Lotto Probability

[GreedyAlgorithm]

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)

This is pretty much what I'm saying by "nonlinearity". Play 1000 times and *then* change money to utility and the picture looks like:

Negative value: Loss of $1000

Positive value: Thrill of the possibility of winning $1million, where the fact that this thrill occurs 1000 times gets washed out, and we ask ourselves "would I pay a thousand dollars for a cheap thrill?"

And in the correct form of this scenario, yes, even if your excitement made it good to play the lottery, it would still be irrational because you're getting "overly excited" about your actually dubious chance at winning.

(Although on the other hand I have trouble coming up with a "rational" reason to get so excited about the World Cup... if enough people agree that a thing is both irrational and good, maybe we need to reexamine the definition of rationality...)

But I would say that in some cases playing the lotto is still rational. Consider the admittedly fictional scenario in Run, Lola, Run.

She desperately needs... 10,000 marks I think? Within a half an hour? and determines the only possible way to get it in time is to win at roulette a couple of times in a row.

Or suppose that you want to start a business that requires lots of capital that you don't have (and you have a bad credit rating or something so that you can't borrow) (and that your age is getting a little bit up there, so the "make some money, turn it into more, etc. plan just doesn't cut it). You might well give up the fries from your lunch for a year to have a miniscule chance.

 

[GreedyAlgorithm]

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.

That's amusing... if 50 million people played a 1/13,000,000 lottery, it would suddenly become even worse to play since you'd be pretty much guaranteed of having to split the prize.

 

[69dodge]

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 )

Hi, BillyJoe. Nice to see you too.

I think that, probably, most people who play lotto don't realize how small the chances are that they'll win. But that's not what I'm talking about. Suppose they know exactly how unlikely it is, and they still want to buy a ticket. Now what? Why shouldn't they? You can't say, "because they won't win." They might. Practically speaking, they won't. They're virtually certain not to. Etc. But strictly speaking, they might.

What sort of "rational" criteria can we use to decide the value of a small chance of winning a large jackpot?

 

[BillyJoe]

Or suppose that you want to start a business that requires lots of capital that you don't have (and you have a bad credit rating or something so that you can't borrow) (and that your age is getting a little bit up there, so the "make some money, turn it into more, etc. plan just doesn't cut it). You might well give up the fries from your lunch for a year to have a miniscule chance.

GA, you remind me of one of the Karamazov brothers, who knows all the reasons for why God doesn't exist but then just believes anyway.

regards,
BillyJoe

 

[delphi_ote]

But how can you use that to pick numbers? Once they start picking numbers, bets are closed.

The second number is now one in 48, then 1 in 47 and so on so the probability does go up. The funny part is, then the least probable (the first number picked), is always picked giving it 100% odds yet it had lower odds in the beginning. I'd say this is correct probability per number picked but useless as it has no impact on the previous number picked. In other words, the individual number probability changes but the probability relationship between each subsequent number is unaffected. Another 3 am contemplation subject nonetheless.

Exactly. The odds that a particular sequence of numbers is selected is independent of the other sequences once the whole thing starts. Though the selection of the first ball gives you information about the second, which gives you information about the third, it's impossible to know where the chain begins.

Basically, you've proposed a lottery where you could pick each number before it was drawn. That would be a lot easier to win.

 

[BillyJoe]

Suppose they know exactly how unlikely it is, and they still want to buy a ticket. Now what?

That's my third scenario. They understand probability, they know exactly how unlikely it is that they will win (for all intents and purposes, the chance is zero). But they must hide this fact from themselves in order to still be able to experience the thrill of possibly winning.

Why shouldn't they?

Because it's irrational.

You can't say, "because they won't win." They might. Practically speaking, they won't. They're virtually certain not to. Etc. But strictly speaking, they might.

You're having a bob each way now

What sort of "rational" criteria can we use to decide the value of a small chance of winning a large jackpot?

The rational criteria is: Is that "small chance" large enough to give you a real chance of winning. We are here discussing the lotto and it is clear that the "small chance" is NOT large enough to give you any real chance of winning.

BJ

 

[Rasmus]

Hi, BillyJoe. Nice to see you too.

I think that, probably, most people who play lotto don't realize how small the chances are that they'll win. But that's not what I'm talking about. Suppose they know exactly how unlikely it is, and they still want to buy a ticket. Now what? Why shouldn't they?

The consensus here so far has been: By all means, do play. But don't think it's a smart thing to do.

You can't say, "because they won't win." They might. Practically speaking, they won't. They're virtually certain not to. Etc. But strictly speaking, they might.

Yes, they might. I might, which is why I play the lottery. But that doesn't make it rational.

What sort of "rational" criteria can we use to decide the value of a small chance of winning a large jackpot?

Well ,a useful criterion would be: Given the desired outcome; what would be the most likely strategy to achieve it?

And, as has been pointed out, playing roulette has better odds.

Assuming a 1:37 chance of getting the number right, and a payout of 1:36, I stand a 1 :1.874.161 chance of making myself a nice little 1.679.616 bucks (by winning 4 consecutive games).

That is about 10 times better than hitting the jackpot in the lottery, so it is irrational to invest your original Dollar or Euro or Pound in the lottery if you wish to become a millionaire.

Playing another game drives my winnings through the roof (even though I doubt anyone would accept that bet) with more money than any Jackpot here in Germany has ever payed out and chances that are roughly three times better.

Rasmus.

 

[nimzov]

most people who play lotto don't realize how small the chances are that they'll win.
(...)
Practically speaking, they won't. They're virtually certain not to.

I disagree. They have a 1:5 chance of winning something.

nimzo

 

[tsg]

I disagree. They have a 1:5 chance of winning something.

nimzo

According to this, which has been the model for this discussion so far, it's 1:32 of winning anything.

Since the arguments agains the negative EV essentially boil down to "but when you win you stop playing", and that very few people will be satisfied enough with the prize for matching 5/6 or less (under $3000) to stop playing, those prizes don't really enter into the discussion.

[edited to correct the amount]

 

[69dodge]

You're having a bob each way now

I don't think so. A very small probability is not exactly the same as a probability of zero.

The rational criteria is: Is that "small chance" large enough to give you a real chance of winning. We are here discussing the lotto and it is clear that the "small chance" is NOT large enough to give you any real chance of winning.

I'm not sure what you mean by "real chance". Would it be fair to say that your position is, "pretend that small but nonzero probabilities are exactly zero" ? That's not unreasonable. But then of course the question arises, how small is small enough.

Let's talk about a case where none of the probabilities is small. Suppose I want to bet on the roll of a six-sided die. If it shows one particular side---two dots, say---I'll win $4. Otherwise, I'll lose $1. Convince me it's a bad idea.

But keep in mind that I'm only thinking about doing it once. So you can't say, "well, if you make lots of similar bets, you'll almost surely lose money". That's true, but I'm not making lots of similar bets. I'm just making one. So, nothing is almost sure. The probability is 1/6 that I'll end up $4 ahead, and the probability is 5/6 that I'll end up $1 behind. If that's what I want to do, why shouldn't I?

 

[tsg]

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?

I'm only concerned with rationality of their reasons for wanting to.

 

[69dodge]

Well ,a useful criterion would be: Given the desired outcome; what would be the most likely strategy to achieve it?

And, as has been pointed out, playing roulette has better odds.

Assuming a 1:37 chance of getting the number right, and a payout of 1:36, I stand a 1 :1.874.161 chance of making myself a nice little 1.679.616 bucks (by winning 4 consecutive games).

That is about 10 times better than hitting the jackpot in the lottery, so it is irrational to invest your original Dollar or Euro or Pound in the lottery if you wish to become a millionaire.

That makes sense.

I wasn't really thinking about comparing lotto to a different gambling game that has better odds. I was just thinking about the idea of playing a game (lotto) with negative expectation vs. not playing anything at all.

Is the issue the negative expectation, anyway? I'd guess BillyJoe wouldn't play lotto even if it had positive expectation, provided the probability of winning was sufficiently low.

 

[tsg]

I'm not sure what you mean by "real chance". Would it be fair to say that your position is, "pretend that small but nonzero probabilities are exactly zero" ? That's not unreasonable. But then of course the question arises, how small is small enough.

When that same person considers that the odds of dying in a plane crash (roughly 20 times more likely than hitting 6/6) aren't big enough to worry about.

 

[69dodge]

I'm only concerned with rationality of their reasons for wanting to.

What kind of reasons do you have in mind?

I don't see how to give a deeper reason here than, "I just want to."

 

[69dodge]

When that same person considers that the odds of dying in a plane crash (roughly 20 times more likely than hitting 6/6) aren't big enough to worry about.

I suppose he's also considering the inconvenience of not flying, which is probably bigger than the inconvenience of paying for a lottery ticket.

 

[tsg]

I wasn't really thinking about comparing lotto to a different gambling game that has better odds. I was just thinking about the idea of playing a game (lotto) with negative expectation vs. not playing anything at all.

Well, in an argument about utility, you have to consider the other uses for that dollar. If you're not going to use it at all, then it has zero utility and you might as well play the lottery. But that is rarely, if ever, the case.

Is the issue the negative expectation, anyway? I'd guess BillyJoe wouldn't play lotto even if it had positive expectation, provided the probability of winning was sufficiently low.

If it was a postive expectation, then the argument concerns what other opportunities for your dollar would yield a higher expectation. And, of course, utility enters that as well. If the EV on the lottery was 1.01 and there was another opportunity that had an EV of 1.5, you'd be much better off with the other opportunity. If the other opportunity had an upper limit of $1000, though, the jackpot of several million may make the lottery a better choice based on utility, even though the EV is lower.

 

[tsg]

I suppose he's also considering the inconvenience of not flying, which is probably bigger than the inconvenience of paying for a lottery ticket.

How many airplane passengers consider the need to fly worth risking their lives? I'm willing to bet it's very few.

 

[Rasmus]

How many airplane passengers consider the need to fly worth risking their lives? I'm willing to bet it's very few.

Depends on how you word the question, I guess. 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?

 

[macgyver]

Well, in an argument about utility, you have to consider the other uses for that dollar. If you're not going to use it at all, then it has zero utility and you might as well play the lottery. But that is rarely, if ever, the case.

I'm having difficulty still with the concept or context of "utility" as it applies here (as well as EV). I've done some looking around, and actually found a paper written on gambling which involved these terms...but the paper was far too advanced in probability theory for a layman.

Does anyone care to try to flesh out the definition of these terms? I feel there's alot being said here that isn't particularly difficult to understand if you speak the lingo...?

 

[nimzov]

which has been the model for this discussion so far, it's 1:32 of winning anything.

Since the arguments agains the negative EV essentially boil down to "but when you win you stop playing", and that very few people will be satisfied enough with the prize for matching 5/6 or less (under $3000) to stop playing, those prizes don't really enter into the discussion.

[edited to correct the amount]

Hi.

Thanks for making the correction, I had made a rough guess since I could not find the odds from the loto-quebec site.

I tend to looks at this one draw at a time. And every time you play 649 type lottery, the dollar you spend will bring you back on average 50 cents. In my opinion the structure of the prize fund is unimportant, as it does not change the average return of you "investment".

nimzo