Lotto Probability

[tsg]

Depends on how you word the question, I guess.

My point is that very few people actually consider the possibility of dying when making their travel plans. It's that unlikely, but much more likely than the slim odds people think are worth spending a dollar on.

My survival is by no means guaranteed if all I do is stay off of an airplane.

Am I risking my life in a more significant way then when I go to the movies - by bus?

That's my point exactly. People do things everyday that have a much greater chance of getting them killed than they have of winning the lottery, without even thinking about it.

 

[Rodney]

No more than dreaming about one particular hand and then getting another particular hand.

There is no difference between me playing 14-27-33-34-40-45 in the lottery and 15-16-27-33-41-49 coming or me winning the jackpot with 2-7-16-17-30-47 being played and drawn. Both events are just as likely.

You just don't usually notice.

Yes, your chances of predicting a particular outcome are low - but it will occasionally happen, the event is rare, but in no way mysterious or special.

So if you had a dream about the winning lotto numbers, would you play them?

 

[Rasmus]

So if you had a dream about the winning lotto numbers, would you play them?

Yes.

Would it be rational?

No.

Would I win?

Most likely not.

Would it be amazing if I did?

No.
I would be the odd one out of all those millions of people that dreamed about their numbers, played them and lost a dollar week after week.

 

[BillyJoe]

You stated: "In fact, those same odds apply to each and every hand in Bridge.
In other words, extraordinarily improbable events happen all the time."

The fact that "those same odds apply to each and every hand in Bridge" has nothing to do with "extraordinarily improbable events happen[ing]."

Let's try again....

1) The odds of being dealt, [13 hearts], or [2s, 6h, Qh, 7d, Jd, 5c, Ks, 2d, 8c, 8s, 10d, 4s, 6s], or [any other hand] in bridge is about 1 in 600,000,000,000.

2) Odds of 1 in 600,000,000,000 are "extraordinarily improbable".

3) Bridge hands are being dealt all the time.

4) Therefore "extraordinarily improbable events happen all the time."

Where is the error in logic?

Yes, any given hand is unlikely, but it's certain that a bridge player will be dealt one of those hands.

And this is the REASON that "extraordinarily improbable events happen all the time."

Now, if the player had dreamed the night before (s)he would receive a particular hand and then received that exact hand, that would be extraordinarily improbable.

This really is a gross understatement. As I say, if someone ever told me beforehand what hand they would be dealt, I would start believing in "cosmic connections".

 

[macgyver]

This really is a gross understatement. As I say, if someone ever told me beforehand what hand they would be dealt, I would start believing in "cosmic connections".

I'd think "this guy is a really good card magician" especially if the predictions happened with any regularity.

 

[Rodney]

Yes.

Would it be rational?

No.

Would I win?

Most likely not.

Would it be amazing if I did?

No.
I would be the odd one out of all those millions of people that dreamed about their numbers, played them and lost a dollar week after week.

How do you know how many people dream about numbers and play them?

 

[Rodney]

Let's try again....

1) The odds of being dealt, [13 hearts], or [2s, 6h, Qh, 7d, Jd, 5c, Ks, 2d, 8c, 8s, 10d, 4s, 6s], or [any other hand] in bridge is about 1 in 600,000,000,000.

2) Odds of 1 in 600,000,000,000 are "extraordinarily improbable".

3) Bridge hands are being dealt all the time.

4) Therefore "extraordinarily improbable events happen all the time."

Where is the error in logic?

The error is in defining an event as extraordinarily improbable after the fact, when some event had to occur. It's sort of like shooting at a wall, then drawing a bullseye around wherever the bullet happened to land. This is not to be confused with an inherently unlikely event, such as flipping a coin 100 times and getting all heads. While it's true that any pattern of 100 coin flips has an equally small chance of occurring, there are many ways in which 50 heads and 50 tails can be obtained but only one way in which 100 heads can be obtained.

 

[tsg]

The error is in defining an event as extraordinarily improbable after the fact, when some event had to occur. It's sort of like shooting at a wall, then drawing a bullseye around wherever the bullet happened to land. This is not to be confused with an inherently unlikely event, such as flipping a coin 100 times and getting all heads. While it's true that any pattern of 100 coin flips has an equally small chance of occurring, there are many ways in which 50 heads and 50 tails can be obtained but only one way in which 100 heads can be obtained.

If you are determining "all heads" to be the only success beforehand, this is true. If, however, all tails or HTHTHTHTHT...., or HHTTHHTTHHTT..., or HHHTTTHHHTTT... or any number of "special" sequences count, then the odds of something "incredibly improbable" go up significantly. The question is no longer "what are the odds of that particular sequence coming up" but rather "what are the odds of someone finding an amazing pattern in 100 coin tosses," which is quite a bit more likely.

The story of "lightning struck at the exact time the winning lottery ticket was being sold" is a case of the former, not of the latter. The question is not "what are the odds that lightning would strike the exact lottery machine as it was selling the winning ticket" which is damned near impossible if predetermined. The question is "what are the odds there will be a coincidence concerning the lottery that somebody will find amazing" which is roughly 1 in 1.

Besides mamapajamas' logic being faulty, the story is very likely apocryphal anyway. If mamapajamas would like to cite a source I'll gladly be corrected.

 

[Rasmus]

How do you know how many people dream about numbers and play them?

A wild guess.

It doesn't matter. Millions of people do play the lottery and somehow pick their numbers. why would my dreaming about the numbers be special?

 

[BillyJoe]

BillyJoe said:

1) The odds of being dealt, [13 hearts], or [2s, 6h, Qh, 7d, Jd, 5c, Ks, 2d, 8c, 8s, 10d, 4s, 6s], or [any other hand] in bridge is about 1 in 600,000,000,000.

2) Odds of 1 in 600,000,000,000 are "extraordinarily improbable".

3) Bridge hands are being dealt all the time.

4) Therefore "extraordinarily improbable events happen all the time."

Where is the error in logic?

---------------------------------------------------

Rodney replied:

The error is in defining an event as extraordinarily improbable after the fact, when some event had to occur.

All my verbs are in the present tense, so you're going to be hard up proving that I was talking about the past.

But seriously, Rodney, there is no real argument here:
You must remember my post was in response to mummypyjama's story about the lightning and the winning numbers. He was astounded at the extreme improbablity (before it happened!) of that event. Yet it happened. I pointed out that extremely improbable (before they happen!) events happen all the time. That is all.

BJ

 

[Rodney]

A wild guess.

It doesn't matter. Millions of people do play the lottery and somehow pick their numbers. why would my dreaming about the numbers be special?

My point is that you really don't know whether there is a correlation between dreaming about lottery numbers and those numbers being drawn. Based on your worldview, you believe that there is no correlation, but you don't have any evidence to support that bellef, as far as I can tell.

 

[Rodney]

All my verbs are in the present tense, so you're going to be hard up proving that I was talking about the past.

But seriously, Rodney, there is no real argument here:
You must remember my post was in response to mummypyjama's story about the lightning and the winning numbers. He was astounded at the extreme improbablity (before it happened!) of that event. Yet it happened. I pointed out that extremely improbable (before they happen!) events happen all the time. That is all.

BJ

My problem with what you said is that the "extremely improbable things happen all the time" explanation can be a convenient way to write off even the most mind-boggling of coincidences with no examination. For example, if 100 coin flips were to produce all heads, I don't think it would be sensible to argue that the pattern of 100 heads and no tails is no different than any of the other 2^100 possibilities, and so there is no reason to think anything unusual occurred.

 

[tsg]

My problem with what you said is that the "extremely improbable things happen all the time" explanation can be a convenient way to write off even the most mind-boggling of coincidences with no examination. For example, if 100 coin flips were to produce all heads, I don't think it would be sensible to argue that the pattern of 100 heads and no tails is no different than any of the other 2^100 possibilities, and so there is no reason to think anything unusual occurred.

It would suggest to me that the coin isn't fair or maybe there is something else going on. But that's not really what we're talking about. A closer analogy is tossing the same coin a billion times, finding a sequence of a 100 straight heads (or any other pleasing sequence), and marvelling at the odds of tossing heads a hundred times in a row. Do it enough times and it's bound to happen.

 

[Just thinking]

So if you had a dream about the winning lotto numbers, would you play them?

Yes.

Would it be rational?

No.

I disagree ... it would be no less rational than playing any other set of numbers. What would be irrational would be expecting them to have a greater chance of winning.

It would also be irrational if they should win and one felt they (the winner) had some sort of supernatural inclination.

 

[Rasmus]

My point is that you really don't know whether there is a correlation between dreaming about lottery numbers and those numbers being drawn. Based on your worldview, you believe that there is no correlation, but you don't have any evidence to support that bellef, as far as I can tell.

Proving negatives 101.

If you think there is something going on, tell me what it is and how to test it.

Until then, I will stay convinced that I have a fair 1:140.000.000 chance of hitting the jackpot for every line of numbers I play. It doesn't matter if I dream of the numbers, pick them randomly, use my birth date and other digits related to my past life or just play 1-2-3-4-5-6 and 0.

Should I win, it was out of sheer luck. Why should dreaming about a set of numbers be any more special than being dealt the right numbers in the quick tip game? And how would that "being special" work?

Why should I even want to look at the idea of it being special?

I don't think it's even a possibility. Should I be wrong, I'll still think I have no way of telling my special way of getting the right numbers apart from simple luck/chance/randomness. So what's the point?

 

[BPScooter]

I'd love to hear why Monte Carlo studies in statistics got that name. Anybody?

 

[BillyJoe]

My problem with what you said is that the "extremely improbable things happen all the time" explanation can be a convenient way to write off even the most mind-boggling of coincidences with no examination.

I'll accept that - as long as you accept that I was doing nothing of the sort

For example, if 100 coin flips were to produce all heads, I don't think it would be sensible to argue that the pattern of 100 heads and no tails is no different than any of the other 2^100 possibilities, and so there is no reason to think anything unusual occurred.

So you are saying that 100 heads in a row has less odds (before the event ) than any of the 2¹⁰⁰ other possibilities? I'm sure you are not saying that, because it is undeniable that each and every string of 100 coin tosses has exactly the same odds. So we seem to have a paradox here. Each and every string has the same odds, but we are surprised when 100 heads comes up (as opposed to any other combination). I am not denying it, I would be extraordinarily surprised too and I would be looking for a setup long before all 100 of them had been tossed. But how is this paradox resolved......
Resolution of the paradox: You are comparing patterned outcomes (or one of them) with non-patterned outcomes and the patterned outcomes are extraordinarly less common
BillyJoe.

 

[BillyJoe]

I'd love to hear why Monte Carlo studies in statistics got that name. Anybody?

Which bodies? I didn't see anybodies! And damned if I care about MC. On the other hand, I would love to know what does BP stand for?

 

[Just thinking]

... "extremely improbable things happen all the time" ...

This can be a very misunderstood/misused expression.

First off, using a straightforward definition, we see that it doesn't make sense; for if something was extremely improbable it should also be rare in occurance. (The reverse, you will soon see, is not always true.) The problem is, just what is it that is extremely improbable?

Let's look at a game of pocket billiards -- A rack of 15 balls upon the break is scattered all about the table; some balls may be pocketed as well. Since no two breaks are exactly the same, one is tempted to say that what was seen was a very improbable event event, since that particular out come was 1 in 1,000,000,000, ... etc. from happenening as it did. But that is not exactly true. Although that particular outcome was indeed rare (a 1 of a kind outcome among billions), a random distribution of billiard balls was for sure to happen. The improbable event would be predicting prior to the break just which distribution was about to play out -- not the distribution itself. Subtle perhaps, but an important distinction. A very rare event did take place, but a very improbable one did not. The same holds true for lottery numbers -- each given outcome is rare, but not improbable -- in fact, a rare outcome is almost always certain (yes, the same winning numbers can repeat).

So, what should the above quote say? ... "extremely rare things happen all the time."

I hope this clears some things up.

 

[69dodge]

So you are saying that 100 heads in a row has less odds (before the event ) than any of the 2¹⁰⁰ other possibilities? I'm sure you are not saying that, because it is undeniable that each and every string of 100 coin tosses has exactly the same odds. So we seem to have a paradox here. Each and every string has the same odds, but we are surprised when 100 heads comes up (as opposed to any other combination). I am not denying it, I would be extraordinarily surprised too and I would be looking for a setup long before all 100 of them had been tossed. But how is this paradox resolved......

You'd look for a setup that resulted in the 100 heads rather than attributing the 100 heads to chance, but you wouldn't look for a setup that resulted in some random-looking sequence rather than attributing it to chance, because, even though the probability of the 100 heads is the same as the probability of the other sequence, the probability of a setup which results in 100 heads is higher than the probability of a setup which results in the other sequence.

A two-headed coin will result in 100 heads in a row. That's relatively easy to arrange. How is anyone going to prearrange for a coin to show TTTTH HTTHT HTHHT HHTTT TTTTH HTHHT HHTTH HHTTH HTHHH HTTHH HTHHH THHHT HHTTH HTTTT HHTTT THHTH TTHTH THTTH THHTT HHHTH? And why would they choose to prearrange that particular sequence rather than any other? The probability of them choosing to prearrange that sequence is basically just as low as the probability of it coming up by chance. If your explanation is just as improbable as the thing you're trying to explain, you're not really getting anywhere.

Given that you got 100 heads in a row, the most likely explanation is that someone somehow arranged that result. Given that you got the random-looking sequence, the most likely explanation is that it just happened by chance.

Once it happens, it's no use saying, "but it was improbable". It happened. Now the only question is, why did it happen?