Just thinking
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Lotto Probability
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Here's my take on this:
When you look at any particular outcome: say of a lotto draw that shows a set of apparently random numbers (ie. no discernable pattern), you can say, an event that looked like that was not improbable.
What I mean by this is that of all the possible, equally likely outcomes, you wouldn't really be able to distinguish this one from a large chunk of the others.
Similar with the jellybeans: all jellybeans are similar, so any particular jellybean is not distinguishable from the others. All draws of jellybeans, then, will appear the same, and none will seem strange.
But what if there were only one red jellybean in a jar of 10000 jellybeans? Now if you draw the red one, you will say that this was an improbable event.
The thing is, drawing that jellybean was no less likely than drawing any of the others. It was no less improbable. But drawing a jellybean like that was very much more improbable (I should just say "less probable") than any of the others, because this one is distinguishable from the otheres.
I think this is the same point BJ was trying to make when he pointed out that the sequence 1,2,3,4,5,6 is no less likely than any other lotto sequence, yet seems much more strange.
The difference between it and the others is that it is "unlike" most other sequences. Most sequences when we look at them are indistinguishable from each other. This sequence falls into the set of sequences that have readily apparent patterns.
Now we can talk about probabilities: A sequence with a readily apparent pattern is much less likely than a sequence without a readily apparent pattern.
I'm not sure it makes sense to say that a sequence, or an event, is probable or improbable without defining what about that sequence we are talking about.
Sorry for the rambling.
When you look at any particular outcome: say of a lotto draw that shows a set of apparently random numbers (ie. no discernable pattern), you can say, an event that looked like that was not improbable.
What I mean by this is that of all the possible, equally likely outcomes, you wouldn't really be able to distinguish this one from a large chunk of the others.
Similar with the jellybeans: all jellybeans are similar, so any particular jellybean is not distinguishable from the others. All draws of jellybeans, then, will appear the same, and none will seem strange.
But what if there were only one red jellybean in a jar of 10000 jellybeans? Now if you draw the red one, you will say that this was an improbable event.
The thing is, drawing that jellybean was no less likely than drawing any of the others. It was no less improbable. But drawing a jellybean like that was very much more improbable (I should just say "less probable") than any of the others, because this one is distinguishable from the otheres.
I think this is the same point BJ was trying to make when he pointed out that the sequence 1,2,3,4,5,6 is no less likely than any other lotto sequence, yet seems much more strange.
The difference between it and the others is that it is "unlike" most other sequences. Most sequences when we look at them are indistinguishable from each other. This sequence falls into the set of sequences that have readily apparent patterns.
Now we can talk about probabilities: A sequence with a readily apparent pattern is much less likely than a sequence without a readily apparent pattern.
I'm not sure it makes sense to say that a sequence, or an event, is probable or improbable without defining what about that sequence we are talking about.
Sorry for the rambling.
Just thinking
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Yes, drawing the red jellybean (as described) was an improbable event -- and will not occur often. Realize though, that in distinguishing the drawn jellybean in a way that makes it different from all the others (the only red one) is what made that described event improbable -- not just the drawing of a jellybean. And it matters not if that description gets mentioned either prior to or after the drawing of it.
If the jar contained 1000 jellybeans where each one was unique, then drawing any single unspecified jellybean will be a rare event (yet easy and common to do) -- but only improbable if that unique jellybean is given singular significance (e.g.; the red one -- or one says "Gee -- what were the chances of my picking this one?" That's painting the bullseye around the target.).
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Just thinking
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Much of decerning probability is based very much on exactly how or when an event is described -- and this is where many (including myself) can become either confused or mistaken.
Roboramma,
In fact, send me one as well.
well done,
BJ
You can print that and frame it - and send it to JT.
In fact, send me one as well.
well done,
BJ
Angus McPresley
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What bugs me is when you hear a pundit say that the 1,2,3,4,5,6 combination is "as good a bet" as any other.
It's actually a stupid(er) bet than any other combination. Not because it's less likely (it's not, as others have pointed out). It's because it's the most commonly selected combination, ergo you would have to split the winnings many ways.
I remember one big lottery in Florida where they announced that if 1,2,3,4,5,6 came up, the payout would be only a few hundred dollars to each person who played it.
For the maximum average payout (or more accurately, to lose money on the lotto less quickly), pick a combination of high numbers higher than 31 -- the month/day numbers are the most commonly chosen, so your odds of a unique combination are lower. Choose non-consecutive numbers too, of course.
It's actually a stupid(er) bet than any other combination. Not because it's less likely (it's not, as others have pointed out). It's because it's the most commonly selected combination, ergo you would have to split the winnings many ways.
I remember one big lottery in Florida where they announced that if 1,2,3,4,5,6 came up, the payout would be only a few hundred dollars to each person who played it.
For the maximum average payout (or more accurately, to lose money on the lotto less quickly), pick a combination of high numbers higher than 31 -- the month/day numbers are the most commonly chosen, so your odds of a unique combination are lower. Choose non-consecutive numbers too, of course.
Just thinking
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Roboramma,
You can print that and frame it - and send it to JT.
In fact, send me one as well.
well done,
BJ
Ahhh ... I already commented on that.
Once Roboramma uses the expression like that, it becomes an entirely different probability or event.
Believe it or not, the drawing of a jellybean like that is not what was done. (It was not presented as one must draw a jellybean like that.) What was done was simply the drawing of a jellybean -- only afterword was that particular jellybean singled out. By waiting to see what bean gets drawn, the like that condition changes to whatever -- hence it has no drawing value, meaning it imparts no special improbability value on the event (the drawing of a jellybean).
I am also awaiting your reply to my modest request. (Post 301)
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Once upon a time is was "a better bet" than any other - but then everyone jumped on the band wagon!
Cyphermage
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If you take 100 instances of 100 random variables and compute their covariance matrix, you will probably find examples of variables with extremely high positive or negative correlation. The predictive power of this model for things in the future, of course, is nil.
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No, I was commenting on the clarity of his post - as an example for you.Ahhh ... I already commented on that.
Once Roboramma uses the expression like that, it becomes an entirely different probability or event.
Believe it or not, the drawing of a jellybean like that is not what was done. (It was not presented as one must draw a jellybean like that.) What was done was simply the drawing of a jellybean -- only afterword was that particular jellybean singled out. By waiting to see what bean gets drawn, the like that condition changes to whatever -- hence it has no drawing value, meaning it imparts no special improbability value on the event (the drawing of a jellybean).
And, of course, he is going to frame one for me as well.
Do you mean this post...I am also awaiting your reply to my modest request. (Post 301)
Sorry, I thought you have having a joke - you know, your idiosyncratic way of interpreting what I write, results in you jokingly asking me to describe "one" event when, of course, I'm obviously talking about "events" - as a group!Can you please describe one?
(idiosyncratic ???)
[in reply to my: Events, which are members of the class "Improbable Events", happen all the time.]
Maybe try this:
Improbable events (taken individually) happen rarely.
Improbable events (taken as a group) happen all the time.
Do you mean that such a correlation is the result of "statistical cluttering" (which occurs merely by chance)?
We have had two recent examples in Australia which are probably the result of "statistical cluttering" . One was the occurence of 7 cases of brain tumour (2 benign) in the same office complex in Melbourne over a period of two years, and the other was the occurence of 12 cases of breast cancer in an ABC office in Canberra. Fortunately the media has played fair and given the view of scientist as well as the hysterical view of some union officials. One unionist is talking about "the tip of the iceberg", in relation to the Melbourne case, and has blamed a mobile phone tower on the roof of the building, whereas the scientists, whilst agreeing that the case should be investigated, are cautioning that they could be statistical clusters and that there is no scientific evidence that EMR causes cancer.
BJ
Rasmus
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I am rather unclear on the math here; but what use is a higher average payout to me, if I forfeit all winnings of games that come up 1,2,3,4,5,6?
If these numbers come up, than I can win 100$ more than if i had played a less visible pattern...
Suppose I draw six numbers and I look at them and they happen to be 1, 4, 12, 15, 23, 36. No one believes it's improbable to draw six numbers and look at them. They believe it's improbable to draw six numbers and look at them and find that they are 1, 4, 12, 15, 23, 36.
Rasmus,
He gave the example of that lottery in Florida to show how poor the winnings are if you pick numbers which have a pattern. He wasn't saying that you should have picked different numbers in THAT lotto draw! He was saying that, in general, if you pick numbers without a pattern, if those numbers come up (and the odds are the same as any other six numbers), the winnings are likely to be larger because many punters go for numbers with patterns.
(Of course this could change when the word gets out - so keep it quiet! )
BJ
He gave the example of that lottery in Florida to show how poor the winnings are if you pick numbers which have a pattern. He wasn't saying that you should have picked different numbers in THAT lotto draw! He was saying that, in general, if you pick numbers without a pattern, if those numbers come up (and the odds are the same as any other six numbers), the winnings are likely to be larger because many punters go for numbers with patterns.
(Of course this could change when the word gets out - so keep it quiet!
)BJ
Rasmus
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Rasmus,
He gave the example of that lottery in Florida to show how poor the winnings are if you pick numbers which have a pattern. He wasn't saying that you should have picked different numbers in THAT lotto draw! He was saying that, in general, if you pick numbers without a pattern, if those numbers come up (and the odds are the same as any other six numbers), the winnings are likely to be larger because many punters go for numbers with patterns.
(Of course this could change when the word gets out - so keep it quiet!
BJ
Yes, I understood that. I do not understand how that should influence my playing strategy, though.
Is it really smarter to play numbers without a pattern? My gut feeling is that yes, but I don't quite see why.
Dodgy,
I see you haven't yet mastered the art of JT speak
"Event 1) Drawing a set of lotto balls (just 6 numbers in general)."
The probability here, if you have interpreted the JT speak correctly, is 1
(This event is not improbable. In fact, a set of six lotto balls definitely will be drawn)
"Event 2) Drawing a specific individual set."
This is pretty clear. The probability here is 1 in 13 million
"The confusion seems to be emerging when one describes Event 1 and then considers the odds of getting those specific numbers drawn. But saying that now describes Event 2."
In other words, don't confuse the probability that six lotto balls will be drawn (ie EVENT 1: Six lotto balls will definitely be drawn. probability = 1), with the probability, before the event, of drawing the six numbers that are actually drawn (ie EVENT 2: Probability = 1 in 13 million)
"Event 1 will result in a rare combination (as will Event 2), but only Event 2 is improbable."
Meaning, Both EVENT 1 and EVENT 2 result in a set of six numbers which were improbable (Probability = 1 in 13 million). However, EVENT 1 (that a draw actually takes place) is not improbable (Probability = 1), whilst EVENT 2 (the probability, before the event, of drawing the six numbers that come up) is improbable (Probability = 1 in 13 million)
"Whether one singles out an individual drawing (outcome) after it happens or predicts a specific combination beforehand, it makes no difference -- one event out of millions is being identified, making that result improbable as compared to all the others."
Fairly straightforward: There are two different time periods here:
Before the draw: The probability of picking the six numbers that will come up is 1 in 13 million.
After the draw: The probability of picking the six numbers that are actually drawn is 1 in 13 million.
"It is not fair (or correct) to believe that since that individual result is so improbable, what was just done (drawing 6 numbers -- and then looking at those 6 that turned up) was an improbable event."
He means that "It is not correct to say....."
Interpretation: Although picking the six numbers is improbable (probability = 1 in 13 million), actually drawing six numbers is not improbable(Probability = 1; ie six numbers are drawn every week!). But, when you actually look at the six numbers that were drawn, you realize that the odds of those particular numbers being drawn was improbable (probability = 1 in 13 million).
So, when you say:
You are agreeing with him and he with you even though you seem to be saying the exact opposite!
Do you see how this works?
(Please. It took me ten pages!
)regards,
BillyJoe
Example: Should you play 1,2,3,4,5,6 or 3,6,13,23,34,47?
The odds of 1,2,3,4,5,6 coming up is 1 in 13 million.
The odds of 3,6,13,23,34,47 coming up is 1 in 13 million.
So, going by the odds, it doesn't matter which of those two you choose.
However, if you win with the numbers 1,2,3,4,5,6, your winnings are likely to be much lower than if you win with 3,6,13,23,34,47.
This is because more people choose numbers with patterns like 1,2,3,4,5,6. So you have to share the money with more people.
Just thinking
Philosopher
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Notice the change, please.
I can't seem to emphasize enough that expecting an outcome of 6 lotto numbers is merely a rare event -- not improbable. It is erroneous to claim that the 6 numbers that actually occured (for Event 1) is an improbable event because there was absolutely no requirement placed upon the outcome. Rare, yes -- improbable, no. BJ, you seem to agree with this later on in your satement, yet you initially claim it to be improbable. Was this just a slip up?
Just thinking
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Yes ... if I read you correctly. By emphasizing the set as a particular set, one can correctly say that the odds of getting that set were millions to one -- but realize that is painting a bullseye around the shot, as one can do that for any 6 number outcome. So there is abosolutely nothing improbable at all in doing that -- it can be done each and every time a drawing is made. Each result, however will be rare -- as exact duplicates will be few and far between.
So although one may look at the outcome and believe it to be improbable for it to come out that way (those 6 numbers you described above), it is not at all an improbable event. In other words, they would be wrong.
Just thinking
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It's OK -- I'm not at all upset with any of this.
What exactly do you mean by the second statement? Taken as a group? If you include enough possible examples of improbable events, then having one happen is no longer improbable -- in other words, having an unspecificed one happen is not an improbable event.
It's like lottery winners. Each and every winner considers their winning an improbable event -- but with so many players there are winners almost every drawing. So having an unspecified winner happen is not an improbable event, hence that argument is fallacious if one looks at these as a string of improbable events that happen often.
Just to be clear ... my example of a rare event (which is not improbable):
The numerical combination of the next 6 lotto balls drawn in my state.
... my example of an improbable event (which is also rare should it happen):
The next winning lotto numbers in my state's drawing will be 4 - 8 - 19 - 20 - 33 - 40.
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