'm assuming everyone chooses their numbers randomly, which is of course wrong)

First, there is a glaring mistake which just shows a lack of understanding - though it does not change the result:
 Quote The expected value is (\$904,000,000 * 1/302,575,350) minus (\$2.00 * .9999999999999999999) = \$0.98.
No, you have to pay for the ticket even if you are winning, so it should be
 Quote The expected value is (\$904,000,000 * 1/302,575,350) minus \$2.00  = \$0.98.

Then, there are a lot of important details which are omitted:

1) You can win fixed prices of \$2 up to \$1,000,000 ( http://www.megamillions.com/how-to-....to-play ) Those add up to an expected win of \$0.255

2) The size JP of the jackpot depends on the number N of tickets sold: according to wikipedia "Approximately 60% of Mega Millions sales is returned to players as prizes;", so each ticket should add an expected .6*\$2 - \$0.255 = \$0.945

The "expected jackpot" is now at \$1,600,000,000, up from \$868,000,000. But that is misleading - it's the annuity version. According the mega millions, the cash-option represents "A one-time, lump-sum payment that is equal to the cash in the Mega Millions jackpot prize pool." It seems that this is 56.5% of the numbers above, so the cash went up from  \$490,000,000 to \$904,000,000 - indicating 438,000,000 tickets sold. Sounds plausible

3) The probability that you have to share the jackpot depends on N, too: the number of winners of the jackpot follows the binominial law, but in this case it can be modeled by the Poisson distribution. If your chance of getting all numbers right is 1/302,575,350 = 1/Q, the the probability that you are the only winner is  exp(- N/Q) That's 23.5% with N=438,000,000.

4) Your expected share of the jackpot is JP/N * (1 - exp(- N/Q)) With N=1, that's \$2.99, with N=438,000,000, that's \$1.58

5) The expected outcome of buying a single ticket for \$2 is thus \$1.58 + \$ 0.26 - \$2 = -\$0.16

6) This result is more realistic than Barry's, though it still ignores taxes - and assumes that there is only the standard ticket.

7) I don't think that this is a good example for gambler's ruin: the probabilities involved are so small. A more interesting question is: would it be a good investment of \$601,150,700 to buy every single combination?

a) The cash-value of the jackpot should increase by \$286,000,000 to \$1,190,000,000

b) You are certain to regain \$77,175,499 in direct wins

c) You are certain to take part in the jackpot, but your expected part is "only" \$629,000,000 (assuming 438,000,000 other tickets out there)

So, you would get back \$706,000,000, that's 17.4%  on your capital. Unfortunately, there will be taxes.

Thanks for the PotW - that was a nice surprise!

According to http://www.lottoreport.com/ticketc....son.htm  , 370,171,655 tickets were sold. The jackpot was 1,537,000,000, so the lump sum is about 870,000,000.

I overestimated the number of tickets, so that the expected share of the jackpot was \$1.66 instead of "only" \$1.58

Still, the expected outcome of buying a single ticket for \$2 was negative: \$1.66 + \$ 0.26 - \$2 = -\$0.08

CeilingCat

Posts: 2162
Joined: Dec. 2007

Quote (Bob O'H @ Oct. 31 2018,04:16)

Quote (steve_h @ Oct. 30 2018,18:11)
EricMH

 Quote @Nonlin.org, I agree with why you say NS doesn’t exist. Only Lamarckianism exists. Great point. There is no reproducing digital code in nature apart from living organisms, and all living organisms are purposeful. Therefore, only purposeful selection ever takes place. I believe that is a categorical disproof of Darwinian evolution.

Reminds me of Gil's  post about mutating the computer doing the emulation for some reason.

I think Upright BiPed (of all people) summarises things nicely

 Quote 110Upright BiPedOctober 29, 2018 at 8:58 pmThere is so much wrong on this thread. It’s depressing.

nonlin is passing out some straight ID gibberish in that thread:
 Quote Pi is not information, but a fact of life. Information resolves uncertainties that only organisms can have. Someone created information by observing the fixed ratio in a circle, so all you need is circumference of A and B and diameter of A to find diameter of B (no Pi needed). Then Archimedes created more information – the algorithm for calculating Pi. We still don’t know and don’t need Pi, but a good enough approximation. ‘Speed’ and anything else also starts with an intelligent agent asking a question and same/another resolving that uncertainty by creating information.

I think that he and EricMH are falling in love.  By the way, EricMH is a captain in the Air Force.  Sleep soundly tonight, your Air Force is guarding you.

Henry J

Posts: 5201
Joined: Mar. 2005

Pi are square.

Freelurker

Posts: 82
Joined: Oct. 2006

Pi are round. Cornbread are square.

--------------
Invoking intelligent design in science is like invoking gremlins in engineering. [after Mark Isaak.]
All models are wrong, some models are useful. - George E. P. Box

stevestory

Posts: 11211
Joined: Oct. 2005

 Quote 305Bob O'HNovember 3, 2018 at 1:41 pmEsric @ 272 – if ASC is a hypothesis test w.r.t. a specific hypothesis, then you should be able to provide the maths to show how you go from the hypothesis to ASC as a test statistic. I can see how you can do that for CSI (because of the relationship between Shannon’s entropy and the multinomial distribution), but not ASC.kf @ 274 – if you have a strong enough maths background, then you should be able to appreciate what I’m asking for, so you’ll also understand that you’re arm waving, and not providing the maths to back up your argument. If you don’t want to feel you’re being condescended to, then do the work to bring your arguments up to standard.

stevestory

Posts: 11211
Joined: Oct. 2005

 Quote 290Antonin November 3, 2018 at 12:42 pmKF, when you, Eric, gpuccio, anyone who thinks ID has some usefulness as an approach in understanding biological systems, can tell the difference between DNA sequences that have some biological activity from those that don’t, without synthesizing them, then I’ll revise my view on ID.

hahahahahahaha

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