The odds of winning lotteries?

July 15, 2008 4:43 PM

How do state lotteries work? Is there a formula for winning or is it truly random?

Scratch games, powerball, megaball, lotto, pick 3, pick 4, cash 5. Do states target lower income areas for big winners? Can you win anywhere you buy a ticket? Is it random? Do they know where the big scratch game winners are being shipped? Are quick picks pre-determined before they are printed, and does the "system" know before the numbers are selected nightly? Is it all legit? Is it truly chance or are there other factors involved? Are they worth playing?

posted by terrier319 to work & money (36 comments total)

No, yes, yes, no, no, no, yes, all chance, no.
posted by buxtonbluecat at 4:50 PM on July 15 [12 favorites]

well, this all depends on if you are on the conspiracy train.... but im sure theres all sort of orginizations, watchdogs and people that would on paper to at least make it look legit.
posted by figTree at 4:53 PM on July 15

"Are they worth playing? "

Easy answer to this as regards all gambling...if the house wasn't making more money than you are, they wouldn't be letting you play to begin with..

Put your money in the bank.
posted by HuronBob at 4:58 PM on July 15 [1 favorite]

It's like guessing the outcome of rolled dice except the dice have 42 to 56 sides depending on the game and the number of dice varies.
posted by junesix at 4:58 PM on July 15

Every $5 you'd like to spend on a lottery put into a 401k. You'll have a 99.999999% chance of being richer than if you didn't.
posted by Freen at 5:01 PM on July 15

It depends on what you mean by random. There are different types of randomness. A lot of lottos use a combination of air and a contraption to create a random drawing of ping pong balls. My guess is that this is far from random and if you were able to simulate this and repeate it a bazillion times, you'd find numbers popping up far more than computer generated random numbers or even natural random processes. My guess, and I say this because the payoffs are large and no one does this, is that it is uneconomical to buy the required number of tickets to bring you within x% of winning. Lottery tickets are generally very expensive, at least in terms of odds of winning. You'd have much better luck with other games of chance, like blackjack, with far less work.

I also seem to remember that state lotteries that make you pick numbers do not usually use computerized random number generators. This is different from scratch offs, of course, but I guess no one wants a $2 microchip picking the numbers, so they use radiation and other sources of natural randomness to pick the numbers. I hope this makes sense.

PS, the better way to go about this is to find the distribution and the compute the cost of the lottery ticket. My guess is that an actual lotto ticket, assuming you figure out the correct distribution, is probably 5-10 cents for most lotteries and probably gets up to 50 cents for those huge payoffs you see once in awhile. I'm pulling those numbers out of my ass though.
posted by geoff. at 5:15 PM on July 15

Oh Bernoulli and Euler both looked at this and calculated the mathematics of lotteries. You might try looking them up, but I'm having a hard time finding references via Google, or at least free references. Note that they were working in sort of a platonic framework, assuming that there was an even chance of picking each number. I believe that with the air power lotteries (absolutely not the radioactive lotteries), manufacturing defects and the way the test is setup will result in a number distribution that will surely favor certain combination over others. I doubt the absolute veracity of the odds listed, though I can't imagine them being so far off that finding the difference between reality and mathematical abstract would yield anything in the real world (unless of course, the lottery ran forever and you had access to unlimited funds).
posted by geoff. at 5:28 PM on July 15

I took a probability course in college. I highly recommend it, if you're interested in questions like these. Here is a bit about the probabilities involved with the lottery.

Personally, I buy one Powerball ticket per week. I look at it a little like Pascal's Wager*: even if the odds of winning are astronomically low (which they are!), the possible payout is life-changing, and the cost to play is negligible. Thus, it's worth it (to me) to spend $1 that I won't even miss each week, in return for the itty, bitty, almost infinitesimal chance that I'll win enough to retire early. Plus, I rather like the cute noise the machine makes when you get lucky and win a tad (usually $1).

As for "if the house wasn't making more money than you are..." and the like, remember: that always holds for the aggregate, but it does not necessarily apply to any given individual. There are always a few people who come out ahead; the decision you need to make is whether the cost of the game is worth exchanging for the very unlikely chance that you'll be the one to join them.

*void where prohibited. Not valid in New Jersey, Connecticut, or in universes where the number of gods might not equal exactly one.
posted by vorfeed at 5:33 PM on July 15 [5 favorites]

Do states target lower income areas for big winners? Can you win anywhere you buy a ticket? Is it random? Do they know where the big scratch game winners are being shipped?

If this were done, someone would know. Lottery employees may be barred from winning, but somehow something would slip out to a friend or something. ("Hey Joe, go buy some scratch-offs from that market down on Elm.") The payoff is too great. There have been lottery scandals before, but likely because of the huge payoff, people get greedy and screw up and get caught (also because there's a bigger payoff to the lottery for keeping the game fair, and known to be such). If this happened, it wouldn't happen for long.

My guess is that this is far from random and if you were able to simulate this and repeate it a bazillion times, you'd find numbers popping up far more than computer generated random numbers or even natural random processes.

I agree. However, a weekly newspaper in my hometown targeted to the black community, at least at one time, kept track of all the numbers that had come up in my state's lottery games, including ones that came up often and those that were "due". No idea if they were useful to anyone, but an enterprising data-hound might try to figure something out. I suspect they replace the balls from time to time though, to prevent any sort of advantage based on a flawed or damaged ball. At least that's what I would do.

Are they worth playing?

Almost never if you're just looking at dollars and cents. Maybe they are, if you recognize the expected value (I assume that's what geoff. is talking about) is less than a dollar and consider the remaining 50-95 cents as entertainment, or if you're risk-accepting.

Another view, though: The probability of hitting the jackpot on Mega Millions is 1 in 172 million. So, when the jackpot is above $172M, it seems like the expected value of the ticket is more than a dollar, and it's worth playing. However, because of the possibility of split jackpots, I don't think you can take that calculation at face value. And since I'm not knowledgeable enough to figure out the real EV... well, call it entertainment and move on.
posted by SuperNova at 5:35 PM on July 15

Also, here in New Mexico, all of the net proceeds from the lottery go to college scholarships, so everyone wins!

(Except me, pretty much every week.)
posted by vorfeed at 5:36 PM on July 15

The reason you see lottery winners from poor neighborhoods is some combination of sad factors leading to higher per capita play, including that
a) chance is their only shot at attaining wealth
b) opportunities for safe enjoyment of delicious anticipation are few
c) a higher proportion of household income spent at places that sell lottery tickets
plus, of course, extra publicity because it makes a good story. My father used to deride lottery tickets as a tax on the stupid, but he was a strict rationalist who believed in Homo Economus and did not account for emotional/behavioral aspects of decisionmaking.
posted by carmicha at 5:37 PM on July 15

Also, here in New Mexico, all of the net proceeds from the lottery go to college scholarships, so everyone wins!

Typically states use a variation of this line, then cut the money they were already spending on college scholarships. So for college-bound kids, it's a wash, the reps get some more money for pork-barrel projects, and the state has, in effect, enacted a tax on the stupid.
posted by chrisamiller at 5:53 PM on July 15

The best lesson on randomness and probability you can get, if you find yourself believing something couldn't possibly be a coincidence:

http://www.saliu.com/bbs/messages/911.html

Just one of many web pages dedicated to the New York lottery draw on September 11, 2002, when on the one-year anniversary of 9/11, in New York, live on television, the lottery draw was "911". I watched it happen live myself while on vacation there.
posted by davejay at 6:00 PM on July 15

You can't improve the odds, but you can (very very very very slightly) improve the odds that you'll split a quickpick jackpot among fewer people. Just avoid using any number between 1 and 12 as your first two numbers, because many people use birthdays for their "lucky number."

Of course, by eliminating those numbers, which may come up randomly, you also decrease your odds of winning. So this is an "advantage" that is so slight it may in fact be a disadvantage. But it's all I got!
posted by stupidsexyFlanders at 6:01 PM on July 15

note: my link is not "the best lesson", as the page itself is kind of sketchy, but the incident itself "the best lesson."
posted by davejay at 6:04 PM on July 15

Do states target lower income areas for big winners?

I'll answer the question by posing a question to you. If you had the power to determine where the "best" lottery tickets would show up, where would you put them?

In poor neighborhoods?

Or in *your* neighborhood?

Adam Carolla: "What has six balls and rapes poor people? The lottery!"
posted by Cool Papa Bell at 6:09 PM on July 15 [1 favorite]

I agree. However, a weekly newspaper in my hometown targeted to the black community, at least at one time, kept track of all the numbers that had come up in my state's lottery games, including ones that came up often and those that were "due".

This, of course, is known as the Gambler's Fallacy.
posted by Jairus at 6:27 PM on July 15

I know two guys who were execs at the NSW lotteries. It was *extremely* secure and completely transparent. Probity was their biggest concern. So as far as fairness goes, in Australia at least, the games are fair and above board.
The odds of winning are, of course, tiny, so it is stupid to play for financial reasons.
I like the anticipation, so buy the cheapest scratchie and stick it to monitor at work. When work just gets too much, I can scratch it and retire. If it doesn't win, I replace it. I buy 3 or 4 a year.
Another nice way to look at it, is that your odds of winning are not much worse if you don't play. It would be unlikely, but you might find the winning ticket lying on the road. And the chances of winning with a purchased ticket are so low that to 5 significant figures or so, they are identical.
posted by bystander at 6:42 PM on July 15

Typically states use a variation of this line, then cut the money they were already spending on college scholarships. So for college-bound kids, it's a wash, the reps get some more money for pork-barrel projects, and the state has, in effect, enacted a tax on the stupid.

Who is stupider -- someone who likes to spend $1 a week on a game, or someone who actually thinks New Mexico, the 48th poorest state per-capita, spent more than 38 million dollars a year on college scholarships before they had any lottery money to pay for them? Be realistic: that's more than we plan to spend on our entire prison renovation package, energy package, or health care improvement package next year.

The lottery scholarship is by far the largest scholarship effort this state has ever had. It is not an unqualified success, particularly with regards to helping minorities and the poor, but it has been a definite boon to the enrollment and local retention numbers. As a matter of fact, it's so huge that the scholarship was recently expected to exceed the total lottery revenue by 2011; we just passed a bill to streamline operating costs in order to keep it going.
posted by vorfeed at 6:55 PM on July 15

I enjoy the anticipation and fantasy of buying an occasional ticket. As noted, the chances of winning are tiny, but the result would be so pleasant. A few tickets a year is cheaper than a movie.
posted by theora55 at 6:55 PM on July 15

The Straight Dope once did a column on how to pick the winning lottery numbers.
posted by Johnny Assay at 6:56 PM on July 15

I worked as an intern for an advertising firm that did the Florida state lottery, and the entire lottery organization was very careful about specifically not targeting low-income areas. Local leaders were ready to jump if there was a new billboard in a low-income area or an ad campaign that targeted a specific group. So I can't even begin to imagine the heat of directing winning tickets toward or away from certain areas.
posted by shinynewnick at 7:08 PM on July 15

Some people win twice.
posted by Wet Spot at 7:58 PM on July 15

State lotteries are run by for profit corporations that hold monopolies on the right to run games of chance in each state. Each state that has a lottery contracts with one or more corporations to administer their lotteries. Those corporations make huge profits, and they pay each state for the privilege of the monopoly by funding college scholarships. One corporation, GTech, runs 70 percent of the lotteries in the US.

The scholarship funds are basically bribes from corporations to the state that make state legislators who are otherwise morally opposed to gambling endorse the lottery. But these corporations aren't sacrificing profits for the good of poor college students. That's why the corporations need state-issued monopolies; because any company that was not required by the state to give a huge portion of the money it collected to state coffers would be able to offer better odds or bigger payouts. The monies that go to scholarships are monies that would, if lotteries could be run in a competitive market, otherwise go to winners.

So your odds in the lottery are dramatically worse than in other forms of gambling. In poker or roulette or whatever, the money you give the casino only has to pay for two things: the casino's expenses (including profit) and winnings. They set the odds to cover those two things. In lotteries in the US, the money you pay for a ticket has to cover the lottery corporation's expenses (including profits), winnings, and a huge payoff to the state. That means that the winnings portion, and thus your expected rate of return, is reduced. You're better off playing poker or slot machines.
posted by decathecting at 7:59 PM on July 15

This is purely anecdotal, but a friend of mine mentioned several times what his mathematics professor in college said about the lottery. The prof claimed that if you buy a lottery ticket, you shouldn't buy one but rather three, but you shouldn't buy any more than that. Your chances of winning only increase if you buy thousands and thousands more after those initial three.
posted by zardoz at 8:01 PM on July 15

If there existed a formula that could allow you to win, and one of us knew it, do you think we would post it here?

There are many talented people who spend their free time doing things like cracking insecure encryption algorithms. If I hear about someone like that winning the lottery, then I´ll start being suspicious.

Are they worth playing? Well, if the ticket is a dollar, and you get a dollar´s worth of enjoyment out of playing the game, yes. Is the expected monetary value of your dollar ticket less than a dollar? Most of the time, yes -- otherwise the lottery would be losing money and the state would quit running it or change the rules.

There are some games where you could expect to turn a profit if you could buy all the possible numbers, except for the risk of the winning number being a popular one that many people picked.
posted by yohko at 8:37 PM on July 15

I never used to buy lotto tickets because of the odds, but these days I buy two or three tickets a year for the fun of anticipating the drawing. It´s cheap entertainment for a dollar.

Unfortunately, I see many people with a poor understanding of the concept of investing talking about investing their money by buying lottery tickets. I see many of these folks ¨investing¨ money in other things that aren´t actually investments. In some cases the lotto would have been a better plan -- and the odds of getting your lotto money back are very low.
posted by yohko at 8:46 PM on July 15

Not that long ago a lottery in Australia, because the major prize wasn't won for so long, accumulated a jackpot that was significantly larger than the cost of playing every single combination.

A syndicate invested a huge amount of money in covering all the combinations, and, of course, they won. I think they doubled or tripled their money at least.

But you've got to remember, this was still a gamble, because they didn't have the exclusive on the winning numbers. They still might have had to share the jackpot.
posted by AmbroseChapel at 11:00 PM on July 15 [1 favorite]

I've always found how lottery drawings are conducted to be fairly interesting. On one hand, they obviously need to be as random as possible — any hint that it's fixed, and people won't play, they'll be a scandal, etc. But just as important as actual statistical randomness (perhaps more important) is that the process be transparent.

A number-picker based on quantum phenomena would be perfectly random, and thus far superior to a pneumatic ball-picker, from a statistical standpoint. But most lottery players wouldn't understand it; it would just be a black box to them. The pneumatic systems not only provide a high degree of randomness, but are also transparent (literally!).

I've heard anecdotally that in addition to the obvious operation of the pneumatic-pickers, there's a whole procedure to maintaining the balls and randomizing them between the machines, to reduce the chance of a pattern developing. I think they also maintain multiple sets of balls, and don't disclose which balls are in use at any time.

So while I suppose it's not impossible for someone to track, based just on results, the very slight a-randomness inherent in the system, and perhaps give themselves a marginally higher shot at winning than they'd have otherwise ... I doubt it would increase your chances enough to make the lottery a winning investment strategy. If you're looking at the lottery as a money-making venture (as opposed to entertainment), the "opportunity cost" of each ticket is what you'd get if you put the money into a "real" investment, or even just a piggy bank. Knowing that the #2 ball is 0.00002% more likely to be chosen than randomness would suggest, or something similar gleaned from analysis of the nearly-random results, is probably not going to get you in the black.
posted by Kadin2048 at 11:03 PM on July 15

The reason to play the lottery is not to win (the mathematical value of each ticket being less than the purchase price excepting the rare accumulated jackpot), but to lease for one day the fantasy of winning and changing one's life. I don't know what the stats are, but at least one person has claimed that 80% of lottery winners declare bankruptcy within 5 years. Also, there are so many people including investors and statisticians watching the lottery that a lot of shenanigans would be detected within weeks or months.
posted by BrotherCaine at 3:03 AM on July 16

Not sure about the scratch-off games, but the drawings are definitely random. In college, I had a summer job at the state bureau of weights and measures. One of the things we were charged with doing was certifying the set of numbered ping pong balls they used in the drawing. I forget the specifics now, but there was an incredibly small tolerance within which all of the balls had to fall in order to be certified as legit. They had to do this before each weekly drawing...
posted by richmondparker at 5:53 AM on July 16

Here is a document that reviews the randomness of the UK national lottery. As they point out, the ball machines are exhaustively tested by independent auditors. I have read a description of this process and it's pretty amazing how close these machines come to simulating a truly stochastic process.
posted by ikkyu2 at 8:00 AM on July 16 [1 favorite]

The prof claimed that if you buy a lottery ticket, you shouldn't buy one but rather three, but you shouldn't buy any more than that. Your chances of winning only increase if you buy thousands and thousands more after those initial three.

The odds of winning with three combinations is exactly three times the probability of winning with one combination. The odds of winning with one million combinations is exactly one million times the probability of winning with one combination.

In other words, there's no "magic number" that increases your odds.
posted by chrisamiller at 8:52 AM on July 16

One of the little one-line thingies that always stuck with me: Lottery: a tax on people who are bad at math.
posted by WCityMike at 9:15 AM on July 16

Here is a document that reviews the randomness of the UK national lottery.

What an interesting read! Fun fact from the doc, page 8: The UK lottery machines are apparently named Arthur, Galahad, Guinevere, Lancelot, Merlin ... and Vyvyan.
posted by Cool Papa Bell at 11:22 AM on July 16 [1 favorite]

For example, there are 100 possible combinations in the garlic lottery. Odds of winning are 1/100.

If you buy 1 ticket, you have a 1% chance of winning. If you buy 2 tickets, you have a 2% chance in winning, and have increased your chance of winning 100%. If you buy 3 tickets, you have a 3% chance of winning and have increased your odds 50%. If you buy 4 tickets, you have a 4% chance of winning, and have increased your odds by 33%. So buying that nth extra ticket will increase your odds, but the percent increase over the nth-1 will progressively go down.
posted by garlic at 2:31 PM on July 29