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Date: 24 Jan 2009 12:39:14
From: - ikabopo -
Subject: Nebraska lottery and public innumeracy
Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
digit permutation on consecutive days. The media jumped on this, saying
that the odds of this happening were a million to 1.

Ugh.

I'm sure all the mathematically inclined people know that the odds of
this happening for any given drawing are 1000 to 1.

If you don't understand why, I'll leave it to others to explain.

-ikabopo-





 
Date: 24 Jan 2009 10:43:57
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 11:39 AM, - ikabopo - wrote:

> Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
> digit permutation on consecutive days. The media jumped on this, saying
> that the odds of this happening were a million to 1.
>
> Ugh.
>
> I'm sure all the mathematically inclined people know that the odds of
> this happening for any given drawing are 1000 to 1.
>
> If you don't understand why, I'll leave it to others to explain.
>
> -ikabopo-

While what you post is true as far as it goes, it's often mis-applied in
gambling circles. The key distinction has to do with how "interesting"
for lack of a better term the initial event in question is.

In your lottery example, all numbers are in some sense equally interesting
initially. So repeating one in your example is only a 1000/1 shot. Now
let's say we do something to make one of the numbers interesting - a
person wagers a dollar on it, and plans to wager all their winnings on the
same number next week if they win. Assuming such a bet was allowed and
there was no vig, it would pay off 1,000,000 to 1, not 1000 to 1. In
other words, the odds went to the square of their initial value just by
making both the initial and second number interesting.

It reminds me of the scene in Casino where the slot cheats are making
jackpots hit. Since a jackpot is inherently interesting, the probability
of two together are P(jackpot in given time)^2, not just P(jackpot in
given time) and the slot dude should have pulled the machines after the
second jackpot, not the third. Most people intuitively understand this
and it shows clearly the flaw in ikabopo's thinking if it's broadly
applied.

Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 24 Jan 2009 10:49:46
From: garycarson
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 1:43 PM, Wayne Vinson wrote:


> second jackpot, not the third. Most people intuitively understand this
> and it shows clearly the flaw in ikabopo's thinking if it's broadly
> applied.
>
> Wayne Vinson
> http://cardsharp.org/
> Wayne (dot) Vinson (at) gmail (dot) com

There was no flaw in ikabopos thinking.

The flaw is in your understanding of what he said.

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Date: 24 Jan 2009 10:55:25
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
> There was no flaw in ikabopos thinking.
>
> The flaw is in your understanding of what he said.

You missed a key point - his post, and fell's, were snide comments on what
I posted yesterday. And in my case, the initial event that got repeated
was already "interesting", not random or arbitrary.

Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 25 Jan 2009 05:34:31
From: Fred Viles
Subject: Re: Nebraska lottery and public innumeracy
"Wayne Vinson" <a7a88fc@webnntp.invalid > wrote in
news:tp4s46xdqb.ln2@recgroups.com:

>"garycarson" <garycarson@alumni.northwestern.edu> wrote in
news:af4s46xfob.ln2@recgroups.com:
(attribution restored)
>> There was no flaw in ikabopos thinking.
>>
>> The flaw is in your understanding of what he said.
>
> You missed a key point - his post, and fell's, were snide
> comments on what I posted yesterday.

Why is that point key?

> And in my case, the
> initial event that got repeated was already "interesting", not
> random or arbitrary.

It may have been "interesting", but it was indeed both random and
arbitrary.

Unlike the example you gave in your first reply in this thread,
neither the hand pattern nor the hand number was bet on in
advance. It was selected after the fact, based not on the pattern
but on its similarity to the hand that followed. How can the odds
of that particular pattern coming up on any particular hand matter
for the first hand, when it was not the basis of selecting the
hand?

The point you've been ignoring is that "interesting" hands in
poker are quite frequent, not 150K-to-1 shots.

ISTM the odds of *some* interesting hand pattern being repeated in
a particular pair of hands is P(odds of a random hand being
interesting)*P(odds of the specific interesting hand being dealt).

The odds of it happening sometime during the course of playing N
hands, which is all that actually happened in your case, is
correspondingly greater.

- Fred


    
Date: 24 Jan 2009 11:09:19
From: FellKnight
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 1:55 PM, Wayne Vinson wrote:

> > There was no flaw in ikabopos thinking.
> >
> > The flaw is in your understanding of what he said.
>
> You missed a key point - his post, and fell's, were snide comments on what
> I posted yesterday. And in my case, the initial event that got repeated
> was already "interesting", not random or arbitrary.
>
> Wayne Vinson
> http://cardsharp.org/
> Wayne (dot) Vinson (at) gmail (dot) com

It was only interesting because you felt it was interesting. It was
really no more mathematically interesting than any other 2 hole card plus
5 board card combination.

Fell
--
"Don't underestimate Fell. He's a smart kid."
- Paul Popinjay, RGP, Nov 15, 2008

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Date: 25 Jan 2009 09:10:59
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
> It was only interesting because you felt it was interesting. It was
> really no more mathematically interesting than any other 2 hole card plus
> 5 board card combination.
>
> Fell


How do you figure that? In poker, just like in the slot machine example,
some outcomes are inherently far more interesting than others.

Blindly ignoring this point is absurd. Hell, by the reasoning some of you
are presenting you would NEVER catch the slot cheats, because each jackpot
isn't a rare enough event to raise your curiosity, and the past ones
already happened and are givens. If you refused to engage in logic that
multiplied the probabilities of those events together, you would never
detect the cheats. Fact.

Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 25 Jan 2009 11:25:52
From: garycarson
Subject: Re: Nebraska lottery and public innumeracy
On Jan 25 2009 12:10 PM, Wayne Vinson wrote:

> > It was only interesting because you felt it was interesting. It was
> > really no more mathematically interesting than any other 2 hole card plus
> > 5 board card combination.
> >
> > Fell
>
>
> How do you figure that? In poker, just like in the slot machine example,
> some outcomes are inherently far more interesting than others.
>
> Blindly ignoring this point is absurd. Hell, by the reasoning some of you
> are presenting you would NEVER catch the slot cheats, because each jackpot
> isn't a rare enough event to raise your curiosity, and the past ones
> already happened and are givens. If you refused to engage in logic that
> multiplied the probabilities of those events together, you would never
> detect the cheats. Fact.
>
> Wayne Vinson
> http://cardsharp.org/
> Wayne (dot) Vinson (at) gmail (dot) com


Sigh.

The 1000 to 1 odds of the lottery repeating are also wrong

I'v e explained this so many times over the years at rgp that I don't want
to bother again.

From watching the movie we don't know that there were any slot machine
cheats, only that some casino exec thought they must be cheating. Hitting
n jackpots within K minutes does not prove that anyone was cheating
(unless the slots were crooked to start with).

Idiot.

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Date: 25 Jan 2009 11:28:14
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
>
> Sigh.
>
> The 1000 to 1 odds of the lottery repeating are also wrong
>
> I'v e explained this so many times over the years at rgp that I don't want
> to bother again.
>
> From watching the movie we don't know that there were any slot machine
> cheats, only that some casino exec thought they must be cheating. Hitting
> n jackpots within K minutes does not prove that anyone was cheating
> (unless the slots were crooked to start with).
>
> Idiot.


If you can't grasp the point that the second jackpot is VERY strong
evidence something is afoot, then you're living in some fantasy land where
bad mathematics trump reality.

Are you really as credulous as you are attempting to claim?

Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 25 Jan 2009 13:42:07
From: da pickle
Subject: Re: Nebraska lottery and public innumeracy
"Wayne Vinson"

> If you can't grasp the point that the second jackpot is VERY strong
> evidence something is afoot, then you're living in some fantasy land where
> bad mathematics trump reality.
>
> Are you really as credulous as you are attempting to claim?

I do not claim any special training or study of statistics and probability,
but I do know that no matter what "the odds" are that something could happen
(that does happen) is "proof" of anything other than it DID happen.

These new "examples" appear to me to be nothing more than extensions of "the
gambler's fallacy".

Watch me flip a coin and wait for it to come up heads x times in a row and
then believe that "the odds" of it coming up heads x+1 in a row are any
different than it was before. Or, as you posit here, it "must" prove me to
be cheating in my flipping for it to happen at all ... if we make "x" just
the right number of times. Otherwise, the "odds" are just "too high."

The probability of you getting pocket aces twice as you originally posted
with the boards that you actually experienced is "1" ... it happened. It
proves only that it happened. It may be that there is cheating and action
flops and many other things going on, but your experience is only proof that
"it happened" ... it does not "prove" anything more.





         
Date: 25 Jan 2009 12:07:20
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
On Jan 25 2009 1:42 PM, da pickle wrote:

> "Wayne Vinson"
>
> > If you can't grasp the point that the second jackpot is VERY strong
> > evidence something is afoot, then you're living in some fantasy land where
> > bad mathematics trump reality.
> >
> > Are you really as credulous as you are attempting to claim?
>
> I do not claim any special training or study of statistics and probability,
> but I do know that no matter what "the odds" are that something could happen
> (that does happen) is "proof" of anything other than it DID happen.
>
> These new "examples" appear to me to be nothing more than extensions of "the
> gambler's fallacy".
>
> Watch me flip a coin and wait for it to come up heads x times in a row and
> then believe that "the odds" of it coming up heads x+1 in a row are any
> different than it was before. Or, as you posit here, it "must" prove me to
> be cheating in my flipping for it to happen at all ... if we make "x" just
> the right number of times. Otherwise, the "odds" are just "too high."
>
> The probability of you getting pocket aces twice as you originally posted
> with the boards that you actually experienced is "1" ... it happened. It
> proves only that it happened. It may be that there is cheating and action
> flops and many other things going on, but your experience is only proof that
> "it happened" ... it does not "prove" anything more.

There is more truth to the "gambler's fallacy" than it's name would
suggest. For example, consider Barry Greenstein's obviously correct
comments on flipping coins in Ace On The River.

The issue here is that there are fundamentally two ways of viewing
probably: forward probability and backwards or "Bayesian" probability.
Forward probability takes a fully understood random system and makes
statements about its outputs. Bayesian probability takes a random system
that's not fully understood, looks at its outputs, and makes statements
about the system.

Clearly the question "Is the deal fair on site X?" is a Bayesian question
- we're looking at what rolls off the deck at site X and trying to
determine the underlying system that produced those outputs.

Yet you will see time and time again that those who argue against me will
adopt forward probabilistic reasoning and make assumptions about the
underlying system which they refuse to question. In other words, in the
case of the "fair deal?" question they're assuming the cards coming off
the deck are independent and no event is any more interesting than any
other. Those are forward probability assumptions, not Bayesian
assumptions, and worse yet they're in essence assuming what they're trying
to prove.

Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 25 Jan 2009 14:45:34
From: da pickle
Subject: Re: Nebraska lottery and public innumeracy
"Wayne Vinson"

> The issue here is that there are fundamentally two ways of viewing
> probably: forward probability and backwards or "Bayesian" probability.
> Forward probability takes a fully understood random system and makes
> statements about its outputs. Bayesian probability takes a random system
> that's not fully understood, looks at its outputs, and makes statements
> about the system.
>
> Clearly the question "Is the deal fair on site X?" is a Bayesian question
> - we're looking at what rolls off the deck at site X and trying to
> determine the underlying system that produced those outputs.


I do not know enough about what you are explaining to have an educated
opinion. I do have an opinion about defining the problem ... the question
being asked is "Is the deal fair on site X."

When asking such a question, you can assume the deal is unfair and see if
you can "prove" it ... or you can assume the deal is fair and see if you can
disprove it. Perhaps this is saying the same thing a different way.
However, you cannot take two "really, really, really rare" events occurring
and use those events as "proof" either way.


> Yet you will see time and time again that those who argue against me will
> adopt forward probabilistic reasoning and make assumptions about the
> underlying system which they refuse to question. In other words, in the
> case of the "fair deal?" question they're assuming the cards coming off
> the deck are independent and no event is any more interesting than any
> other. Those are forward probability assumptions, not Bayesian
> assumptions, and worse yet they're in essence assuming what they're trying
> to prove.


I am not arguing against you or with you ... I am just saying that my
limited training in statistics leads me to think that the occurrence of
"rare" events in succession does not "prove" anything at all. The proof of
non-random events requires a different sort of analysis of statistically
significant samples.

Whether one assumes the cards coming off the deck are independent or NOT
independent, one cannot rely on a few "memorable" events (two straight
flushes in a row) as proof of anything other than you have observed two
memorable events.




      
Date: 25 Jan 2009 09:27:03
From: FellKnight
Subject: Re: Nebraska lottery and public innumeracy
On Jan 25 2009 12:10 PM, Wayne Vinson wrote:

> > It was only interesting because you felt it was interesting. It was
> > really no more mathematically interesting than any other 2 hole card plus
> > 5 board card combination.
> >
> > Fell
>
>
> How do you figure that? In poker, just like in the slot machine example,
> some outcomes are inherently far more interesting than others.
>
> Blindly ignoring this point is absurd. Hell, by the reasoning some of you
> are presenting you would NEVER catch the slot cheats, because each jackpot
> isn't a rare enough event to raise your curiosity, and the past ones
> already happened and are givens. If you refused to engage in logic that
> multiplied the probabilities of those events together, you would never
> detect the cheats. Fact.
>
> Wayne Vinson
> http://cardsharp.org/
> Wayne (dot) Vinson (at) gmail (dot) com

Not so.

It simply means that the casino staff from the movie Casino were correct
in waiting for the 3rd jackpot to notice an irregularity.

Fell
--
"Don't underestimate Fell. He's a smart kid."
- Paul Popinjay, RGP, Nov 15, 2008

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Date: 25 Jan 2009 11:32:33
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
> Not so.
>
> It simply means that the casino staff from the movie Casino were correct
> in waiting for the 3rd jackpot to notice an irregularity.
>
> Fell

Nope. You failed to follow the logic to it's inevitable conclusion. If
you can't multiply the probability of the first event with the second
event, you can't multiply the second with the third by the same reasoning.
It's all just P(jackpot) all day long, and you'll never think anything is
afoot even after the 10th one hits. There is no fundamental difference in
multiplying P(jackpot 1) * P(jackpot 2) vs multiplying P(jackpot 2 ) *
p(jackpot 3) and so on down the line. Either you multiply or you don't.

Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 25 Jan 2009 11:48:57
From: FellKnight
Subject: Re: Nebraska lottery and public innumeracy
On Jan 25 2009 2:32 PM, Wayne Vinson wrote:

> > Not so.
> >
> > It simply means that the casino staff from the movie Casino were correct
> > in waiting for the 3rd jackpot to notice an irregularity.
> >
> > Fell
>
> Nope. You failed to follow the logic to it's inevitable conclusion. If
> you can't multiply the probability of the first event with the second
> event, you can't multiply the second with the third by the same reasoning.
> It's all just P(jackpot) all day long, and you'll never think anything is
> afoot even after the 10th one hits. There is no fundamental difference in
> multiplying P(jackpot 1) * P(jackpot 2) vs multiplying P(jackpot 2 ) *
> p(jackpot 3) and so on down the line. Either you multiply or you don't.
>
> Wayne Vinson
> http://cardsharp.org/
> Wayne (dot) Vinson (at) gmail (dot) com

Whatever you say, Wayne. It's been far too long for RGP to be without
your stubborn obtuse argumentative style when you are clearly wrong.

Fell
--
"Don't underestimate Fell. He's a smart kid."
- Paul Popinjay, RGP, Nov 15, 2008

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Date: 24 Jan 2009 11:04:35
From: Steam
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 9:39 AM, - ikabopo - wrote:

> Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
> digit permutation on consecutive days. The media jumped on this, saying
> that the odds of this happening were a million to 1.
>
> Ugh.
>
> I'm sure all the mathematically inclined people know that the odds of
> this happening for any given drawing are 1000 to 1.
>
> If you don't understand why, I'll leave it to others to explain.
>
> -ikabopo-

Actually no, it is 1 in 1000, not 1000 to 1. The odds are 999 to 1.

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Date: 25 Jan 2009 11:29:05
From: garycarson
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 2:04 PM, Steam wrote:

> On Jan 24 2009 9:39 AM, - ikabopo - wrote:
>
> > Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
> > digit permutation on consecutive days. The media jumped on this, saying
> > that the odds of this happening were a million to 1.
> >
> > Ugh.
> >
> > I'm sure all the mathematically inclined people know that the odds of
> > this happening for any given drawing are 1000 to 1.
> >
> > If you don't understand why, I'll leave it to others to explain.
> >
> > -ikabopo-
>
> Actually no, it is 1 in 1000, not 1000 to 1. The odds are 999 to 1.

That's not right either, the actual odds are much, much less than that
(because we aren't flipping a coin twice, we're flipping it hundreds of
times then looking for a sequence of HH someplace in the very long
sequence of flips).

Putting all this efforct into an exact computation of a bad model is a
true waste of effort.

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Date: 25 Jan 2009 14:34:33
From: Steam
Subject: Re: Nebraska lottery and public innumeracy
On Jan 25 2009 11:29 AM, garycarson wrote:
> >
> > Actually no, it is 1 in 1000, not 1000 to 1. The odds are 999 to 1.
>
> That's not right either, the actual odds are much, much less than that
> (because we aren't flipping a coin twice, we're flipping it hundreds of
> times then looking for a sequence of HH someplace in the very long
> sequence of flips).
>
> Putting all this efforct into an exact computation of a bad model is a
> true waste of effort.

Of course what you are saying is correct. The odds of 999 to 1 are the
odds of it happening THIS time. I'm pretty sure that is what ikabopo was
attempting to show as well. However, I cannot argue with your point, the
odds of it ever happening over 1000s of trials does actually speak well to
the original post, since it was about how rare or unusual the event was,
and it really should be expected to happen over 1000s of trials.

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Date: 24 Jan 2009 17:54:38
From: - ikabopo -
Subject: Re: Nebraska lottery and public innumeracy
Good call. Odds and probablity are different. But obviously you get
the point of my post.

-ikabopo-



Re: Nebraska lottery and public innumeracy

Group: rec.gambling.poker Date: Sat, Jan 24, 2009, 11:04am (EST-3) From:
a74baac@webnntp.invalid (Steam)
On Jan 24 2009 9:39 AM, - ikabopo - wrote:
Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
digit permutation on consecutive days. The media jumped on this, saying
that the odds of this happening were a million to 1.
Ugh.
I'm sure all the mathematically inclined people know that the odds of
this happening for any given drawing are 1000 to 1.
If you don't understand why, I'll leave it to others to explain.
-ikabopo-



Actually no, it is 1 in 1000, not 1000 to 1. The odds are 999 to 1.
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Date: 25 Jan 2009 02:51:56
From: Steam
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 2:54 PM, - ikabopo - wrote:

> Good call. Odds and probablity are different. But obviously you get
> the point of my post.
>
> -ikabopo-
>
We are in agreement on the main point of the post.

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Date: 24 Jan 2009 17:54:38
From: La Cosa Nostradamus
Subject: Re: Nebraska lottery and public innumeracy
Funny thing, it doesnt seem to happen more than once in 3 years for any
state. If every state had a lottery, it should happen in one state, at
least once a month. Do we hear of this phenomenon once a month ? See it is
rigged but the masses see the riggedness from the wrong side.
On Jan 24 2009 5:54 PM, - ikabopo - wrote:

> Good call. Odds and probablity are different. But obviously you get
> the point of my post.
>
> -ikabopo-
>
>
>
> Re: Nebraska lottery and public innumeracy
>
> Group: rec.gambling.poker Date: Sat, Jan 24, 2009, 11:04am (EST-3) From:
> a74baac@webnntp.invalid (Steam)
> On Jan 24 2009 9:39 AM, - ikabopo - wrote:
> Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
> digit permutation on consecutive days. The media jumped on this, saying
> that the odds of this happening were a million to 1.
> Ugh.
> I'm sure all the mathematically inclined people know that the odds of
> this happening for any given drawing are 1000 to 1.
> If you don't understand why, I'll leave it to others to explain.
> -ikabopo-
>
>
>
> Actually no, it is 1 in 1000, not 1000 to 1. The odds are 999 to 1.


Atheism is drawing dead

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Date: 25 Jan 2009 23:03:21
From: - ikabopo -
Subject: Re: Nebraska lottery and public innumeracy
When the lottery drawing repeats itself in Ohio where I live, it does
not make the news, except for maybe a 20 second blurb, or a tiny
article. It certainly doesn't get reported nationally.

I wonder if the fact that this happened in Nebraska has anything to do
with why it made national news. I have a feeling that if this occured
in states like Massachusetts, New York, or Washington, it would not be a
big deal. But if this happened in somewhere like Wyoming, Montana,
etc., where the population is perhaps not as numerate....you get my
point.
(I don't even know which of the previously listed states actually even
have lotteries, by the way.)

For the record, I was not trying to be snide to any RGPers in this post.
I read CardSharp regularly and enjoy it.

-ikabopo-




Re: Nebraska lottery and public innumeracy

Group: rec.gambling.poker Date: Sat, Jan 24, 2009, 5:54pm (EST-3) From:
a6f44ce@webnntp.invalid (La=A0Cosa=A0Nostradamus)
Funny thing, it doesnt seem to happen more than once in 3 years for any
state. If every state had a lottery, it should happen in one state, at
least once a month. Do we hear of this phenomenon once a month ? See it
is rigged but the masses see the riggedness from the wrong side. On Jan
24 2009 5:54 PM, - ikabopo - wrote:
Good call. Odds and probablity are different. But obviously you get the
point of my post.
-ikabopo-
Re: Nebraska lottery and public innumeracy
Group: rec.gambling.poker Date: Sat, Jan 24, 2009, 11:04am (EST-3) From:
a74baac@webnntp.invalid (Steam)
On Jan 24 2009 9:39 AM, - ikabopo - wrote: Recently the Nebraska
lottery's 3 digit lotter drawing picked the same 3 digit permutation on
consecutive days. The media jumped on this, saying that the odds of this
happening were a million to 1. Ugh.
I'm sure all the mathematically inclined people know that the odds of
this happening for any given drawing are 1000 to 1. If you don't
understand why, I'll leave it to others to explain. -ikabopo-
Actually no, it is 1 in 1000, not 1000 to 1. The odds are 999 to 1.
Atheism is drawing dead
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Date: 25 Jan 2009 22:41:34
From: Wayne Vinson
Subject: Re: Nebraska lottery and public innumeracy
> For the record, I was not trying to be snide to any RGPers in this post.
> I read CardSharp regularly and enjoy it.

Fair enough. I misinterpreted your post then. Sorry.



Wayne Vinson
http://cardsharp.org/
Wayne (dot) Vinson (at) gmail (dot) com

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Date: 24 Jan 2009 10:46:16
From: FellKnight
Subject: Re: Nebraska lottery and public innumeracy
On Jan 24 2009 12:39 PM, - ikabopo - wrote:

> Recently the Nebraska lottery's 3 digit lotter drawing picked the same 3
> digit permutation on consecutive days. The media jumped on this, saying
> that the odds of this happening were a million to 1.
>
> Ugh.
>
> I'm sure all the mathematically inclined people know that the odds of
> this happening for any given drawing are 1000 to 1.
>
> If you don't understand why, I'll leave it to others to explain.
>
> -ikabopo-

Can you explain it to Wayne Vinson?

Fell
--
"Don't underestimate Fell. He's a smart kid."
- Paul Popinjay, RGP, Nov 15, 2008

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