Friday, October 15, a happy French won 220 million euros at the Euromillions, i.e. the
biggest jackpot of the history of the European lottery. Isn’t this a good time to ask yourself if math can’t match the winning numbers?
The Loto was invented in Genoa in the 16th century. The principle was to draw five numbers out of 90, corresponding to the five councilors taken at random from among the 90 senators to form the city council. We were betting on the outcome of this draw. Since then, two questions have arisen for the players: do certain numbers appear more often? Are some issues more profitable than others?
How to earn more by playing so much?
The first question is therefore to know if the French gaming company “cheats” while the second question allows us to ask ourselves if there is a better game strategy than playing numbers at random. We will see that the answer to the first question is no, and that the answer to the second question is yes.
There is a consensus among statisticians to believe that there is no cheating in the draws. Random draw involves some numbers appearing a bit more than others, but within limits considered normal. The number that appeared the most between May 19, 1976 (date of the first printing) and October 1, 2014 is 1 with 834 occurrences and the least published number (over the same period) is 29, with 651 occurrences.
Statisticians believe there is no cheating in the draws © LesColporteurs / Pixabay
Note that the Française des jeux has no real interest in tampering with the prints, because it is taking the risk of killing the
goose that lays golden eggs. And to say that there is no cheating implies that the
probability that a given number comes out in the next draw is always the same whatever the number and in particular whatever the number of times it is released before.
All the sites, newspapers and other hucksters who claim otherwise are therefore just liars. If all these fortune tellers really believed they had the secret to winning, it would be surprising if they shared it!
To illustrate the point, remember that the Shadoks had built a
rocket that had a one in a million chance of working. So they hurried to miss the first 999,999 times to finally succeed. Hence their motto: “the more it fails, the more likely it is to work”.
The legendary rocket of the Shadoks © ORTF / AAA
We can also think of Rita mae brown : “Madness consists in doing the same thing over and over and expecting different results” (quote often wrongly attributed to Albert Einstein).
Should we therefore play the numbers at random? It’s a little less simple than it looks. Some numbers are played more often (eg birthdays) and therefore not all puzzles are played the same number of times. The most played grids therefore pay less when they come out, because the winnings must be divided between more winners. So to paraphrase the Shadoks: “the more a grid is played the less it pays”.
The winning numbers
It is therefore tempting to play the numbers that the others do not play… Unfortunately the Française des jeux does not publish any statistics on the combinations played. However, we see that the winnings are very variable and therefore that all the grids are not played the same number of times.
The Euromillions draw is broadcast on television © FDJ
The absence of data is obviously conducive to all the fantasies of martingale. Moreover, if the game could be rational, all the combinations would be played about the same. So the number of winners would be less variable between the different draws and the winnings would be roughly the same every week. The number of high wins would therefore drop and this would limit the attractiveness of the game.
Is the situation hopeless? Not quite. Researchers proposed a statistical method to estimate the frequency of use of numbers in the tables of
Loto players. For this they use the numbers of winners in the various ranks. If all the numbers were played as much their frequency of occurrence would be 1/49 = 0.0204. Number 7 is the players’ favorite number and it is played 1.7 times more than it would be if the players chose at random. The least played grid and therefore the most profitable was in 2014 grid 32-38-39-40-41-43. It’s up to you to see if you want to try your luck!
Beyond the Loto, computers or social networks and their algorithms, mathematics makes it possible to predict the tides, to decode secret messages, to create musical melodies, and even to multiply the knots of ties. By revealing the hidden beauty of theorems right down to the heart of our daily lives, the book Mad about math sheds new light on mathematical concepts and
their uses. You will discover the visible face of mathematics, that without equation.
This analysis was written by Avner Bar-Hen, professor of statistics and big data at the National Conservatory of Arts and Crafts (CNAM).
The original article was published on the website of The Conversation.
