Mega da Virada reaches 1 billion reais: the odds of winning, according to science, and everything you need to know

These percentages are applied to the revenue the lottery hopes to make.

From 2020 to 2025, the nominal and real value of the main price increased:

According to Caixa Econômica Federal, since its first edition in 2009, Mega da Virada has already awarded 130 bets who tried their luck and reached six dozen millionaires. The figures that stand out the most are:

5, 33 and 36 – four times each

3, 17, 20, 29, 34, 41, 56 and 58 — 3 times each

But are there ways to increase the probability of winning? Are there combinations and numbers with more or less chances? And does participation in prize pools and collective games increase the probability of having to worry about possible wealth taxation?

Which is more likely: being struck by lightning, being born with six fingers, being bitten by a shark, or winning Mega da Virada?

BBC News Brasil spoke to four mathematicians to answer this question and others.

According to a calculation by statistician Euler Alencar, published on the Caixa website, the probability of winning the main prize with all six numbers is 1 in 50,063,860, or a chance of 0.000001997%.

The number of possible combinations of six numbers, taking into account the 60 available, is more than 50 million.

It’s like you randomly put 50 million names in a bag and someone reached in and pulled out your name.

According to Diego Marques, professor in the mathematics department of the University of Brasilia (UNB), what defines a person’s chances of winning the lottery is the number of possible combinations in a given drawing.

“The more games possible, the lower the chances of winning,” explains the mathematician.

According to mathematicians, it depends on the number of bets. But if we consider that in 2023 they will have exceeded 485 million, this is a very unlikely event, because there are just over 50 million possible combinations of six numbers.

“If we have 80 million single bets, the probability of not having a winner is around 20%,” calculates Gilcione Nonato da Costa, professor at the Department of Mathematics at the Federal University of Minas Gerais (UFMG).

“But of course, as the number of bets increases, this probability decreases,” observes the mathematician, estimating that with 150 million bets, the chance that no one gets all six numbers right drops to 5%.

Mega da Virada, however, has a little extra for punters: it is not cumulative, like other Mega-Sena competitions throughout the year.

So, if no one hits all six numbers, the prize goes to whoever gets five and four, and the chances of winning are then more favorable.

This happens because, by playing six numbers, but only having to match five, it is as if the player is playing several games at the same time, as the possible combinations of five numbers or less become more diverse.

According to mathematicians, the only way to have a better chance of winning is to play more games.

This can be done in two ways: by playing several games of six numbers or by betting on more numbers, in what is called a multiple bet.

But obviously, the more numbers you select, the more expensive the game will be.

To bet on six numbers, the minimum to play, the game costs R$6. To bet on seven, this value increases to R$42.

“The more games you play, the more chances you have to win. And the chance of betting on more numbers is the same (as playing more games),” says UnB’s Marques.

“For example, if you bet on seven tens, it’s the same as betting seven times on six tens. The probability in both cases goes from 1 in 50 million to 1 in 7 million. So, in fact, it’s a good strategy,” explains the mathematician.

But why do multiple bets increase the chances of winning?

“When you bet on seven numbers, you only have to get six of them. You have a ‘big’, a dozen that you can get wrong and that increases your chances considerably. You can get any one wrong and get the other six right, that increases your luck by seven,” he explains.

Costa, from UFMG, agrees and leaves a suggestion: instead of doing several cheaper draws, it is better to play a single draw for R$42.

The mathematicians’ answer to this question is simple: no.

“The probability of getting any combination of six tens is the same. It doesn’t matter whether you play the numbers you dreamed of or the numbers 1, 2, 3, 4, 5 and 6. The probability is the same: 1 in 50 million. That won’t change,” says UnB’s Marques.

“Someone might say, ‘Wow, but 1, 2, 3, 4, 5, 6 never came up.’ But I can give millions of examples of combinations that never came out. So, actually, 1, 2, 3, 4, 5, 6 is just one of the combinations and the chances of it coming up are the same as any other.”

Always close to Mega da Virada, reports showing the most drawn numbers to date are common in the press.

People then ask themselves: is it better to play these numbers or not to play them?

“The truth is that it doesn’t make the slightest difference. What happened in the past does not influence the future draw. This is a fundamental premise of an honest draw,” says Moacyr Alvim, professor at the School of Applied Mathematics of the Fundação Getulio Vargas (EMAp-FGV).

“The bottom line is this: Ignore the numbers from the past, because they won’t help you at all.”

UFMG’s Costa, however, warns that when you play on heavily staked numbers as birthday dates – which limits guesses to the 31st, which is the maximum number of days in a month – the chances that you end up splitting the prize with other birthday bettors increases.

Here’s some good news: betting in groups actually increases your chances of winning.

“In general, in the pools, people gather a lot of people to be able to make these bets with ten, eleven tens. So the chance increases because everyone gives a little, we add a few hundred or thousand reais and we can make a lot more bets,” explains Marques.

“It’s the smartest and most practical way to increase your chances. You gather your friends, win a lot of money and compete with more combinations. With the disadvantage that the prize is shared, but it’s a good strategy”, recognizes Costa.

“The chance of winning is the same: 1 in 50 million. Your luck will not change at all, whether it is you alone who plays or the entire planet Earth,” explains the UnB professor.

“The chance of winning is individual, it does not depend on the number of bettors. But the prize you will win in the event of a draw clearly changes,” explains Alvim, from FGV.

In Mega da Virada, he recalls, there are two “antagonistic forces”.

“At the same time as the number of bettors increases, there is also a much larger prize, as it has been accumulating throughout the year. Given the high number of bets, it is more likely to split the prize with someone than to win alone, but even sharing it, the value is so high that it must be higher than what is normally paid out by Mega-Sena for the rest of the year.”

“It is much more likely that you will be bitten by a shark than winning the Mega-Sena,” warns Régis Varão, mathematician at Unicamp.

According to him, it is estimated that there is a one in 10 million chance of being bitten by a shark, so there is 5 times more chance of finding yourself in the jaws of the big fish than of becoming a millionaire on the 31st.

The same logic applies when it comes to getting a lightning bolt in the head.

“The chances of being struck by lightning are approximately one in 1 million, that is to say you have 50 times more chance of being struck by lightning than of winning the Mega-Sena,” Varão calculates.

Finally, approximately one in 10,000 people are born with six fingers.

“This means that it is about 5,000 times easier to be born with six fingers than to win the Mega-Sena,” explains UnB’s Marques.

The Brasilia professor says there is an expression in the mathematical world for this.

“The lottery is a tax on people who don’t know mathematics,” he jokes.

“It’s not to discourage anyone, but really, from a mathematical point of view, the chances are very low. But I played, I think the psychological aspect of dreaming about what we would do, it’s cool, it’s good for us. Behind the coldness of the numbers, there are things that help us.”

Alvim, from FGV, reminds us that we must be clear that the lottery is not a form of investment.

“Anyone who thinks that if they are smart enough or invest a lot of money they have a chance of winning is doing something stupid. It is not an investment, the game is designed so that the vast majority of people lose money,” he observes.

“It’s just fun. As fun as it is, I think it’s worth it. For example, I bought a Mega-Sena ticket and gave it to my mother-in-law as a Christmas gift.”

*This report was originally published in December 2021 and republished with updates in December 2025.