Lotto Probability

[Rasmus]

See, if you want to rationally justify playing the lottery occasionally, stop calculating in terms of dollars, and start calculating in terms of happiness

A buck or two every week or so has no effect on your ability to use money to buy happiness (assuming you can afford that buck or two). So the cost in happiness units *is* zero. Not just approximately zero, but it really does not make any difference.

Whereas winning would be *huge*. So even if it's infinitesimally probably, the payoff in terms of happiness-buying potential (assuming you assume being uber-rich would be uber-nice) is huge*tiny>0.

So in terms of utility/ happiness-buying-potential, as long as you keep your playing within bounds you can well afford, the expected payoff actually is positive.

That said, I've only very occasionally bought a scratch and win, and don't really ever play the lotto...

I am not sure; I guess I could find other ways of investing even tiny amounts that would have a better payoff. Maybe I could even find a risky strategy that might make me rich.

Suppose I invested in some silly pennystock; it might not be entirely impossible that some insignificant company discoveres or develops something big that would drive their stock through the roof. Chances might even be beter than with the lottery ...

 

[macgyver]

And the fallacy is that there is a significant difference between the two.

Well, there is a significant difference between the two, just as much as there's a difference between yes and no. The odds might be lousy, but so what?

It also depends on what game you're playing. Generally I'll keep my gambling dollars for fund raising draws. Local hospitals do it, so for $100 a ticket you get something like a 1 in 14 chance of winning something. I haven't won anything and the odds of winning the big prizes are still crappy. However, at least a portion of my money went to the hospital...or school, so I don't see a down side.

The fallacy is in believing that the odds are better than they really are. I don't think it's irrational to play a lottery necessarily, as long as you aren't spending the money before it's won!

 

[rudar]

I am not sure; I guess I could find other ways of investing even tiny amounts that would have a better payoff. Maybe I could even find a risky strategy that might make me rich.

Suppose I invested in some silly pennystock; it might not be entirely impossible that some insignificant company discoveres or develops something big that would drive their stock through the roof. Chances might even be beter than with the lottery ...

Sure. You might. That would only suggest that the lottery would then be sub-optimal.

My point was that if you do the math in dollar units, you end up with a negative payoff (about half the sales go to prizes, half to ``charity'', and a small slice off the middle runs the thing). If, however, you convert the dollars to their utility value, and assume that the conversion does not scale linearly, you can end up with a small positive payoff. That you might be able to get a slightly larger small positive payoff in otherways does not negate that observation, right?

 

[BPScooter]

1 dollar/year * (number of year a Lottto has been legal in your state) * N of spouses, children that are legally entiltled to spend on Lotto = 50 at least.

50 dollars/year split on a nice Lotto number pool = 0

So why do I still feel bad about this? Dang, they all want to drop dollars. I will find another way to get that 50 bucks in my hands. Foot massage... I think/

 

[BillyJoe]

Rasmus,

....it was an interesting experience to realize that it didn't feel nice to be attacked for something silly I am doing. I wonder how that tranlates to the woos when they have to face the voice of reason.

Sorry you saw it that way. I didn't feel as if I was attacking you, especially not for being silly. I was merely trying to point out something about probabilities, how difficult it is to understand, and how you can fool yourself that you understand and even when you do understand. I've been there, probably still am.

It isn't rational to play lotto and, in order to get some "thrill out of possibly winning", you have to hide this fact from yourself.

Anyway, it seems after a few posts from Dali, tsg, and macgyver, that you have changed your point of view. That can be hard to do. The gain is that you now know more than you did before. That can't be too bad.


On the other hand, rudar and tkingdoll still need a bit of working over.


regards,
BillyJoe

 

[tkingdoll]

On the other hand, rudar and tkingdoll still need a bit of working over.

Say wha? I do believe that Rasmus credited my post with giving him perspective.

 

[LW]

It isn't rational to play lotto

... if you assume that the utility function of having money is linear.

 

[Starthinker]

I remember reading a Sci-Fi novel when I was a kid (Larry Niven I think) where an alien race had run a lottery to allow another race to procreate. The purpose was to breed "luck" into the race, because after several generations of lottery draws only the "most lucky" families would still exist....

Seemed appropriate to our pondering probability on this thread...

I think that was Ringworld and the lottery wasn't to breed lucky people. The lottery was just to give people the right to breed and after many generations the aliens worked out that certain bloodlines won the lottery in succession so they must be lucky bloodlines hence their offspring would have children (assuming they won the lottery and if they did it added to their luck) that were predesposed to be "lucky", hence having one of these people on your crew drew luck to the crew. They never told this theory to the humans. The woman in question was the 7th generation lottery winner. Or something like that. It never made sense to me as anyone alive must have had parents that won the lottery or they wouldn't have breeded so by default every living person would be equally lucky.

 

[tsg]

Well, there is a significant difference between the two, just as much as there's a difference between yes and no. The odds might be lousy, but so what?

Except that this is the difference between "not in your lifetime" and "never". As far as how it can affect you, there's very little difference at all.

It also depends on what game you're playing.

Of course. I was only speaking about the 6/49 and similar lotteries.

The fallacy is in believing that the odds are better than they really are.

There is a case to be made that very few people really understand just how unlikely it is. If you spent $4,000 a week on lottery tickets for 60 years, you could reasonably expect to win (6/6) once. And Teek has a good point: from what I can find, it appears the odds of dying in a plane crash (per flight) are roughly 1 in 700,000. That means you are about 20 times more likely to be killed in a plane crash than you are to win the lottery. Yet people still fly, and a fear of flying is often called irrational. People generally have trouble visualizing numbers that are really big or really small. And this number is very, very small.

I don't think it's irrational to play a lottery necessarily, as long as you aren't spending the money before it's won!

Not spending more than you can afford on the lottery just means it isn't irresponsible. It doesn't make it rational. It is my opinion that if you have any expectation of winning the lottery at all you are probably overestimating your chances by several orders of magnitude. In the grand scheme of things, it is just a dollar and so the harm caused by buying a lottery ticket is pretty minor (providing you can afford it). If it makes you happy, by all means, play. But realize that your happiness is very likely the result of an irrational expectation of winning.

 

[Starthinker]

Here's a little tidbit that I was toying with. I was looking at the Powerball and it says the odds of winning are 1 in 146,107,962. Now I'm taking that as meaning there are 146,197,962 different combinations. What if, after every drawing, they retire that combination so that if it ever comes up again (a very slim chance indeed) they draw again. Now, and you may have to check my math, at two drawings a week that's 104 drawings a year it would take roughly 444,211 years to get the odds down to 100,000,000. So, the ILLUSION is that your odds are better with each draw as you've eliminated one combination, so they could use that as a gimmick to increase sales, and they really wouldn't have to worry about anything changing. In reality, to the average person on the street the odds don't really change, but chances are they don't know that or don't care.

Sorry, I'm always thinking of ways to increase sales.

 

[Number Six]

I think taking that combo of numbers out after it's picked would make things too complicated while not attracting more players. After all, it's not like people say "I want to play lotto, but the odds are just not quite good enough. If they improved a little then I'd play."

As someone said, people simply don't understand the odds. "You can't win if you don't play." Yeah, and you can't die in a car crash on the way to the store to buy a lotto ticket if you don't try to play, and that's a heckuva lot more likely than winning the lotto.

 

[nimzov]

Suppose I invested in some silly pennystock; it might not be entirely impossible that some insignificant company discoveres or develops something big that would drive their stock through the roof. Chances might even be beter than with the lottery ...

If I want to loose less money, I'd choose lottery over pennystock.

On average, 1 dollar spend on the lottery will earn you 50 cents (may vary depending on country) and much of the rest is going in government programs. Now 1 dollar spend on penny stock on average will earn you what ? Nor more than 10-20 cents I guess.

nimzo

 

[macgyver]

It never made sense to me as anyone alive must have had parents that won the lottery or they wouldn't have breeded so by default every living person would be equally lucky.

This may be why I remembered it as attempting to breed a lucky race, rather than an individual. It was over 20 years ago that I read this....I'm surprised I remembered the author's name!

 

[tkingdoll]

If people who are aware of the odds, such as Rasmus, want to play the lottery anyway, that's their choice. Perhaps the fun is in the daydreaming about what the money could buy, and the few minutes thrill of watching the numbers come out. If you can afford to play, and want to, it harms no-one. I personally find it irrational, but it harms no-one. However, I am vehemently anti-lottery at present because the UK lottery company, Camelot, are profit-making. That makes zero sense to me. Why would I give a company my money for an almost zero chance of a return?

Equally, when people use the "it's for a good cause" argument, I ask them why they don't simply donate £1 per week to their favourite charity. That way, the charity gets more of the money and they aren't lining the pockets of Camelot. And they also get control of which charity gets their cash.

But I must say, if I were going to bet money on the outcome of an event (which is what the lottery is), isn't a much safer bet something like a sporting event? 6 horses, 1 in 6 chance of winning. Put your £1 on a horserace every week, I'm sure you'd wind up more satisfied than with the lottery. Smaller returns, but a much greater chance of winning, and the same thrill of anticipation. Maybe that's just me.

When I get into debates with friends over the lottery, and they give me "but someone has to win" argument, if "yes, but it won't be you" doesn't work, I use one of two approaches.

1) Ask them if they think they might win that week. If they say yes, bet them £5 they won't win. No-one ever takes the bet, but it really hammers the point home to them that it's really not a chance significant enough to spend £1 on.

2) This is bending the logic a bit, but it's a good physical demonstration (some people respond better to that than a concept). Ask them what the odds of, say, the number 10 being picked from 49 balls is. They will (hopefully) answer that it's 1 in 49. Ask them what the odds of getting heads on a coin toss is. Hopefully they will say 1 in 2, or more likely 50/50.

Then you ask them to confirm that the coin toss odds are better than the 49 ball odds, or ask them which outcome they are more likely to bet on. They should say the coin toss.

Then bet them £1 that they cannot toss a coin and get heads 6 times in a row. They might take the bet, in which case, you will probably be £1 better off and they will realise that if they can't get 6 heads in a row, what chance is there of getting 6 numbers?

Or, they might refuse the bet, in which case, get them to do the coin toss anyway, just to see. I like to get them to do the coin toss exercise several times, increasing the bet each time, to represent each week's lottery draw and to show just how hard it is.

Like I say, one day this may backfire on me and I'll lose a few quid, but that would be so funny it'd be worth it.

(Edited to fix typo)

 

[macgyver]

Except that this is the difference between "not in your lifetime" and "never". As far as how it can affect you, there's very little difference at all.

I'm not debating the magnitude of the difference, just that it exists. The reason I feel that's important is that it pertains to the further assertion that the behaviour is irrational.

If it makes you happy, by all means, play. But realize that your happiness is very likely the result of an irrational expectation of winning.

I agree with the first statement, but your second statement furthers my point. It is possible to play the lottery with the attitude "I have no chance now, but with a single entry I now have a >0 chance". This doesn't necessarily require an irrational expectation of winning, just the rational belief that there is a difference between 0 and 1.

I agree with the statement that having an expectation of winning (certainly to the point of planning your spending of the winnings) is irrational, but I differ on the idea that playing at all is irrational.

However, I don't think the following point has been discussed:

I think it IS completely irrational to buy more than one entry on any of these lotteries. That would definitely mean you have no concept of the odds that you are playing. While there is a difference between 0 and 1, there is essentially no difference between 1 in 13,000,000 and 2 in 13,000,000

 

[tsg]

I'm not debating the magnitude of the difference, just that it exists.

In the post I was replying to, you stated it was a significant difference. It was that statement I was addressing.

I agree with the first statement, but your second statement furthers my point. It is possible to play the lottery with the attitude "I have no chance now, but with a single entry I now have a >0 chance". This doesn't necessarily require an irrational expectation of winning, just the rational belief that there is a difference between 0 and 1.

I'm afraid I fail to see how the difference between "impossible" and "extremely improbable" can rationally justify spending a dollar on it, especially when events that have probabilities of occuring that are much higher aren't worth worrying about.

However, I don't think the following point has been discussed:

I think it IS completely irrational to buy more than one entry on any of these lotteries. That would definitely mean you have no concept of the odds that you are playing. While there is a difference between 0 and 1, there is essentially no difference between 1 in 13,000,000 and 2 in 13,000,000

There is essentially no difference between 0 in 13,000,000 and 1 in 13,000,000 either, but you are saying that it is enough to justify spending the dollar. Why wouldn't doubling your chances justify spending two dollars?

 

[macgyver]

In the post I was replying to, you stated it was a significant difference. It was that statement I was addressing.

True, you have me there...

I'm afraid I fail to see how the difference between "impossible" and "extremely improbable" can rationally justify spending a dollar on it, especially when events that have probabilities of occuring that are much higher aren't worth worrying about.

There is essentially no difference between 0 in 13,000,000 and 1 in 13,000,000 either, but you are saying that it is enough to justify spending the dollar. Why wouldn't doubling your chances justify spending two dollars?

And here. I felt it necessary to see my argument to conclusion...but I concede.

Now I want my money back! Oh, and also read the first line of my sig

 

[nimzov]

There is essentially no difference between 0 in 13,000,000 and 1 in 13,000,000 either, but you are saying that it is enough to justify spending the dollar. Why wouldn't doubling your chances justify spending two dollars?

Let's not ignore the fact that there are intermediate prizes beside the jackpot.

Look at it this way.

If you play one dollar, you have roughly a 1 chance out of 5 of winning back you dollar, PLUS 1 chance out of 14 million of winning the jackpot.

It is irrational to play but not as much as some people say.

nimzo

 

[tsg]

Oh, and also read the first line of my sig

I've seen it before. I always thought it was pretty offensive. But that's just my opinion.

 

[tsg]

Let's not ignore the fact that there are intermediate prizes beside the jackpot.

Look at it this way.

If you play one dollar, you have roughly a 1 chance out of 5 of winning back you dollar, PLUS 1 chance out of 14 million of winning the jackpot.

The intermediate prizes, including the one you mention, and the jackpot have a negative expected value. Over the long run you will spend more money than you will win.