Lottery tickets purchase=mental illness?

[cho oyu]

Don't know about your math, but I wish I owned a casino that I could invite you to Just because black comes up 100 times in a row does not change the odds that black or red will come up next time. I understand it is not intuitive, but each draw is unrelated. By your logic if you "invested" $46,795 (146,000,000/60/52) a week you would be guaranteed a win in your lifetime. This is not true.

The math isn't quite correct (although it's very close to first approximation). If one were to buy multiple lottery tickets a week, I would assume no two would have the exact same numbers. As such, your odds of winning increase with each additional ticket you buy.

The total number of possible plays is a combination of, say, 50 numbers taken 7 at a time. C=50!/(7!*43!)=5x10^11.

Your odds of winning with 1 ticket are therefore about 1 in 99884400.

If you buy 2 tickets that week, the odds of winning with the second ticket are 1 in 99884399 (if the first doesn't win). If you were to buy all 99884400 tickets one week, you would be guaranteed to win. Another way to look at this is that if you buy 2 dependent tickets in one week, the odds are 2/99884400.

Realistically, when looking at small numbers of purchases every week, this shift in odds is negligible.




If you invested $46000 every week, you are never guaranteed to win in your 1:146,000,000 scenario. The reason is that each drawing is independent of the last. Ignoring the fact that the 46000th ticket you buy each week is likelier to win than the first (the difference is only 1/146,000,000 vs 1/(146,000,000-46,000), here is your chance of winning (this exactly follow Justin's math):
Odds of winning in one ticket: 1/146,000,000.
Odds of not winning on one ticket: 1-1/146,000,000
Odds of not winning on 146,000,000 tickets in a row: (1-1/146,000,000)^146,000,000
Odds of never winning=36.788%
Odds of winning=63.212%

So even if you spent $146,000,000 over the course of 60 years, there is still less than a 2/3 chance that you will ever win the jackpot.

Now, including the math that you buy 46795 tickets every week for 60 years for a total of 146,000,000 tickets, you have:
Odds of winning in one week: (46,795/146,000,000)
Odds of not winning in one week: (1-46,795/146,000,000)
Odds of not winning over lifetime: (1-46,795/146,000,000)^(60yrs*52wks)
Odds of never winning: 36.782%
Odds of winning: 63.218%

As you can see, buying over 46000 tickets each week as compared to one ticket each week only makes a 0.006% difference in the likelihood of winning after buying $146,000,000 worth of lottery tickets.

My way of putting it is that the lottery is a tax on the mathematically disinclined.


(Edit: Ugh. Never post while doing three other things that all require 100% of your attention. All the math in here is correct, but I certainly did make the explanations confusing.)

 

[bots2019]

Don't know about your math, but I wish I owned a casino that I could invite you to Just because black comes up 100 times in a row does not change the odds that black or red will come up next time. I understand it is not intuitive, but each draw is unrelated. By your logic if you "invested" $46,795 (146,000,000/60/52) a week you would be guaranteed a win in your lifetime. This is not true.

Didn't see anywhere in Justin's post where he guaranteed a win, in fact he stated that your odds would be 1/1,560.

As a certified math nerd I can attest that calcuations are correct, and consistent with each ticket being independent. Probabilities are cumulative (each time you play your total odds of winning increase), but that doesn't indicate that the results of each 'test' aren't independent.

You could think of each play independently, with the odds of success 1/146,000,000. On your first play, you have exactly 1/146,000,000 cumulative odds of winning. On your second play your odds of winning are also 1/146,000,000, but your cumulative odds of HAVING WON are now (1/146,000,000)^2 + (1/146,000,000)*(145,999,999)*2. In words this can be thought of the odds of winning BOTH times + the odds of winning then losing + the odds of losing then winning.

A much simpler way to approach this over the long run is be determining the odds of having lost every time (which is what Justin did). In that case, it's just:

Losing Out = ((145,999,999/146,000,000))^attempts.

To determine your odds of winning one or more times just subtract 1-Losing Out.

Pretty basic prob & stats really. However, I still wouldn't say your odds are anywhere close to good, or that it's not a terrible investment.

 

[DJRR]

You are 100% correct, however I have won well over $1000 over the course of a couple months doing just what you say can't be done. Lifetime I am up several thousand

I did not say that it could not be done, just that your probability of success does not change. You still have a 48.65% chance of winning on any one spin. I doubt that you trust your theory enough to put down 50 or 100 grand when you think it is time.

Theoretically, if you had unlimited money, you could bankrupt the casino by doubling your bet each time. Eventually you would be correct.

If no one won then the casino would go out of business because they need enough transactions to drive the outcome to the expected result which is 2.7% of everything wagered in your example. Perceived winners lead to more action and more profit for the owner.

 

[lets-retire]

I doubt that you trust your theory enough to put down 50 or 100 grand when you think it is time.

If I had the money to bet the trends absolutely.

 

[justin]

Didn't see anywhere in Justin's post where he guaranteed a win, in fact he stated that your odds would be 1/1,560.

As a certified math nerd I can attest that calcuations are correct, and consistent with each ticket being independent. Probabilities are cumulative (each time you play your total odds of winning increase), but that doesn't indicate that the results of each 'test' aren't independent.

....

Pretty basic prob & stats really. However, I still wouldn't say your odds are anywhere close to good, or that it's not a terrible investment.

Thanks Bots for the double check. I didn't think my high school basic probability and statistics would fail me.

DJRR, just for your info, if you played $46,795 a week for 60 years, your cumulative probability of winning one or more jackpots would only be 63.2%.

So, DJRR, go ahead and open up that casino using your probability rules, I'd like to pad the FIRE stash a little.

Just to clarify, I know that the lottery is never a good investment from a net present value perspective. I was simply trying to point out that playing something as small as $30/wk for a long period of time could better your odds from 1 out of 146 million to 1 in 1,560. Still a long shot, but given the massive payoff, I'd say the odds aren't too bad to consider playing the game. Not that I would ever do it, because I'd rather save the money and accumulate a larger nest egg. And I only play when the expected payout from a $1 ticket approaches $1 (as in $0.6-0.7).

 

[DJRR]

Thanks Bots for the double check. I didn't think my high school basic probability and statistics would fail me.

DJRR, just for your info, if you played $46,795 a week for 60 years, your cumulative probability of winning one or more jackpots would only be 63.2%.

So, DJRR, go ahead and open up that casino using your probability rules, I'd like to pad the FIRE stash a little.

Just to clarify, I know that the lottery is never a good investment from a net present value perspective. I was simply trying to point out that playing something as small as $30/wk for a long period of time could better your odds from 1 out of 146 million to 1 in 1,560. Still a long shot, but given the massive payoff, I'd say the odds aren't too bad to consider playing the game. Not that I would ever do it, because I'd rather save the money and accumulate a larger nest egg. And I only play when the expected payout from a $1 ticket approaches $1 (as in $0.6-0.7).

LOL, I am not so quick to surrender. You are not playing 146 million times. You are only playing 60x52= 3,120 times Shouldn't this be your N

Odds of winning in one ticket: 1/146,000,000.
Odds of not winning on one ticket: 1-1/146,000,000
Odds of not winning on 3,120 drawings in a row: (1-1/146,000,000)^3,120
Odds of never winning=99.998%
Odds of winning=.002%

This seems more consistent with reality because I know many people who have played for their whole life, but no one who has ever won. Certainly not 2/3 of the people.

 

[justin]

LOL, I am not so quick to surrender. You are not playing 146 million times. You are only playing 60x52= 3,120 times Shouldn't this be your N

Well, if you are playing $30/week, that is 30 tickets per week, times 3,120 weeks in 60 years. Or 93,600 unique plays during a lifetime.

 

[bots2019]

LOL, I am not so quick to surrender. You are not playing 146 million times. You are only playing 60x52= 3,120 times Shouldn't this be your N

Odds of winning in one ticket: 1/146,000,000.
Odds of not winning on one ticket: 1-1/146,000,000
Odds of not winning on 3,120 drawings in a row: (1-1/146,000,000)^3,120
Odds of never winning=99.998%
Odds of winning=.002%

This seems more consistent with reality because I know many people who have played for their whole life, but no one who has ever won. Certainly not 2/3 of the people.

But I doubt the people you know are putting down 47K a week on the lottery!

Your math here is correct. The difference is in Justin's scenario 30 tickets were purchased for each drawing. In cho's scenario 46,795 tickets were purchased per week.

Sc1: 1 tix per week, as you noted odds of winning at least once = .002%
Sc2: 30 tix per week, odds of winning = .064% (or 1/1560)
Sc3: 47,795 tix per week, odds of winning = 63.2%

Also note that "odds of winning" means scenarios that result in one or more wins. Under Sc3 your expected number of wins is actually 1.0, you only end up a winner 63.22% of the time due to the occurrence of scenarios with multiple wins.

Regardless, I think we can all agree lotto isn't a winners game (except for the gov't)!

 

[justin]

Regardless, I think we can all agree lotto isn't a winners game (except for the gov't)!

In financial terms, it is definitely a losing proposition. However I personally receive entertainment value out of playing the lottery. Plus, in North Carolina, 30% of all my lottery expenditures go straight to education spending. Where else can I potentially win 100's of millions of dollars AND support a good cause like education?

 

[roadtoharvard]

I don't know what says more: The fact that they spend $30 a week on lottery tickets or the fact that someone was bothered enough by this to post it on a message board asking for "help" to get them to stop. My mom acts similarly in regards to the lottery and i long ago stopped caring when she goes on and on about her "future winnings". I instead just learned to enjoy that aspect of her too because overall she's a great person.

 

[DJRR]

Sc1: 1 tix per week, as you noted odds of winning at least once = .002%
Sc2: 30 tix per week, odds of winning = .064% (or 1/1560)
Sc3: 47,795 tix per week, odds of winning = 63.2%

LOL. I got caught in my own trap. 1 in 1,560 seems so much better than .064%, but they are equivalent No wonder why I stink at picking stocks

 

[bots2019]

LOL. I got caught in my own trap. 1 in 1,560 seems so much better than .064%, but they are equivalent No wonder why I stink at picking stocks

Glad you came around. Even a poor stock picker will beat a lottery "investor" I guess

 

[kombat]

I was simply trying to point out that playing something as small as $30/wk for a long period of time could better your odds from 1 out of 146 million to 1 in 1,560. Still a long shot, but given the massive payoff, I'd say the odds aren't too bad to consider playing the game.

I think the fallacy here is in portraying "$30/week" as a trivial amount. As I showed in my post, if you took that $30/week and invested it at 10% for the same time period (60 years), you'd be guaranteed $5.2 million.

What I'm saying is, I don't understand why you're saying a 0.0641% chance of winning the lottery is "not bad odds," when the same money could give you a virtually 100% chance of $5.2 million.

Heck, if you really want to play with numbers, what if we could take 60 years' worth of $30/week payments all up-front at the beginning and invest them, instead of spreading it out over 60 years? $30/week * 52 weeks/year * 60 years = $93,600. That's your total outlay. That's how much you'd spend on lottery tickets in your example in order to earn a 0.0641% shot at winning the lottery (or a virtually guaranteed $5.2 million using my plan). If you instead invested all that money at the very beginning, at 10%, then sat back and waited that 60 years, you'd have $28.5 million!

 

[Milton]

It drives me crazy when they constantly tell my DW and I how much they'll give us next Wednesday (Jeez thanks), or what type of house or new car they are getting. The way they go on, it's like they actually believe that they are going to win. They aren't poor, and dreaming is fine, but is being this enthralled with the lottery and announcing your plans daily some sort of mental disorder? Any advice on how to tactfully get them to stop talking about their vast winnings that will almost certainly never materialize?

People who endlessly talk about themselves (or their possessions, spouses, children, hobbies, vacations, etc.) are always boring. You can't do much to change such behaviour, so either (i) accept it and rationalize that their positive qualities - presumably they have some - outweigh the negatives, or (ii) keep all future contact with them to an absolute minimum.

If they can afford it, and I'm assuming the $30 or so is not a financial drain, and if it makes them happy to dream, I'd let it go.

I would add: even if they can't afford it, and the $30 or so is a financial drain, I'd let it go. There is no indication in the original post to suggest that they would welcome any [-]well-meant advice[/-] criticism of their choices.

I have about 30 different mutual funds I picked out 14 in 2 days once just divided the money between all the ones I was considering and couldn't decide.

Wow.

 

[Darryl]

Spent $1 yesterday I'll probably buy another one in 2 or 3 or 4 weeks as long as I don't check yesterdays ticket I get to daydream a bit. Cheap entertainment at my current level.

 

[DJRR]

I think the fallacy here is in portraying "$30/week" as a trivial amount. As I showed in my post, if you took that $30/week and invested it at 10% for the same time period (60 years), you'd be guaranteed $5.2 million.

What I'm saying is, I don't understand why you're saying a 0.0641% chance of winning the lottery is "not bad odds," when the same money could give you a virtually 100% chance of $5.2 million.

I think that hits the nail on the head. It also helps explain the talk of the middle class squeeze we hear about. $30 per week = $1,560 per year. If you took standard advice and saved 10% of your income that = $15,600 or $7.5 an hour ~ the minimum wage next year.

In 2 generations (60 years) you could take your family from minimum wage poverty to top 10% status if you invested consistently, but most people never will

You still have to find a way to live on the 90%, but most people do not remain at minimum wage forever either. I routinely see low wage people in 7-11 spending $10 per DAY on coffee, half smokes, cigarettes and lottery tickets.

You do need discipline, a horizon that extends beyond your life, and to avoid people like Kyosaki that say investing in mutual funds is for suckers but it is still very doable to change your family history in the good ole US or A.

 

[justin]

I think the fallacy here is in portraying "$30/week" as a trivial amount. As I showed in my post, if you took that $30/week and invested it at 10% for the same time period (60 years), you'd be guaranteed $5.2 million.

What I'm saying is, I don't understand why you're saying a 0.0641% chance of winning the lottery is "not bad odds," when the same money could give you a virtually 100% chance of $5.2 million.

I agree that the obvious method to maximize expected payouts/NPV's is to not play the lottery and invest what you would otherwise spend. My statement that 1 out of 1560 odds are pretty good only goes to counter the argument that "well, it's a 1 out of 146,000,000 chance of winning - odds so distant, there's no point in playing". When in reality, the cumulative probability of a lifetime of playing $30/wk leaves you with a significantly greater chance of winning (even though you have a negative NPV on the transaction).

Let me make it clear that I am not suggesting playing the lottery is in any way a wealth-maximizing endeavor. I only wanted to counter the perceived nearly impossible nature of winning the lottery, when in fact, played at the $30/wk level, there is a 1 out of 1560 chance of winning.

I figure when I play a $1, I have an expected payout of around $0.5 or so after taxes. The $0.50 that I'm losing is more than replaced by the excitement of the "what if" - in other words, pure entertainment value. Folks that blow $30/wk every week knowing that many weeks the jackpot is as low as $8 million lump sum baffle me. Guess they get more entertainment value out of wishing they were rich instead of actually becoming rich through saving money.

 

[Texas Proud]

I think the fallacy here is in portraying "$30/week" as a trivial amount. As I showed in my post, if you took that $30/week and invested it at 10% for the same time period (60 years), you'd be guaranteed $5.2 million.

What I'm saying is, I don't understand why you're saying a 0.0641% chance of winning the lottery is "not bad odds," when the same money could give you a virtually 100% chance of $5.2 million.

Heck, if you really want to play with numbers, what if we could take 60 years' worth of $30/week payments all up-front at the beginning and invest them, instead of spreading it out over 60 years? $30/week * 52 weeks/year * 60 years = $93,600. That's your total outlay. That's how much you'd spend on lottery tickets in your example in order to earn a 0.0641% shot at winning the lottery (or a virtually guaranteed $5.2 million using my plan). If you instead invested all that money at the very beginning, at 10%, then sat back and waited that 60 years, you'd have $28.5 million!

I know you will have a good amount... but you forgot the other government 'lottery' called TAXES... they get you coming and going...

 

[bright eyed]

In terms of the OP, I think it is not the fact they play lottery, or even the amount, but that they spend so much mental energy investing in the lottery as their path to their "future."

That to me is more disturbing for many reasons.

They aren't paying attention to their reality and will likely be disappointed with their outcome - no real savings (or not enough) and no lottery.

As a caring family member, that would disturb me too. But I don't think there is anything you can do about it. They seem quite wedded to the idea and would resent you for pointing out their inadequate logic. As long as it's not quite like a gambling or other addiction where the $30/week is causing them big financial problems (other than inefficient use of that $30/week)...then you have to let it go...

like the penguins on madagascar say, "just smile and wave..."

 

[lazygood4nothinbum]

neither the fantasy nor all the math in the world means a thing. you will only win the lottery if god commands it or if you are lucky enough for blind fate to name you the chosen one. that is its grand allure. are you worthy? muhaha.

 

[Moemg]

I'm not a lottery player but last year I got into Hgtv's dream home frenzy .I was convinced that I'd win .I had decided I would invite all my friends and family to use the home for several months and then I'd sell it .The night they were going to surprize the winner I stayed dressed with make-up on in case it was me . Okay ,maybe that was a little nutsy but it gave my family a good laugh .

 

[Achiever51]

I'm not a lottery player but last year I got into Hgtv's dream home frenzy .I was convinced that I'd win .I had decided I would invite all my friends and family to use the home for several months and then I'd sell it .The night they were going to surprize the winner I stayed dressed with make-up on in case it was me . Okay ,maybe that was a little nutsy but it gave my family a good laugh .

ROTFLOL!!!
If I recall correctly, something like 44 million entries were submitted to HGTV for the latest Dream Home sweepstakes...including two from me!

 

[NinjaPigeon]

Tax on the stupid or not, I like the lottery and will continue to play. And when I win, you guys aren't getting any of it

 

[justin]

Tax on the stupid or not, I like the lottery and will continue to play. And when I win, you guys aren't getting any of it

Yeah... what's 4% of $150 million again?

 

[samclem]

Tax on the stupid or not, I like the lottery and will continue to play. And when I win, you guys aren't getting any of it

You tell them! Remember, NinjaPigeon, I'm your only true friend here. What will we do with the money?