William M. Briggs

Statistician to the Stars!

Pick Your Lotto Numbers With a Greater Chance to Win? Paper From Brazil

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
” 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.

The so-called Lotto Rainbow

The so-called Lotto Rainbow

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:

His comparative results.

His comparative 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.


  1. “The Mega, and I’m suppose had the Super, has…” Say what? And the rest of the paragraph doesn’t make much sense either, but I’ll assume that’s just the goofy method of selecting numbers. My spidey-sense says this is all loopy justification for separating addicted gamblers from more of their cash by offering secret inside information. When Nature and Science publish questionable stuff, how hard is it to get a bogus paper published in an obscure journal? But such a credential could impress the naive gambler.

  2. Briggs

    March 22, 2014 at 8:17 am


    My enemies removed the commas which I surely placed there. They’re becoming wilier by the day.

  3. Typical tout stuff.

    First question that should be answered: Why are you selling this instead of using it generate lots of cash for yourself?

    In some ways it’s just like at the track. You don’t want others betting with you. If he’s using this for himself then he’s splitting his paychecks.


    as a Third

  5. So they figured out a way to remotely control ping pong balls via a mathematical algorithm? That sounds impressive.

  6. The process he uses looks to be a variation of the roulette ‘big number/big wheel’ strategy, which supposedly works because some roulette wheels are perfect and do not produce equally likely results.The more likely conclusion if there were patterns in the Super Sena is that the Super Sena results were not random, and I see no testing of that hypothesis. In theory if you could make enough observations of a non-prefect roulette wheel or non-random lottery then you could detect patterns caused by the imperfections but even a simple ‘big wheel’ system with the wheel divided into hexrants requires 20+ observations of a wheel with no changes to suspect a hexrant which is more likely to pay-off, and that is only with 6 possible results.

  7. How would one test the results of a lottery (any lottery) to estimate the odds of its being non-random? Shouldn’t this be a preliminary step in this?

  8. I think what he is saying is that if your goal is to maximize your expected winnings, you want to minimize your chance of splitting the pot with other players.
    Some combinations of numbers are overplayed (e.g. birthdays), and some combinations of numbers are underplayed. Play the underplayed combos.

  9. What combos are under played

  10. I’ve just finished testing Gianella’s theory: it definitely changes something, but I’m not sure what. I downloaded all past results for the California lotteries, then used his theories to determine the most regularly occurring pattern of his groups, then, within that, selected four different types of results: most frequently occurring numbers, least frequently occurring numbers, least recently occurring numbers, and then a group consisting of numbers due to recur based on the average period between their appearance: for example, if 8 recurs on average every ten days, and it’s now ten days since we had an 8, then that’d be a good pick.

    I then tested the program against itself: what would it have picked for any given past result, basing its grouping and number selections on known results up to that date, and what would it have scored?

    The Mega Millions and Powerball lotteries have changed their rules within the last year or two, so I discounted that data, since there’s not enough valid history to mean anything. However:

    Within the Fantasy 5 lottery (results exist dating back to 1992) the system would’ve made a profit of about $200 over the last six months in both the Most Frequent and Closest Interval methods. In Super Lotto (results dating back to the year 2000), it would’ve made a profit of $6 in the Most Frequent method. The other two methods both made a loss in both cases. Over the past year, it would’ve made a profit in the Closest Interval method within Fantasy 5, but lost money in all other cases.

    Interestingly, this tells us that:
    (a) While luck has no memory, standard deviation just might…
    (b) If the results mean anything at all, then depth of historical data matters. Fantasy 5 is played every day; Super Lotto is played twice a week, thus there are about ten times as many past results for Fantasy 5. However, the disproportionate win amount is mitigated by the fact that Super Lotto is a lot harder to win in the first place: there’s a greater number spread, and there’s also a mega number, which complicates things (I didn’t apply Gianella’s theory to the mega number, since it doesn’t really apply).

    Conclusion: I’m not convinced. It’d be nice to believe that the program achieves something, but in reality, the profits I’m seeing are due to a couple of fairly significant individual results, rather than the trend of winning more often than losing that one would expect to see if the method was really working.

  11. Further to previous comment: What I can tell you is that Gianella’s correct about one thing: certain patterns stand out as being far more common than others. For example, in Fantasy 5 (numbering his groups starting with 1), the pattern 1, 2, 3, 4, 4 and two other patterns I can’t remember have happened about three or four more frequently than any other pattern (1, 2, 3, 4, 4 is (at the moment) the most frequently-occurring one). It’s not a sliding scale, either: there are the three most significant patterns, then a sudden drop-off in frequency, from thousands of occurrences for the top three, to a couple of hundred at best for anything else. That, at least, is very interesting, and something similar happens in all the lotteries (but each with different patterns), not just Fantasy 5.

  12. What the paper says, but does not explain, is that using number systems to avoid common chosen numbers will result in fewer wins being split with fewer people. Not more wins.

  13. Your odds do not change, but the odds of splitting your wins can be influenced.

  14. Further investigation (and programming) reveals that Gianella’s method has the following effect upon one’s chances: less than zero. Looking at its historical success over three California lotteries, I can see that its overall odds of producing a win are actually slightly worse than random chance – but not enough less that one can say it’s really making a difference: it falls within a margin of error one would expect given the number of historical games for which one can download data.

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