The Blaze ran a story with headline “Mathematician Thinks There’s a Way to Pick Your Lotto Numbers With a Greater Chance to Win“.
Turns out Renato Gianella thinks he’s discovered a way to boost the odds of winning a lottery which, as far as I could discover, is no longer in existence.
But I don’t buy it; at least, I don’t think I do. Gianella wrote the paper “THE GEOMETRY OF CHANCE: LOTTO NUMBERS
FOLLOW A PREDICTED PATTERN” in Revista Brasileira de Biometria, an obscure journal. I don’t mean any insult to Gianella, but the paper, which is (mostly) written in English is difficult to follow. (Of course, if I wrote a paper in Portuguese the results would be dismal.) I gather the journal couldn’t afford a copy editor, because there are misspellings, many words running into one another (perhaps Gianella learned English from a German?), a lack of equation numbers, and similar difficulties.
Gianella writes of the Brazilian Super Sena, a lottery which appears to have folded up shop in 2001. I believe it was replaced then by the Mega Sena, a gamble which I’m guessing is operated similarly to the Super Sena, but with more numbers (i.e. a lower chance to win, but with higher jackpots).
That’s a lot of supposing, I know. But I’m not done guessing.
The Mega, and, I’m supposing, the Super, has two bins, the first with balls labeled 0-5, and the second with balls labeled 0-9. A ball from the first bin is drawn—say, 0—then one from the second—say, 3. The string “03” makes 3 (“00” becomes 60). Six times this is done. I haven’t been able to learn for certain, but it looks like if there is a duplicate number drawn, it is tossed out and there is another drawing, so that the final result gives 6 unique numbers. (Allowing duplicates would make an enormous difference in the probabilities.)
One more cute twist: the Mega allows you to buy up to 15 numbers, but you still only have to match 6 to win. The cost of buying 6 numbers is (I think) 1 Brazilian real, but the cost of buying 15 is 5,005.
I couldn’t follow Gianella’s math, which has a funny feel to it (funny strange, not funny ha ha). I also think he’s made a logic mistake. This table from The Blaze shows Gianella’s method.
Gianella first forms “monochromatic” groups, those rows of colored numbers. And from these, he asks how numbers from different groups can combine in various ways, say one red with two greens. And from those various combinations, using some opaque (to me, but I’m lazy) combinatoric methods, he figures his probabilities.
Problem is, there’s no reason in the world to group the strings “00”, “01”, “02”, …, “09” into one color, and the strings “10”, “11”, …, “19” into another, and so on. The machines just spit out balls with writing on them. The groupings are what we humans see. So it appears that his results would change if we were to, say, swap the green “89” with a red “61”, because this would change the combinations. And if that’s so—if we can swap any string, which we obviously can—then his method, assuming all swaps, give the standard result.
The third reason I don’t buy it is this table of results:
The templates are his groupings of colors combinations. The theoretical probability are what his model predicts and the observed frequency is what was seen (over some period). Do these two columns really differ? Well, yes they do. But do they differ enough to be suspicious that he’s on to something? No: not really.
Just as I was about to give up on the paper entirely, I read his final words:
As a main aspect, it reveals that, although all bets are equally likely, behavior patterns obey different probabilities, which can make all the difference in the concept of games, benefitting [sic] gamblers that make use of the rational information revealed by the Geometry of Chance.
“Behavior patterns”? As of patterns in behavior of the gamblers? Do the Sena payouts depend on the gambler’s behavior? The big lottery jackpot payouts here in the States (Mega Millions, Power Ball, etc.) do depend on gambler behavior—the more people who buy tickets the higher the chance of smaller winnings (winners might have to share jackpots). But payouts are different than chances of winning, which are the same for all. I admit to leaving the paper feeling very confused.
Gianella has set up a site to cash in on his tricks. He uses his methods on the American lotteries, too, but unless I’m badly mistaken, he’s fooling himself.
Thanks to reader Kent Clizbe for alerting us to this story.