in reply to Picking (potentially) winning lottery numbers

Nice hack! This begs the question, though, what is the optimal choice in light of what other people will do? If it turns out that some numbers are more likely to occur than others, then rational people will choose those numbers. So if more people do choose those numbers, the pot will be split amongst a greater number of players, thus you will win less. So maybe you're better off choosing numbers that come up less frequently. Ah, but hang on, another rational choice is to choose the numbers that come up less frequently, because their turn has gotta come soon. So more people will choose those numbers, leading to smaller payoffs to you when you win.

The fallacy at the root of these kinds of arguments is that the balls have a notion of what went before. If ball 32 hasn't come up in the 276 previous games, that doesn't mean it's more or less likely to come up than any other ball in the next game. They have no history of what went before.

Which is to say that if you want to play Lotto (a.k. Fool's Tax) and write a script to pick Lotto numbers for you, start with a truly random source. I recall reading some time ago that the "autopick" selection of some country, where you pay and the computer fills the coupons with random numbers for you, was flawed. The numbers it chose were not really random. The numbers failed the Kruskal-Wallis test, Mann-Whitney test, or some damn thing. As the numbers were not truly random, and the actual number selection was, well, those autopick coupons just didn't win as often. Chance? Design?

update: cleaned up the prose in a couple of spots -- ahhh, proofreading.

Random numbers should not be generated with a method chosen at random. Some theory should be used. -- Donald Knuth.

--
g r i n d e r
  • Comment on Re: Picking (potentially) winning lottery numbers

Replies are listed 'Best First'.
Re: Re: Picking (potentially) winning lottery numbers
by scain (Curate) on Jul 24, 2001 at 18:46 UTC
    g r i n d e r ,

    Thanks. All of what you say is largely true, although one thing that was picking at the back of my brain was what if the balls do have some history. For instance, what if the paint used to put numbers on the balls resulted in some balls being (slightly) heavier than others? Presumably then, with enough tests, it would become apparent which balls were more likely to come out. (I don't know how they are actually picked from the machine but presumibly gravity is involved somehow.) Anyway, I don't really buy that arguement, and I think there would have to be too many trials to determine if it were true.

    But it is amuzing that you could make equally rational sounding aurguments for picking most common and least common balls; that's why I display both :-)

    Scott

[reply]
      You can make a better argument for not putting money into the lottery.

      But that said, if you flip a US penny, there is a slight bias towards coming up heads. Not enough of one in practice to be useful though. (It is easiest to see if you balance the pennies on end and then whack the table.)

[reply]
      In the UK, at least, there are multiple sets of balls, and multiple machines to pick them and balls are replaced frequently. This all stops trends developing, and making the results as random as ever.

      I'd be interested in it being able to calculate my chances of winning anything, and doing some manipulation with that (like what if I choose two sets of numbers for a week.)

      --
      RatArsed

[reply]
        RatArsed,

        Calculating the chances of winning is fairly trivial. Assume the drawing has 50 balls from which 6 balls are drawn without replacement. The chance of picking:

        • one right is 6/50
        • the second one right is 5/49
        • third 4/48
        • forth 3/47
        • fifth 2/46
        • sixth 1/45
        To get the chances of picking them all right, multiply all those probablities together: 6.29299e-8, or about 1 in 15.9 million.

        Scott

[reply]
Re: Re: Picking (potentially) winning lottery numbers
by tachyon (Chancellor) on Sep 05, 2001 at 23:22 UTC

    As the numbers were not truly random, and the actual number selection was, well, those autopick coupons just didn't win as often. Chance? Design?

    Whilst I am as much of a conspiracy theorist as the next man this statement flies in the face of what you just said. Any valid selected numbers (random or not) have the *same* chance of winning. 1-2-3-4-5-6 is not random but has the same chance of winning as 14-36-21-1-7-8

    BTW most lotteries drawn with balls are not random. The weight of the paint for the numbers and other things that lead to differences between balls skew the results. Unfortunately the skew is just not enough to be able to profit from.

    The famous story of breaking the bank at Monte Carlo was supposedly true and due to imbalance of the roulette wheel. The advantage in roulette it that the house's margin is ~3% so you don't need too much skew to screw that.

    cheers

    tachyon

    s&&rsenoyhcatreve&&&s&n.+t&"$'$`$\"$\&"&ee&&y&srve&&d&&print

[reply]

In Section Cool Uses for Perl