William M. Briggs

Statistician to the Stars!

Has Couple Found Formula To Win Lottery?

I stole that title from WNBC’s web site, where they have a similarly titled story. The only reason I bring this to your attention—the story itself is ludicrous on its face—is that it is another piece of evidence that either (A) reporters care more about their hair than the organ under it, or (B) reporters are willing to say anything to gain viewers.

Of course, both (A) and (B) might be true.

It’s Friday afternoon; we might as well have a laugh. Here’s the story

Verlyn and Judith Adamson of Mount Horeb each claimed a $350,000 jackpot this week for having the winning numbers in the state SuperCash drawing last Saturday.

But they didn’t mention at the time that they also held two more of the winning tickets.

They claimed two more $350,000 jackpots Thursday. All four were purchased at different locations, but with the same numbers and for the same drawing…Verlyn Adamson, an accountant, said earlier in the week that he’s a big fan of math puzzles. He claims he developed a formula for lottery picks, but his winnings have been small until now.

[Their lawyer] said the Adamsons are “exploring patent protection” for the equation.

OK, I’ll bite. Why mention that they bought the tickers at different locations? It’s the same set of numbers on each ticket for the same drawing! It makes no difference where you bought them. The “reporter” obviously didn’t bother to look up the fact that the SuperCash drawing is a standard ball draw: “Choose 6 different numbers from 1 through 39” (it took me nearly 30 seconds to find this; time I could have spent combing my hair).

You can, in this lottery, increase your winnings by buying multiple tickets, a practice which must be exceedingly common. But note that the Adamson’s didn’t win four different draws, just the same draw with four tickets with the same numbers. I feel stupid for harping on that observation, but apparently it wasn’t obvious to the “reporter.” It’s also not clear how many winning tickets they had: according to the SuperCash rules, you get two plays per ticket, so if they had four tickets they would have won eight jackpots, not four. Well, who cares about details?

Poor Adamson is now going to dump a substantial portion of his winnings (those not confiscated by the government) on a patent application for a formula for winning the lottery. I doubt his lawyer, who will of course be paid a fee, will discourage them. But I fear (and hope) the Patent Office won’t oblige them in the end.

If I were a cynic, I’d guess Adamson and his lawyer don’t care about the patent. It’s likely that they will be willingly persuaded to part with the formula for a fee, perhaps several times. How else did the “reporter” get the story in the first place?

I wonder how many people who pay for access to his formula will wonder why he’s selling it, because Adamson could make a boatload more by just using it himself.

Oh, yes. The reporter, as he must have learned in J School, provided balance by quoting a mathematician saying (in politer language than this) that Adamson was crazy.

If, and I know the odds of this are vanishingly small, any reader wants to know why such a formula is impossible, just ask and I’ll create a post explaining it.

17 Comments

  1. You mean you will give me the formula free of charge? Mustn’t be worth a lot then πŸ˜‰

  2. Since I don’t know how these numbers are selected I obviously can’t say a formula which predicts them is impossible.

    I will say it should be impossible; don’t use a formula or algorithm to generate the numbers.

    When I encountered random number generation in the 1960s – yes, the 1960s – random sequences were desired to test guidance systems and other gear. Then, as now, there were quasi-random algorithms available but none, by definition, produce absolutely random sequences.

    So we looked at radioactive decay counts, the low noise in undriven vacuum tubes, and cosmic ray detection. And there were other suggestions, it has been a long time and I’m not acquainted with what was used after 1965.

    A lottery generator should be driven by random physical events measured when ticket sales have stopped. They won’t crack those!

  3. Alan D. McIntire

    August 22, 2008 at 7:34 pm

    I’ll give you the formula free of charge. Edward Thorpe mentioned in in a “Gambling Times” article years ago.
    There are
    (49*48*47*46*45*44)/6! =13,983,816 possible selections in California’s 6/49 game.

    In a progressive lottery, once the payoff odds for a single winning ticket is greater than about 14,000,000 to 1, buying a lottery ticket gives you a positive expectation. You only buy one ticket because of the Kelly money management formula.

    Using that system, you should be able to double your investment every couple of million years.

    – A. McIntire

  4. Jonathan Guthrie

    August 22, 2008 at 9:05 pm

    K: My understanding that modern noise-based random number generators (including ones that are built into modern CPU’s) use thermal noise in semiconductor diodes as their noise source. They are subject to bias, so you’re supposed to combine several of them to reduce that bias.

    Assuming that the lottery draws are random, they should not be predictable. Heck, if you’ve got a really good cryptographically secure pseudorandom sequence generator, it won’t be predictable, either. On the other hand, delivering “true randomness” is surprisingly hard and verifying randomness is only slightly less hard. Generating good random numbers is important because a great many security protocols, rely upon good random numbers to work.

  5. Jonathan: Thanks. Somehow it never occurred to me that a random number generator might be in a CPU. I can see that it could be handy in simulations.

    Our desire at that time was to generate sequences and store them so that test data would be both random and repeatable.

    Why we needed more than one very long sequence – or didn’t just use an algorithm (they were actually pretty good) – I can’t recall. Probably because we were spending government money.

    No doubt some quantum effect device could be used today.

    w/o much thought on the matter, I wonder: Can you ever prove randomness? Maybe so, mathematicians are quite clever. But it strikes me that all you can ever do is show a given output has some high probability of being random.

    Getting too fancy is common. As you said, drawing numbers out of a hat will work. But you first have to put the numbers into the hat at random. Life is hard.

  6. Briggs

    August 23, 2008 at 5:17 am

    Ok, Ok, you guys talked me into it. I’ll make two separate postings on the lottery:

    1. Randomness and random numbers. There’s more than a bit of confusion here which I hope I can explain,
    2. Lottery strategy’s per se and why these are useless. Most, or even all, of these strategies center around numerological-like methods which are misunderstood.
  7. One pattern I have noticed is that in the Massachusetts numbers game, i.e., 4 numbers between 0 and 9, payoffs are larger for any combination of 0, 6, 8 and 9 because most players seem to be constrained to 1,2,3,4, 5 and lucky number 7. Of course since the payoff for a $1 ticket is never more than around $7000 it is always lousy bet. Low numbers pay out in the $4 to $5000 range. SUch ganes are of course a tax on innumeracy!
    I am with Alan – I never play until the expected discounted after tax winnings are greater than the cost of the bet.

    Alan:
    What is the “Kelly money management formula”?

  8. Well, I’ll be damned, but in europe we have a thing called “euro-millions”, in which every week a lucky guy gets at least 15million euros (times the jackpots, which occur often enough), and I bet there is no way anyone can guess the “algorithm” in it.

    Why?

    Because it consists of balls going in circles with a wind generator inside a glass dome, and then a ball gets sucked in, quite randomly. An algorithm is truly impossible because no one can guess beforehand the exact microscopic events that go through while the balls get thrown into the dome (and dome imperfections, quantum effects, etc).

    One time did I try to convince my colleagues to fill a ticket with a number sequence like 1-2-3-4-5, for it had exactly the same probability than others (like d’oh!). I was unsuccessful, for people really believe that if they put numbers that appear to be random, then they have a more shot! (I should stop trying to poke fun at them, in the end, it’s always me who looks dumb, oh the humanity!)

  9. Luis

    Agree that 1-2-3-4-5 etc has exactly the same probability but it probably won’t win you the same amount. This is because there are bound to be quite a few people who put down these numbers so, if they did come up, your winnings would be split across all of those people (because the 15million euro is the winning prize draw and is split equally across all winners).

    You are therefore equally as likely to A winner with 1-2-3-4-5 etc but your chances of being the ONLY winner of 15 million euro a higher with a “random” selection of numbers.

  10. James:
    Jeepers, the least you could do is give me a little credit!! πŸ˜‰

  11. Sorry Bernie!

    The main thing that I picked out from your post (and others) that surprised me is that you have to pay tax on your winnings. You don’t have to pay tax in Europe (or New Zealand where I’m currently based) as, if you did, then you would be able to claim a tax deduction for your losses as well – same goes for any other type of gambling as well.

  12. James:
    Apparently you file with a W2G. Since I only bet when the prize reaches about $140 million – I have never filed one!!

  13. Alan D. McIntire

    August 25, 2008 at 7:17 pm

    The object of using the Kelly system is to maximize the rate of growth of your bankroll when making positive expectancy bets. On negative return bets, you bet zero.

    If you have a 10% edge, by betting only 1/10,000 of your bankroll on each bet, you probably won’t suffer a bad run of luck and go broke, but you won’t make very much money. On the other hand, betting 40% of your bankroll when you have a 10% edge will increase your profits, but also increase the likelihood that you’ll suffer a bad run of luck and go broke.

    The optimum formula, when you win A times a bet with probability p, and lose the bet with probability (1-p), is to
    bet f= ((A+1)p -1))/(A) of your bankroll on each bet.

    For an even money bet where you have a 1% edge (1.e you win 50.5% of the time and lose 49.5% of the time) you bet
    ((1+1)(.505)-1)/1= 1% of your bankroll on each bet.
    If you have a biased roulette wheel where you win 1/30th of the time instead of 1/37 as on an unbiased wheel, you bet
    f=(35+1)(1/30)/35 or f= 6/175
    of your bankroll on each bet.

    The growth rate of your bankroll will approach
    G =p ln(1+Af) + (1-p)ln (1 -f)

    After N bets, your expected balance is
    exp( N * G)

    On my lottery example above, I should bet
    ((14,000,000)/(13,983,816))-1 all divided by 13,983,816
    or 1/1.2 billion of my fortune on a lotter ticket. If I bet more,
    my bankroll will not grow as rapidly as that of someone using the Kelly formula.

  14. Alan:
    Many thanks for tutorial. Of course, if you also happen to have the winning numbers please let me know.

  15. Hey, it’s perfectly possible he has a formula that picked his winning numbers. Just ridiculous that those numbers had any better chance of winning than any others πŸ™‚

    Anyone want to buy a formula for generating lottery numbers? Going cheap..?

  16. Dear Mr. Briggs.
    I could not find an email button on your blog, so I will post here in hopes you see it.
    I was wondering if you could do a statistical break down on speeding in terms of real road safety. In my neck of the woods, the police often have large scale crackdowns on certain roads to catch speeders. They often boast of catching 150+ speeders at 20 +km/h over the speed limit in a 12 hour period etc etc. Yet within that period there were no accidents, nor was their any fatalities on those roadways, it seems to me they are full of hot air when it comes to speeding, being such deadly problem. I think it is more revenue oriented than safety.

  17. He did it again????

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