By more than try Abel Caballero, the beginning of Christmas (at least in Spain) is not marked by the lighting of the lights of Vigo, but by a much more consolidated tradition: the raffle of the Christmas Lottery. Every December 22, thousands of Spaniards tune in to TV, radio or press the ‘F5’ key on their computers every so often in the hope that the children of San Idelfonso sing your number. However, the probability of this happening is very low, as much as choosing a name at random from the census of a city and getting it right.
The question is… Are there ways to expand that probability?
1 in 100,000. The Christmas Lottery generates excitement and makes thousands of Spaniards get out of bed on December 22 with a special tingle: the hope of seeing how their bank accounts suddenly add a handful more zeros. That is undeniable. Just as it is that, if we leave aside the illusion, the chances of our tenth(s) winning are very small.
Lower case.
The data speaks for itself and leaves little room for hope: in the hype 100,000 balls enter with numbers from 00000 to 99,999. Your number has the same exit options as the other 99,999, one 0.001% probability.
Mathematics VS hope. “In these cases the probability is easy to calculate. Since all numbers are equally probable (there is a ball for each number), it would be calculated with Laplace’s rule: the number of favorable cases divided by the number of possible cases,” comments Miguel Ángel Morales, mathematician and author of the blog Gaussians for almost two decades.
“Assuming that we have only one tenth, the probability of winning El Gordo would be 1 (there is only one Gordo) in 100,000 (since there are 100,000 numbers that enter the draw). That is, a probability of 0.00001.”
What does that mean? Since talking about drums, tenths and statistics can be too abstract, Morales transfers the figures to something we are much more accustomed to: people. In this case we would exchange the tenths for cards and the drums for the municipal registry of a medium-sized city.
“Let’s imagine that we have a DNI of someone from Santiago de Compostela and a list with the names of all its inhabitants (about 1,000,000),” reflects the professor. “The probability would be similar to the one we have of choosing one of those names at random and turning out to be the person with the DNI that we had at the beginning.”
“If we talk about the total number of prizes, the way to calculate the probability would be the same: we would have to change the 1 (a single Gordo) for the number of prizes. Sticking to the main prizes, as there is a First, a Second, a Third, two Fourths and eight Fifths, the probability of getting a main prize with a single tenth would be 13 divided by 100000, 0.00013.”
The big question. There is no Christmas without its Lottery and there is no draw in which it is not considered the same question: Do we have any way to increase our chances of success, however slim they may be? Is there any way to scratch a little more probability, even a few tenths? The answer is yes. And not.
The starting data is what it is, but precisely for this reason our chances of being happy on the morning of December 22 increase as the number of different tenths that we have in our portfolio increases.
More options? More tenths? “The only way to increase the probabilities is, effectively, to buy more tenths of different numbers,” confirms Morales. “If we have five of different numbers, the probability of winning the jackpot would be 5 in 100,000, which is 0.00005. There are no more mathematical ways to increase the probability of winning a prize.”
That is, if what you want is to “maximize” your chances of success, you will have no choice but to put more eggs in the basket. Having more bills of the same number (even if you have a hunch) will only help you win more money in case that combination wins, it does not increase your options.
“Speaking of refund, the probability would be one in ten if we have a single tenth. Obviously, buying more tenths with different endings would help us have a greater probability of getting that refund,” he adds.
And Doña Manolita or the ‘tricks’? The Christmas Lottery is not only peculiar because of the Gordo, the stones and its symbolic value. It is also because in it statistics and pure hunch go hand in hand (just like in other games of chance). Hence there are people willing to endure long lines outside to buy a tenth at Doña Manolita or to always play the same number, perhaps a special number that coincides with your birthday or the date your child was born. Works? Do these ‘tricks’ improve our chances?
Morales is very clear about whether the latter (repeating a number year after year) influences our fortunes: “No, it does not increase it. All draws are independent, which means that what comes out in a draw does not depend on what happened in the previous ones. They have no memory. Mathematically speaking, always playing the same number does not increase the probability of winning.”
The administrations of “luck”. There is also no difference between buying a tenth at the corner fruit shop or doing it in administrations so famous like Doña Manolita, The Bruixa d’OrLotería Valdés or El Gato Negro. Manuel García, an expert in Statistics at the European University, was also very clear about this a few days ago in an interview with the diary ACE.
“They give out more prizes because they sell more numbers, not because they are luckier. It’s a self-fulfilling prophecy effect. It’s very important because since it has that reputation (I don’t know how it originates) people usually go there to buy. They are the ones that sell the most numbers and have the best chance of giving out more prizes.”
25% more likely? A quick review of the press these days shows headlines about forms of increase to 25% the probabilities of success or mathematical geniuses who have managed to win more than 10 times the lottery and earn millions. It’s true? Are there ways to achieve such amazing results?
The answer is again yes and no. Yes, there are, but they are so complicated that their profitability is simply more than questionable. For example, García recognizes that there is a way to achieve more or less a 25% probability of winning the Christmas Lottery Jackpot, but it requires a lot of work and, above all, a more than considerable investment: buy 25,000 tenths.
“There is no mathematical strategy to increase the probability of success. If we buy 25,000 tenths (of different numbers), we would have a 25% chance of obtaining the Gordo, since 25,000 among 100,000 is 0.25, which is equivalent to that 25%,” agrees Morales. “But of course, the expense would be 500,000 euros, which is greater than the prize received with El Gordo.”
“You could be lucky and hunt the Gordo and some other prize and, in the end, obtain a greater benefit than the expense you have made, but the risk is very high considering that the probability of hitting the Gordo would be only 25%.”
One name: Stefan Mandel. Around these dates it is also common for the name of Stefan Mandela Romanian mathematician who supposedly found a way to increase his chances of success in the lottery. In fact they say he won more than 10 draws in different countries, a streak that was cut after the authorities adapted their regulations.
In his case the key was a method called “combination reduction”but not much is known about it nor does it seem to be a perfect recipe. In fact, it probably has the same problem as the 25% formula: it requires a large outlay.
Without infallible formulas. “I suspect that the thing was to play many combinations of the lottery in question, which would be equivalent to buying many different tickets for the Christmas Lottery,” explains Morales, who remembers another strategy that is associated with Mandel: take advantage of large draws (for example million-dollar jackpots) to monopolize combinations and increase the chances of success in the hope of taking home the prize. It sounds good, but it has its ‘buts’.
Neither time nor resources. “The latter makes sense when the price of all those combinations is less than the big prize of that lottery, but that has certain logistical problems and a great risk. As usually happens in EuroMillion-type lotteries, I’ll give you an example. In this game, there are a whopping 139,838,160 combinations, almost 140 million. Let’s suppose that in a draw, the cost of all of them is lower than the first prize, so it would be interesting to play all of them.”
“Is there material time to carry out the necessary procedures to have all the tickets and pay for them all? Is the necessary money available for this, knowing that each combination costs 2.50 euros?” he asks.
The risk, always present. Even in such extreme cases the formula is not infallible. “Let’s assume that the answer to both questions is yes (although I doubt it). We would, therefore, have all the winning combinations of all the categories of that lottery. Are we willing to risk that there is another winner of the first category (and of all the others) with whom, in that case, we would have to share the first prize (and the others)? Because, if that happens, we may end up losing money,” warns the professor.
Images | Aiaraldea Gaur eta Hemen (Flickr) and SELAE 1 and 2
GIPHY App Key not set. Please check settings