Lottery tickets purchase=mental illness?

[TromboneAl]

If the chance of heads for one coin toss is 50%, the chance that you will get heads at least once if you flip the coin twice is 75%.

Here are the four possible outcomes:

HH
HT
TH
TT

and in three of four, you get a heads at least once.

But I wouldn't say that spending $93,600 , to get a one in 1,560 chance of winning big is fairly good odds.

Invest that $30/week at 6.5% interest and you get: $1,060,842.22

With a 9% return, you'd have $ 3,455,837.97

[lets-retire]

Originally Posted by DJRR

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.

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. Each night we wrote down the result of each spin and each night the nightly probabilities of winning were approximately the same. With that said the outcome of the individual spin cannot be determined, however the overall results of all spins will approach the expected odds of the occurrence on the wheel. So in your example the odds of each spin is 18 to 37 either red or black and 1 to 37 green on a European wheel. The odds of winning each spin is small, however since overall the results will approach the stated odds that is how one has to bet trends not individuals. Even when we lost our stake we still stood around and wrote results and the outcomes were always about the same for the night.

You can yell and scream about how it can't be done and that I must be under reporting my losses. I won't argue, because I know what I have done and I still have the memories, in most cases (some were lost to the drunken stupor of vacations taken) of weekly vacations taken with the winnings. I also have the memories of depositing the money in the bank to buy cool things. I recently went out to a local casino with the DW and showed her how I won all of the money I did. I forgot how boring it was and I do not have the desire to do it again, even thought I walked out up three times what I carried in, including the losses my wife had.

[ats5g]

Originally Posted by LOL!

Jason Zweig discusses all this in his new book: Your Money and Your Brain.
You gotta read it, but basically once you win big you are hooked just like you can be hooked on cocaine. Your brain gets re-wired and there's nothing you can do about it.

For those of the MTV generation , check out Jason's talk about this [halfway down the page]. See also, Jason's website.

- Alec

[kombat]

Originally Posted by justin

Assuming you buy 30 tickets per week, 52 weeks per year for 60 years, your odds of winning once during your lifetime are approximately 1 out of 1,560.

OK, but if you took that $30/week and invested it in an index fund instead, and that fund returned 10%, then after that same 60 year period, you'd have $5.2 million. Granted, assuming a 10% average rate of return on the market over a 60 year period is a bit of a "gamble," but in my opinion, it's much more likely than 1 in 1,560 odds.

[kombat]

Originally Posted by DJRR

Just because black comes up 100 times in a row does not change the odds that black or red will come up next time.

This is absolutely true. However, the more games you play, the more likely that you'll be present when black does hit. If red means a $1 loss, and black means a $50,000,000 win, then someone who plays the game 5 times has a much better chance of winning than someone who only plays one spin and then walks away.

I understand your point - the odds of each individual game do not change. But you can improve your own personal cumulative odds by playing more games.

Say you're in Vegas and you walk up to a bank of $1 slot machines. They all offer 50/50 odds winning, but a win rewards you with $1000 (consequently, it's a very popular casino). You simultaneously put a dollar in 10 machines. Statistically, half of them should produce wins (at $1000 each). Of course, the odds for each individual machine remain 50/50. Meanwhile, your wife selects a single machine (same odds) and puts a dollar in it. Are you claiming that you and your wife both have the same odds of winning $1000?

[cho oyu]

Originally Posted by DJRR

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]

Originally Posted by DJRR

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]

Originally Posted by lets-retire

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]

Originally Posted by DJRR

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]

Originally Posted by bots2019

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]

Originally Posted by justin

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]

Originally Posted by DJRR

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]

Originally Posted by DJRR

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]

Originally Posted by bots2019

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]

Originally Posted by bots2019

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]

Originally Posted by DJRR

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]

Originally Posted by justin

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!