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Lotto Probability

BillyJoe said:
Yes, that's why I said to substitute each set into the first question.
Okay, so far so good....

What if I rephrase those questions slightly:

1) Would you say that next week's lotto numbers coming up 1,2,3,4,5,6 is IMPROBABLE ?
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Yes.

2) Would your answer be the same if I substituted any other of the 13 million sets of six lotto numbers in the above question?
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Yes -- but isn't this exactly what you wrote for question 2 the first time? Anyway, my conditions remain as before.
 
Just thinking said:
Yes -- but isn't this exactly what you wrote for question 2 the first time? Anyway, my conditions remain as before.
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Yes, but it substitutes into a different sentence.
There is actually a subtle difference in the tense if the verb: from "will come up" to "coming up", but they are both in the future so, I think, there is no real difference.

Again a suble change....

1) Would you say that next week's lotto numbers coming up 1,2,3,4,5,6 is an IMPROBABLE event?

2) Would your answer be the same if I substituted any other of the 13 million sets of six lotto numbers in the above question?

Does this make any difference to you answer?

BJ
(I will be back in 4 hours)
 
OK, BJ -- I think I see where you're heading.

Suppose I had absolutely no knowledge of the lotto outcomes for one year -- 52 weeks with 52 drawings (each week a different outcome of 6 groups of numbers). And you came along and said to me ...

"Would it be improbable for week one's combination to be 3, 6, 18, 19, 40, 44 ?"

Of course, I would say yes. And guess what -- you gave me the actual winning combination to week one.

And then you do this for all 52 weeks -- each time asking me if that specific week would result in a specific group of 6 numbers and whether it was improbable for it to come out that way.

You would claim ... "Ah HAH! See? Improbable events occuring with extreme regularity."

But because you accepted any and all events as being within bounds you have eliminated all improbability. Each week you waited for the winning numbers and accepted whatever came out -- you essentially accepted all 13 million combinations each and every week. So, in each case you presented me with P = 1, yet to me it appeared as P = 1/13,000,000. What seemed improbable really was not improbable at all.

So, am I wrong in where you were going?
 
JT

I'm not trying to catch you out or anything. I'm trying to find out exactly where our thinking diverges. We may both be correct in different ways and we may gain an insight into each other's point of view. We may, in fact, find one of us made a mistake, but I don't see an obvious one yet. I tried one way and it lead nowhere because there were too many jumps. I am trying to go step by step to find the exact point where we diverge.

Please bear with me.
Can we please try this to see if it works....

1) Would you say that next week's lotto numbers coming up 1,2,3,4,5,6 is an IMPROBABLE event?

2) Would your answer be the same if I substituted any other of the 13 million sets of six lotto numbers in the above question?

Again, I really do just want a yes/no answer :(


BJ
 
BillyJoe said:
JT,
Can we please try this to see if it works....

1) Would you say that next week's lotto numbers coming up 1,2,3,4,5,6 is an IMPROBABLE event?
Click to expand...

Yes.

2) Would your answer be the same if I substituted any other of the 13 million sets of six lotto numbers in the above question?
Click to expand...

It depends on how those numbers are arrived at and if any limitations are placed upon them.

Again, I really do just want a yes/no answer :(
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I'm sorry, BJ -- but I thought I was getting to our differences. I guess being late at night (for me) and all I was trying to reach a conclusion and just blurted that out.
 
Just thinking said:
It depends on how those numbers are arrived at and if any limitations are placed upon them.
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I should probably let BillyJoe speak for himself, but...

He wants to ask you lots of separate questions, one for every possible combination of numbers, like this:

  • Would you say that next week's lotto numbers coming up 1,2,3,4,5,7 is an IMPROBABLE event?
  • Would you say that next week's lotto numbers coming up 1,2,3,4,5,8 is an IMPROBABLE event?
  • Would you say that next week's lotto numbers coming up 1,2,3,4,5,9 is an IMPROBABLE event?
etc.

Except it's a pain to list them all explicitly, because there are so many of them. So, his question 2 is not the same sort of question as his question 1. It's not a real question by itself. It just describes, in a brief way all at once, a whole bunch of different questions, and it's those questions that he wants you to answer. (If your answers to all of them are the same, then you can describe your answers in a similarly brief way all at once, for example, by saying "yes, to all of them". But, in actuality, there are lots of separate questions, and lots of separate answers.)
 
Just thinking said:
It depends on how those numbers are arrived at and if any limitations are placed upon them.
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You sound a little suspicious of the second question.

There is no need to be: All it means is to make a list of all possible sets of six lotto numbers (there are about 13 million of them) and substitute them one by one into the first question. The second question is just the first question repeated 13 million times with a different set of lotto numbers each time. You should end up with about 13 million answers. If your answer to the first question was "yes", your answer to all the other 13 million questions should also be "yes".

Okay?

BJ
 
69dodge said:
Except it's a pain to list them all explicitly, because there are so many of them.
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Slight derail:

I was going to attempt to the same approach, listing and numbering the possible answers. Of course, I was only going to write down the first few and the last few. I got stuck on figuring out how the 2nd last sequence would look like, and i needed an example for somewhere in the middle of the list.

So far, I managed to generate the list (split up in 14 separate text files.) I only can't open them because of their size. :D

I will try and come up with a generator for single lines by number now. But it was really helpful to see that the numbers took a total of 3.4 Gig (including HTML-Formatting, though.)
 
Just thinking said:
Yes.
As now explained -- Yes.
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Okay. two more questions...

1) Would you say, then, that we have about thirteen million improbable events to throw into our bag labelled "Improbable Events"?

2) Would you also say that we have another thirteen million for the following week, and every week into the future for as long as the lotto is drawn?

Please bear with me, we can't be too far away.


BJ
(back after about 6 hrs sleep)
 
BillyJoe said:
Okay. two more questions...

1) Would you say, then, that we have about thirteen million improbable events to throw into our bag labelled "Improbable Events"?
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Actually, this question is not so straightforward ... it seems to me a bit misleading (unintentionally, of course -- I'm sure you do not intend for it be so.) Although each event can be improbable (expecting a specific set of 6 numbers to be drawn) -- once all grouped together where one is forced to pick one (making whatever event turns up a guaranteed unspecified event), we go from the single case to the general. Each event now becomes only rare in that it will only be specified after the numbers are known -- eliminating the improbable event of "the chances of a, b, c, d, e, f occuring", where each letter is a specific number. Why? Because one will then accept whatever comes up as the "improbable" event.

So, to answer your question right now, I would answer No.

2) Would you also say that we have another thirteen million for the following week, and every week into the future for as long as the lotto is drawn?
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Here again, I would say No.

But at this point -- I have a question for you ...

Is the drawing of 6 unspecified lotto balls an improbable event?
 
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Just thinking said:
Actually, this question is not so straightforward ... it seems to me a bit misleading (unintentionally, of course -- I'm sure you do not intend for it be so.) Although each event can be improbable (expecting a specific set of 6 numbers to be drawn) -- once all grouped together where one is forced to pick one (making whatever event turns up a guaranteed unspecified event), we go from the single case to the general.
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You are speculating about a possible next step and thus not asking the question asked about *this* step.

I find this very unhelpful.


But at this point -- I have a question for you ...

Is the drawing of 6 unspecified lotto balls an improbable event?
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You need to rephrase this. Is it improbable that a person will attempt to draw lottery numbers and be successful? No, it is almost guaranteed to happen.
 
Rasmus said:
You are speculating about a possible next step and thus not asking the question asked about *this* step.

I find this very unhelpful.
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No speculation involved ... look at what is mentioned in the next question.

... as long as the lotto is drawn?
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Clearly a drawing is involved in both, as the second is nothing more than repeating the first endless times in a row.

Anyway ... my answer to both questions remains as NO.
 
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Just thinking said:
No speculation involved ... look at what is mentioned in the next question.



Clearly a drawing is involved in both, as the second is nothing more than repeating the first endless times in a row.

Anyway ... my answer to both questions remains as NO.
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Okay,

I don't quite agree, but I guess I will leave this to BilyJoe for the time being and thus avoid further obfuscating the discussion.


Edit: I don't quite dissagree
 
JT,

Question 1 is meant to stand alone. I am posting two questions at a time to speed things along because our posting times do not overlap much. So how would you answer question 1, free of any assumptions about what happens next. We can deal with that issue when it arises. Remember I am trying to home in on exactly where our thinking diverges.

1) Would you say, then, that we have about thirteen million improbable events to throw into our bag labelled "Improbable Events"?

Just to be clear, "thirteen million improbable events" means "improbable event X thirteen million", not "a set of thirteen million improbable events".


BJ
(The answer to your question is "No")
 
BillyJoe said:
JT,

Question 1 is meant to stand alone. I am posting two questions at a time to speed things along because our posting times do not overlap much. So how would you answer question 1, free of any assumptions about what happens next. We can deal with that issue when it arises. Remember I am trying to home in on exactly where our thinking diverges.

1) Would you say, then, that we have about thirteen million improbable events to throw into our bag labelled "Improbable Events"?

Just to be clear, "thirteen million improbable events" means "improbable event X thirteen million", not "a set of thirteen million improbable events".
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I'm afraid it would still be NO.

Even if we ignore your second question posted with this one, Question 1 still is based on the drawing of 6 lotto balls -- just look at the previous questions that lead to this one; they are based on lotto drawings of 6 balls and the likelyhood to an outcome.

Besides ... how could it not be a set of 13 million improbable events when you ask "...we have about thirteen million improbable events to throw into our bag ... " ? Sounds like a set containing 13 million different elements to me.

(PS: I'm saving your answer to my question for later.)
 
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