Lotto Probability

[BillyJoe]

Of the pace a bit here, but...

I think he just doesn't NEED to talk to get what he wants. ( Apparently Einstein didn't speak until he was three, but that is contentious )

My wife didn't talk till she was three. She had two "big brothers" and twin sisters five years older than her. She didn't NEED to speak either. She is not Einstein, but her comunication skils are amazing.

I also better understand why you would be offended by my sig line....

There is a soution.....
(I'm not really offended by it and I wouldn't really judge you for it, but it's the sort of thing you might think of, have a private chuckle, shake yourself back into order and forget about. What do you think?)

BJ

 

[BillyJoe]

....oops. I see it's gone! (Could have sworn I saw it there just a second ago)

 

[macgyver]

What do you think?

BJ

I have thought, and have responded out of respect for those I respect on this forum...

But I have to admit...it still makes me laugh...

 

[GreedyAlgorithm]

And has been, and has also been discussed.

If you're going to jump into the middle of an argument you might at least have the courtesy to read it first.

Oh, I definitely read it. But in my experience every debate about the <lottery/insurance/other probabilistic scenarios which do not come up often enough in an individual's lifetime to justify approximating the distribution normally> is improved by frequently reminding everyone that EV considerations, if used before utility is applied instead of after, are virtually worthless.

Looking back on your posts, I notice the following:

I never said it can't be. If the pleasure you derive from playing is worth more to you than the cost of the ticket, go for it. But if that pleasure is at all derived from the possibility of winning, I suggest that your understanding of how really unlikely it is may not be as much as you believe it is.

I'm betting we have very similar positions. This gets to the actual meat of these debates, which is almost always "why do individuals assign such high/low utility to outcomes like X"? It's not even "what should the 'true' utility function be", since that's often a matter of personal preference.

Your (quite valid) rebuttal was a specific instance of the nonlinearity of utility, showing that the EV calculations I (and you, it seems) thought macgyver was implicitly making before applying utility instead of after were not useful. I wanted to make that clear.

Let's say that it isn't necessarily irrational to gamble, but only irrational if the odds make it nearly impossible to win. In that case, playing one draw in a 6/49 would be irrational, because your odds are 1 in 13,000,000.

However, playing every draw for your lifetime (or until you win) brings the "lifetime odds" of winning the lotto into the realm of possibility. The only question now becomes "will it happen early or late or never?"

I find this ironic, because it suggests that to play once or twice is irrational, but to play compulsively isn't....

Oh, but now he's talking about rationality and irrationality again, whether compulsively gambling is better than a one-off, and is trying to base it on calculations done before utility is applied. So... I'll reiterate, demonstrably justified, that utility is a nonlinear function of money.

 

[macgyver]

I wanted to make that clear.

But you didn't, not to me anyway, and I started this post with this request:

I'm curious if this can be explained to a mathematically challenged individual like me:

Unless your intention is to impress us that you know something about probability (which perhaps you do), your input is worthless if you can't frame it for the audience this debate was intended to address.

I've found tsg's (and others) comments useful, and part of the purpose of this thread is to simply debate the ideas, both mathematic and psychological. My intent was to learn more about a subject I've honestly spent very little time thinking about.

Oh, but now he's talking about rationality and irrationality again, whether compulsively gambling is better than a one-off, and is trying to base it on calculations done before utility is applied. So... I'll reiterate, demonstrably justified, that utility is a nonlinear function of money.

The rational/irrational issue keeps coming up because of the human factor in this debate. I was reframing the debate to consider a different scenario. The rest of your input I find completely useless.

I think you're missing the spirit of the debate, and focussing on the mathematical "correctness". In the latter, you win...another notch in your slide rule...in the former I'd like to continue with others who accept the fact that I don't have a clue what you are talking about.

 

[GreedyAlgorithm]

Unless your intention is to impress us that you know something about probability (which perhaps you do), your input is worthless if you can't frame it for the audience this debate was intended to address.

I've found tsg's (and others) comments useful, and part of the purpose of this thread is to simply debate the ideas, both mathematic and psychological. My intent was to learn more about a subject I've honestly spent very little time thinking about.

The rational/irrational issue keeps coming up because of the human factor in this debate. I was reframing the debate to consider a different scenario. The rest of your input I find completely useless.

I think you're missing the spirit of the debate, and focussing on the mathematical "correctness". In the latter, you win...another notch in your slide rule...in the former I'd like to continue with others who accept the fact that I don't have a clue what you are talking about.

I don't intend or expect to impress anyone. But either the human factor has to be included correctly in any calculations that occur or the calculations should be left out of discussions about the human factor. Now if you're saying that all the numbers are but inspiration for debate about the human factor, then that's fine. But realize that if you really are trying to use mathematics to understand it, then you have to accept that "mathematical 'correctness'" is important.

 

[macgyver]

I don't intend or expect to impress anyone. But either the human factor has to be included correctly in any calculations that occur or the calculations should be left out of discussions about the human factor. Now if you're saying that all the numbers are but inspiration for debate about the human factor, then that's fine. But realize that if you really are trying to use mathematics to understand it, then you have to accept that "mathematical 'correctness'" is important.

Again, you seem to be missing the point. I think perhaps it's a language barrier problem. You may have something useful to say, but you're not speaking a language your audience can understand. Let me put my point into your language as an illustration:

If:
A= macgyver's current understanding of the subject of this thread

and:
B=change in macgyver's understanding of the subject of this thread attributable to GreedyAlgorithm

then:
A+B=A

Solve for "B"

I really do want to understand the subject matter, but if you're going to jump into the debate with "non-linear utility" and "EV", you'll have to start at square one and define your terms.

I defined the terms of the thread quite clearly at the start, and gave a very clear indication of the mathematical skillset I present. If you want to talk over heads, then there's just no point.

 

[tsg]

There is a soution.....
(I'm not really offended by it and I wouldn't really judge you for it, but it's the sort of thing you might think of, have a private chuckle, shake yourself back into order and forget about. What do you think?)

I have thought, and have responded out of respect for those I respect on this forum...

But I have to admit...it still makes me laugh...

Just for the record, it was not my intent to have you remove it. I do find it offensive because of the (quite possibly irrational) negative connotations I associate with the word "retard", but that is my opinion only, and I wouldn't have even said anything about it at all had you not specifically pointed it out. If you wish to keep it, I certainly won't be insulted in any way. If you decide not to for other reasons, that's okay too, but don't decide based on respectful considerations for me. I am certainly not owed any.

 

[tsg]

Oh, I definitely read it. But in my experience every debate about the <lottery/insurance/other probabilistic scenarios which do not come up often enough in an individual's lifetime to justify approximating the distribution normally> is improved by frequently reminding everyone that EV considerations, if used before utility is applied instead of after, are virtually worthless.

Except that the flaw in the utility argument is dependent on X million dollars having more utility than X million * $1. This may well be the case but the fact is by the time you have any reasonable chance of winning you will have spent well more than $1. The negative EV is only there to show that you would be much better off putting the lottery money in a savings account to accrue interest (or even playing roulette, for that matter) and having the discipline not to touch it until such time as it has a suitable utility value. It really only applies to the case of spending an insignificant amount of money on the lottery, which is fine. I've watched a dollar blow away down the street because I was too lazy to chase after it. But the fact is the majority of people who play the lottery at all are playing it fairly regularly and believe they can beat the odds.

Where the irrationality of playing the lottery really comes into play is the belief that even the slightest chance of winning makes it worth playing, while events that are far more likely to occur and have far more devastating consequences if they do aren't worth worrying about.

 

[BillyJoe]

I really do want to understand the subject matter, but if you're going to jump into the debate with "non-linear utility" and "EV", you'll have to start at square one and define your terms.

To be fair, that bit about non-linear utility and expected value has come up before. Greedy Algorithm is, I assume, trying to further this debate. His terminology probably makes very good sense to him and, who knows, he could possibly have put it in even more impenetrable language.

I have a sense of what he means, as I did the first time it was raised. And, if I am correct, I think what he is saying is almost beside the point. If I may explain...

Negative value:
Loss of $1

Positive value:
1) The possibility of winning $1million.
This is an irrational reason for playing, as we all agree, because there is no real chance of winning;
2) Thrill of the possibility of winning $1million.
This is, at base, irrational because "the thrill" is possible only as a result of lack of recognition or denial of (1)

So, an individual might still get a positive value out of playing lotto if...
1) He hasn't ever thought about probability
2) He doesn't doesn't want to hear about probability (primary denial)
3) He knows about the probability but chooses consciously, or subconsciously, to deny it (secondary denial).


But maybe, if we welcome him back into the fold, GA might elaborate on his contribution and further this discussion.


BJ

 

[macgyver]

Just for the record, it was not my intent to have you remove it. I do find it offensive because of the (quite possibly irrational) negative connotations I associate with the word "retard", but that is my opinion only, and I wouldn't have even said anything about it at all had you not specifically pointed it out. If you wish to keep it, I certainly won't be insulted in any way. If you decide not to for other reasons, that's okay too, but don't decide based on respectful considerations for me. I am certainly not owed any.

I had intended to remove it any way, prior to your comment about it (which is a valid one). I found the whole "sig" thing a bit distracting to be honest, but I had to try them on for size.

I was more concerned that people might discount my opinions on matters completely unrelated to the sig, just because of negative feelings toward it. I feel no need to apologize for my sense of humour, but I'm not callous either.

 

[macgyver]

But maybe, if we welcome him back into the fold, GA might elaborate on his contribution and further this discussion.
BJ

I have no desire to exclude anyone from this discussion, including GA, I'm only asking that he "dumb it down" for dummies like me!

Believe me, I could write a sentence related to my work that would be concise, grammatically correct, and completely meaningless to anybody outsite the trade, but it would be useless for me to try and explain myself to a layman using the same language.

If GA really knows what he's talking about (and I'm sure he does) then he'll be able to explain it to somebody who doesn't...

 

[macgyver]

Anyway, let's attempt to lift this train back onto the rails....

Could we have a look back at post #179?

I'm not sure that this has been addressed? If it has, then I've missed the point....again....

 

[BPScooter]

I have such a hold on my $$ that I can't even remember the last time I let go of one on a lotto. That $ that I don't spend is another $ I can use to give Kid Scooter 4 quarters or save a $ to go to Costco and get a 5 pound bag of toilet paper. Sorry, y'all, but there are tightwad skeptic economies involved, and since these # games are not likely, I save my $.

 

[BillyJoe]

POST #179

...playing one draw in a 6/49 would be irrational, because your odds are 1 in 13,000,000.

However, playing every draw for your lifetime (or until you win) brings the "lifetime odds" of winning the lotto into the realm of possibility. The only question now becomes "will it happen early or late or never?"

I find this ironic, because it suggests that to play once or twice is irrational, but to play compulsively isn't....

The real question I have though, is how valid is the "lifetime odds" calculation?

First try, to get the ball rolling.....

The purchase price is $1 and you play every week for fifty years
1 * 50 * 50 = 2500 plays in a life time (50 years).
Money spent = $2500
Odds of winning = 13,000,000 / 2500 = 5200.

This means that, if 5200 people play the lotto every week for 50 years, chances are that 1 out of these 5200 people will win the million dollars.

Or, looked at another way....
It's analogous to you throwing one dollar away every week for your whole life so that once, at some point in your life you can dip your hand into a barrel containing 5200 marbles and picking out the only golden one which you can swap for a million dollars.

BJ

 

[BillyJoe]

I have no desire to exclude anyone from this discussion, including GA, I'm only asking that he "dumb it down" for dummies like me!

The problem is you can't force people to help you

 

[BPScooter]

Doesn't this all imply that all available players are indeed playing? Or that if and when induced, they might play? The real-world Lotto games do not operate under these conditions.

 

[BillyJoe]

Doesn't this all imply that all available players are indeed playing? Or that if and when induced, they might play? The real-world Lotto games do not operate under these conditions.

Real-world lotto games attract plenty of players don't you worry your l'il head about that, they not all as bright as you 'n' me.

 

[69dodge]

Let's say that it isn't necessarily irrational to gamble, but only irrational if the odds make it nearly impossible to win. In that case, playing one draw in a 6/49 would be irrational, because your odds are 1 in 13,000,000.

However, playing every draw for your lifetime (or until you win) brings the "lifetime odds" of winning the lotto into the realm of possibility. The only question now becomes "will it happen early or late or never?"

I find this ironic, because it suggests that to play once or twice is irrational, but to play compulsively isn't....

The real question I have though, is how valid is the "lifetime odds" calculation?

I don't think there's a unique definition of rationality here. Different people want to do different things, and who's to say what it's rational to want?

But, with that caveat, I'd tend to say that the more you play, the less rational you're being. Why? Well, let's look at the two extremes. If you never play, you're certain not to win anything nor to lose anything. If you play for a really long time---such a long time that you're virtually guararanteed to win the jackpot many times (and, of course, lose the much smaller price of a ticket many more times)---then overall you're practically certain to lose money, because, after all, the people who run the lottery have set up the odds so that they make money. And the longer you play, the more you'll lose.

This is not quite a mathematical proof, because, again, if someone wants to play the lottery every day, knowing the odds, then that's simply what he wants. But, still, it seems sort of reasonable that if playing for a very long time is much worse than not playing at all, then playing for a shorter amount of time ought to be considered somewhat worse than not playing at all.

To address your post more directly, while playing for a lifetime might move winning the jackpot into the realm of possibility, it also increases the amount of money you spend on tickets, and that needs to be taken into account as well because losing all that money is certainly within the realm of possibility too.

 

[BillyJoe]

I don't think there's a unique definition of rationality here. Different people want to do different things, and who's to say what it's rational to want?

Well, I don't understand this at all.

So, we're okay with people who want to play lotto - because they believe they have a reasonable chance of winning (because they don't care about probability, or because they don't understand it, or because they understand it but consciously or subcionsciously deny it) - because, you know, whose to say what is rational for anyone to want?

Sounds like a version of postmodernism to me, Dodgy.

BillyJoe
(Nice to see you again )