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Math Science

Patterns in Lottery Numbers 563 563

markmcb writes "Most everyone is familiar with the concept of the lottery, i.e., random numbers are selected and people guess what they will be for a cash prize. But how random are the numbers? Matt Vea has conducted a pattern analysis of the MegaMillions lottery, which recently offered a sum of $370M (USD) to the winner. Matt shows that the lottery isn't as random as it may seem and that there are 'better' choices than others to be made when selecting numbers. From the article, 'A single dollar in MegaMillions purchases a 1 in 175,711,536 chance of landing the jackpot ... a player stands a mildly better chance of winning a partial prize through the selection of weighted numbers.'" Includes some excellent charts of his analysis.
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Patterns in Lottery Numbers

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  • by Anonymous Coward on Thursday November 01, 2007 @03:16PM (#21200715)
    We need a "badatmath" tag.
  • by eldavojohn (898314) * <> on Thursday November 01, 2007 @03:20PM (#21200767) Journal
    How does the outcome of thousands of already drawn balls assure that same frequency will continue to occur?

    These differences aren't that compelling. To me I would say, "Congratulations, you have found some deviation from equal frequency for all balls. But this would happen in any instance of drawing these balls."

    I'm concerned that this has been an exercise in deviation in pseudo random systems. The same could be done with a computer simulation and similar results would be found.

    I hate to say it but this study points out to me that the lottery is actually pretty much as close to random as it could get. In fact, the summary of the paper states that if there were some event to skew this, then you could achieve a small bonus:

    However, in the event there is some peculiar factor skewing the ball selection such that any of these trends continue, a player stands a mildly better chance of winning a partial prize through the selection of weighted numbers.
    However this peculiar factor can not only be identified but if it exists, it is highly unlikely it is anything even remotely observable.
  • by WillAffleckUW (858324) on Thursday November 01, 2007 @03:23PM (#21200819) Homepage Journal
    No, not just statistical, but from life.

    I have participated in both lotteries (and have won up to $1000 in them, and made more than I ever spent).

    I have also participated in raffles - and won similar payouts.

    As to the lifestyle impact, it is a provable truism that most maximum payout winners do not actually improve their lives.

    It's like when I got an inheritance - the best thing you can do with that is max out your retirement funds and pay off debt, and then put much of the rest in paying down your mortgage. Most people blow it, though.

    The difference between being rich and poor is usually how much you save and what you buy. Lottery tickets can be a fun diversion, cheaper than getting drunk, but they are not a wise use of cash.
  • by king-manic (409855) on Thursday November 01, 2007 @03:24PM (#21200839)

    Instead of using absolute dollar figures for your analysis, you should use lifestyle impact.

    e.g. One dollar a week == no lifestyle impact; $370MM payout == off the charts lifestyle impact.
    Also, for 1 dollar a week you are buying a mild emotional high when checking the numbers and a mild emotional low when you find out that math pwned you again.
  • by Ancient_Hacker (751168) on Thursday November 01, 2007 @03:25PM (#21200843)
    Yes, you will see patterns.

    And if you look up in the night sky, you'll see an archer, a bull, a big and a small dipper.

    What's your point?

  • Re:Conclusions... (Score:5, Insightful)

    by Hatta (162192) on Thursday November 01, 2007 @03:27PM (#21200879) Journal
    Of course you can't conclude much from this analysis. In any random distribution you're going to see random statistical fluctuations causing some clustering. Some numbers will get picked more than you'd predict by chance, just by chance. And necessarily some numbers will be picked less often than you'd predict by chance. The upside of this is that you can predict the extent of this clustering and compare that to the actual data to see if it's rigged.
  • by sm62704 (957197) on Thursday November 01, 2007 @03:27PM (#21200887) Journal
    One of the slogans for the Illinois lottery used to be "you can't win if you don't play", but I figured every time I didn't play, I won $1. Its both stupid and ironic that many of the same people bitching about taxes pay this voluntary tax!

    At the astronomical odds against winning, I figure my chances of finding a winning ticket on the ground are only marginally worse than my chances of buying a winning ticket. So rather than give extra money to the government so it will be funnelled to politically connected rich people, I just watch the ground.

  • Missing data (Score:5, Insightful)

    by Richard W.M. Jones (591125) <rich@annex[ ]org ['ia.' in gap]> on Thursday November 01, 2007 @03:29PM (#21200909) Homepage

    While you can analyse the numbers that come up, the interesting data isn't usually available to you: namely what numbers people are betting on. For example in the UK lottery it is known that about 10,000 people a week bet on 1, 2, 3, 4, 5, 6. So that automatically is a really bad choice because if that combination came up, you would get £prize / 10,000.

    Example: if lots of people bet on (eg.) birthdays, then you'd expect the people to select numbers > 31 less frequently, which means you could try to cover bets with numbers > 31 and have a greater payout. Without the distribution of betting numbers though you can't tell.


  • by nweaver (113078) on Thursday November 01, 2007 @03:30PM (#21200929) Homepage
    Any statistical deviation in the balls is going to be microscopic.

    Rather, observe the following. When a progressive jackpot gets large enough, a single winner would have a positive expectation value, but multiple winners have negative value.

    Thus what you need to do is not pick something that is "more likely", you need to pick combinations that normal players would NOT choose, as your odds of winning are the same, but your odds of having to share a win go way down.

    EG, something like 7 8 9 10 11 12 13

    Given the raw stream of what numbers people choose, there are probably lots of such "less likely" patterns you could use.
  • Ummm.... (Score:4, Insightful)

    by Otter (3800) on Thursday November 01, 2007 @03:34PM (#21201001) Journal
    1) These guys did an impressive amount of work, but seem to be completely oblivious to proper statistical analysis. It would have been nice to have seen a p-value somewhere in there.

    2) You don't get an edge in the lottery by picking numbers that are more likely to come up; you get it by picking numbers that other players are less likely to choose (e.g. >31), so that you don't have to split your win with as many others.

  • by Ungrounded Lightning (62228) on Thursday November 01, 2007 @03:36PM (#21201025) Journal
    You're already losing by buying the ticket.

    No, not really. Your state is getting paid revenue (supposedly for education around here - not always).

    Which is just the excuse they used to get it through.

    But money is the ultimate fungible commodity. (That's its whole purpose, after all.) Any amount that the lottery puts into the schools the state government can neglect to put in when they set the next budget. So the effect is that the lottery money goes to the pet projects of the legislature (in a roundabout-on-paper fashion).

    Also, you are getting a chance to win the Jackpot...


    For the smaller ones the payoff is small enough to not matter. Further, the odds are short enough and the players play often enough that the payoff quickly approaches the expectation - usually $0.50 for every $1.00 played. (They take your money and give half of it back in chunks.)

    For the big jackpots the odds are typically in the ballpark of being hit by lightning 10 times. And while the payoff typically has a "half the pot" number, it's paid out over a long enough period that you're just getting the INTEREST on the payoff, while the state keeps the principal, making the effective value much lower. (In some cases you have the option to select getting a much lower payout right away, which proves the point...) And then the federal government takes a cut. So the expectation is 'WAY less than $.50 out for every $1.00 in.

    Lotteries are a voluntary tax on innumeracy (mathematical illiteracy).

  • Re:Conclusions... (Score:5, Insightful)

    by Maxo-Texas (864189) on Thursday November 01, 2007 @03:51PM (#21201275)
    Exactly, a couple years back at vegas, the roulette wheel spun black 13 times in a row.

    Thats like 1/.48^13th.

    Random things.. happen.

    Randomly- some poor investing sod out there has made every choice correctly and been hammered by random market events.

    Likewise- some lucky fool (that thinks he is brilliant) has picked google or tasr or crox on some non-logical basis and won big.

    That's why you use Mutual Funds and ETF's. You get average performance. You lose the home runs, but you also lose the strike-outs.

  • by wiggles (30088) on Thursday November 01, 2007 @04:05PM (#21201551)
    Umm, the money doesn't go into the public school fund, it goes into the general fund. They only tell you it goes into the school fund. What really happens is, for ever dollar the lottery collects, they put that dollar into the school fund, which means they don't have to allocate that dollar to the school system from the general fund. In the end, the schools don't get any more money, it's just more money the state legislators have to spend on pork barrel projects.
  • by dazedNconfuzed (154242) on Thursday November 01, 2007 @04:10PM (#21201633)
    To turn those numbers around:

    You have to admit that driving to work 5 days a week has less of an impact (good or bad) on someone's lifestyle than getting killed in a car crash does (again, good or bad).

    That the odds of ending up terminated on a highway are far higher than getting an "off the charts lifestyle impact" lottery payout doesn't seem to affect anyone's choice in making that daily drive.
  • by XPisthenewNT (629743) on Thursday November 01, 2007 @04:14PM (#21201731) Homepage
    An intelligent older gentleman told me once that he plays the lotto every week. I thought this was a silly waste of money too, but he explained that he got entertainment value from imagining how he would spend the money. This entertainment he felt was worth far more than he spent on tickets.

    Just because you probably won't win doesn't make it worthless. Try buying a ticket. Go on, you won't get addicted to gambling, but you might have fun ;)
  • Re:Conclusions... (Score:5, Insightful)

    by joranbelar (567325) on Thursday November 01, 2007 @04:32PM (#21202065) Homepage

    Exactly, a couple years back at vegas, the roulette wheel spun black 13 times in a row.

    Thats like 1/48^13.

    Random things.. happen.

    And guess what? Last night in Vegas, the roulette wheel spun this:

    Red, Black, Black, Red, Black, Red, Red, Black, Red, Red, Red, Black, Red.

    That's like 1/.48^13th.

    A lot of people would be better off in understanding "randomness" if they would just realize that these two situations have exactly the same probability. Humans just assign more "meaning" to certain sequences than others.
  • Re:Conclusions... (Score:2, Insightful)

    by pclminion (145572) on Thursday November 01, 2007 @04:57PM (#21202477)

    But your example has 8 reds and 5 blacks. The other example had 13 blacks. As far as the probability of any particular SEQUENCE, yes, these probabilities are the same. But there are MANY possibilities where there were 8 reds and 5 blacks, but only ONE possibility with all 13 being black. So the two situations, if you look at it purely in terms of how many reds and blacks were hit, are very different.

    Or to put it another way, the chances of getting 13 blacks in a row are 1/48^13. The chances of getting 8 reds and 5 blacks, in SOME order, is far higher than that.

  • by Luke Dawson (956412) on Thursday November 01, 2007 @05:04PM (#21202579)
    Parent should be modded insightful IMO (even if unintentional). As light-hearted a jest as it may be, it really exposes a lot of what I hate about people's priorities. Just imagine what could be achieved if instead of pissing money away on lottery tickets people instead put that money into their favorite charity. Yes, I know most lottery commissions also donate large sums to charities but that's still only a fraction of the money actually generated through ticket sales. Just imagine if, say, $370M was instead invested in medical research? I know, maybe not as fun as getting your weekly high, but still.
  • by pclminion (145572) on Thursday November 01, 2007 @05:19PM (#21202809)

    In other words, if I flip a coin 10 times and see Heads 10 times, that's not a guarantee that the 11th time will be heads; in fact, the probability of getting 11 heads is so small that you'd be better off betting on tails.

    Classic Gambler's Fallacy. How on earth could previous coin flips influence the probability of the current flip? Try brushing up on your own statistics, instead. There are plenty of GOOD criticisms of this guy's work -- yours isn't one of them.

  • by R2.0 (532027) on Thursday November 01, 2007 @05:53PM (#21203417)
    "perhaps I should call it a government lie. It's Enron accounting."

    Right on the Gov't, wrong on Enron. It's Social Security accounting.

    1) pay money into the general fund, but allocate it to a "fund" that only exists on paper
    2) Loan the money from the phantom fund to the general fund - i.e. to itself
    3) the general fund pays interest to the phantom fund - i.e. to itself
    4) when the phantom fund goes negative, pay the principal back from the general fund - i.e. to itself
    5) ?
    6) Lockbox! Err, wait...Profit! does this work again?
  • by Trogre (513942) on Thursday November 01, 2007 @08:23PM (#21205331) Homepage
    That's why you get with an organization that sends photos too.

Yes, we will be going to OSI, Mars, and Pluto, but not necessarily in that order. -- Jeffrey Honig