How to Win Euromillions According to Math

Are you curious about how to win Euromillions? If so, don’t use statistics. Instead, use combinatorial mathematics and probability theory to understand how balls behave in a random lottery draw.

From understanding the odds to selecting the best numbers, let’s explore the science of making intelligent choices while clearing up some common myths and superstitions.

Level up your Euromillions strategy with math. Let’s begin.

how to win the Euromillions 5/50 according to Math

The Odds of Winning The Euromillions

Knowing how to win Euromillions requires understanding the game’s challenges. The Euromillions game is a 5/50 lottery format. So, the rule is to pick five numbers from 1 to 50. With this format, there are 2,118,760 ways to combine numbers.

However, to win the jackpot, you are required to match the extra two lucky stars of 12 numbers so that the actual odds become 1 to 139.8 million.1

Your odds of winning the jackpot are so minuscule that you have a better chance of becoming the next Prime Minister of the U.K.

You heard the saying that the probability of being killed by a shark is higher than winning the jackpot. But think about this: if you don’t swim in the ocean, there is no chance that you meet the shark in the first place.

Likewise, to win Euromillions, you must be in it to win it.

Fortunately, in the Euromillions game, you can also win 12 more likely prizes ranging from £2.50 to £130,554.30, giving you a 1 in 13 chance of winning any prize.2

Therefore, the probability of a single ticket not winning any prize is 0.9231. Consequently, the chance of losing twice in a row is 85%.

P(losing twice) = 0.92312 tickets = 0.8520

If you purchase nine tickets, you’ll have a 50/50 chance of winning any prize. However, there is no assurance of success. To attain a 99.99% guarantee of winning a prize, buying about 115 tickets may be necessary. We use the complementary of P(losing) to calculate this guarantee, as shown below.

P(winning any prize) = 1 – 0.9231115 tickets

This guarantee most likely secures the lowest-tier prize since the probability favors matching two main numbers. As you can see, securing minor prizes, let alone the jackpot, is very challenging. So don’t believe if someone says you can profit from the Euromillions game by frequently winning small prizes.

You cannot predict the next winning combination in Euromillions.

So, if superstitions, hot numbers, lucky numbers, quick picks, and random selections do not help, what will?

Mathematics remains the only tool.

How to Win Euromillions Mathematically

Hot and cold numbers don’t exist. People mistakenly believe that if a number occurs frequently in the past, the same number will be drawn more often in the future. This belief must be corrected because all numbers have an equal chance of being drawn.

Likewise, all combinations share the same likelihood of winning. In short, you cannot beat the odds of the Euromillions game. You cannot manipulate the probability. And you cannot predict the next winning numbers due to its randomness.

That begs the question:

How to win Euromillions when numbers and combinations have an equal likelihood of winning in a truly random game?

And here’s the answer.

Buying more tickets can increase your chances if you want to win Euromillions. However, buying many tickets can be useless if you don’t do it strategically. You must know how to make informed choices and be intelligent for most draws.

Let me explain.

Follow the Behavior of a Random Lottery Game

Even though all combinations have equal chance, all hope is not lost. In reality, compositions are not created equally because of their varying odds.

Take a look at this combination below:

10-12-14-16-18

You might probably observe the following:

  • All the numbers belong to the 10s group since the first digit of each number starts with one;
  • The combination is exclusively made up of even numbers;
  • Numbers are consistently skipping one number.

This combination exhibits an unfavorable frequency ratio. Therefore, it is not a sensible choice to win Euromillions.

And here’s why:

A truly random lottery game distributes the probability evenly across the entire range of numbers. Because of this fair distribution of probabilities, a combination that is made up of numbers from one group is a rare event. And you will rarely notice a winning combination that is predominantly even numbers. A random lottery game will not favor even numbers over odd numbers, nor will it favor low numbers over high numbers. A lottery game is fair.

I don’t know about you, but I advise Euromillions players to follow the behavior of a random lottery draw. Let me elaborate on the details below.

Understanding Your Gut Feeling

Take a look at the following combinations:

1-2-3-4-526-27-28-29-30
6-7-8-9-1031-32-33-34-35
11-12-13-14-1536-37-38-39-40
16-17-18-19-2041-42-43-44-45
21-22-23-24-2546-47-48-49-50

Most players say it doesn’t matter what combination you choose because a lottery draw doesn’t care.

However, if asked if they will spend money on the above combinations, none will take the risk.3

And why not?

If they believe all combinations have the same chance of winning, why fret?

You see, people don’t trust their understanding of probability.4

There must be a mathematical explanation for why part of you screams and says you can’t bet on certain combinations.5

Fortunately, this random behavior can be calculated mathematically to help you make informed choices and win Euromillions. But to do this, you must use the right mathematical tools.

Shifting Strategies from Statistics to Combinatorics and Probability.

We don’t use the tools of statistics when finite elements are involved because a finite structure provides sufficient data to infer the composition of the game without resorting to data sampling.

Since our knowledge of the game is adequate, any questions we ask about the Euromillions game are probability problems to solve rather than statistical ones.

We use combinatorial mathematics and probability theory to understand the behavior of lottery balls in a random setting, offering valuable information for making informed choices.

For instance, we can ask, “What is the likelihood of drawing 10-12-14-16-18?”

We can rephrase the question to make it more quantifiable:

“What is the probability of purely low and even numbers?”

We can see that the probability is 0.0003738035, which means this event will likely occur about four times in 10,000 draws. Needless to say, you don’t want to spend money on 10,000 tickets only to get four favorable shots.

In Euromillions, two combinatorial groups are calculated to have an average frequency ratio of 1:14, which translates to approximately 689 favorable shots for 10,000 tickets.

Armed with these mathematical insights about the game, you can now make informed decisions if you aim to win Euromillions.

If combinations are equally likely, why do we have different frequency ratios?

Frequency Ratio: Understanding Your Advantage

Euromillions players cannot change the underlying probability or beat the game’s odds. But you can calculate all the possible outcomes and make the right decision based on those calculations.

And making intelligent choices is possible when you know the difference between odds and probability.

What is the difference?

Let me show you how they differ in terms of their formula:6

We use the formula below to express probability:

Probability is equal to the number of favorable combinations over the total number of combinations

And below is what we use to express odds:

Odds is equal to the number of favorable combinations over the difference between the total number of combinations and the favorable combinations

Probability measures the likelihood of an event, while odds are the ratio that compares the number of ways you succeed and fail. In mathematical parlance, odds refer to either odds in favor or against, but in the lottery, we normally use odds in favor or simply odds.

Consider the odds as the ratio of favorable to unfavorable shots.

Odds are the ratio of favorable to unfavorable shots. This is an important ratio when learning how to win the Euromillions

So, the difference between odds and probability is described in the following way:

Probability = Chance

Odds = Advantage

You cannot control the probability or beat the game’s odds, but you can at least choose better odds that are acceptable to you based on your risk tolerance.

The Mathematical Strategy is in Choosing Better Odds

Here in Lotterycodex, we suggest a more granular approach to winning the Euromillions. We use the composition of different combinatorial groups to measure varying odds. However, we do not use the term odds for combinatorial groups because this term is usually associated with winning and losing.

To avoid ambiguity and maintain consistency, we use the term frequency ratio to describe odds but at the same time highlight the relative frequency of each group, offering a clearer representation of favorable shots rather than framing it as winning or losing.

For example, there are 53,130 ways to combine five even numbers, so the frequency ratio is calculated to be 1 to 39.

Frequency Ratio (5-even) = 53,130/2,065,630 = 1:39

There are 690,000 ways to combine 3-odd and 2-even numbers. If we calculate the odds, we get:

Frequency Ratio (3-odd-2-even) = 690,000 / 1,428,760 = 1:2

To understand why you should choose one composition over the other, comparing them side by side can help.

This frequency ratio analysis for odd and even combinations shows that a 5-even combination will only occur 3 times in 100 draws. This frequency ratio comparison gives you a mathematical clue on how to win the Euromillions

Read How to Win the Lottery According to Math

As can be seen, if you play the 0-odd-5-even combination, you can expect to get three favorable shots after playing 100 draws. This means spending money on 100 draws for a measly three favorable shots.

On the other hand, if you play a more balanced 3-odd-2-even composition, you get one favorable shot and two unfavorable ones in three attempts. On average, you get 33 favorable shots in 100 attempts.

Let’s see how the frequency ratio can impact strategy over time.

Who gets the best shots in 20 years? Olive has a ratio of 1 to 2. Emma has a ratio of 1 to 39. Therefore, Olive gets 693 best shots while Emma gets only 52 in a span of 20 years.

Your job as a lotto player is to win the game; therefore, the last thing you want to do when playing Euromillions is to bet on a combination with an unfavorable frequency ratio. Read The Lotto Secret: The Math of Winning

Your goal is to win the lottery, and the first thing you should know when playing Euromillions is to peruse the frequency ratio. It’s all about getting the best shots possible and getting you closer to the jackpot. You cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you can make informed choices from a data-driven angle. Even choosing not to play lotto is a strategy by itself if you think the odds don’t go in your favor.

These varying frequency ratios help you understand how the Euromillions game behaves over time.

Of course, you cannot predict the next winning numbers. But you can predict the outcome of the Euromillions game to an extent based on the law of large numbers.7

Let’s peek at the past Euromillions results and see how the game follows the law of large numbers.

The Euromillions Game Follows the Dictate of Probability and the Law of Large Numbers

The Euromillions draws follow a consistent behavior over time.

The image of randomness shows streaks and clusters.
The picture above suggests that a true random draw provides sensible tips on making informed choices when playing the lottery. Know more: A Truly Random Lottery with a Deterministic Outcome.

From April 16, 2004, to March 15, 2024, there were 1,705 Euromillions draws. Therefore, we calculate the expected frequency by multiplying the probability by 1,705.

Expected Frequency = Probability X 1,705

In the case of the 3-odd-2-even composition with the probability of 0.3256621797655230, the expected frequency will be 555.

Expected Frequency(3-odd-2-even) = 0.32566 x 1,705 = 555

Doing similar computation with the rest of the odd-even groups, we will come up with a completed comparison table below:

This is Euromillions odd-even analysis as of March 15, 2024 with 1705 draws.  The graph shows apparent agreement between probability prediction and actual draws.

Read How to Win the Lottery According to Math

As you can see from the graph above, you should notice the agreement between the prediction and the actual results of the Euromillions game. The agreement proves that the Euromillions game follows the dictate of the probability and the law of large numbers.

Thanks to combinatorics8 and probability theory.9.

Certainly, you don’t need historical results to make such high-accuracy and high-precision predictions.

How to Choose the Best Euromillions Numbers

Earlier, we discussed that any questions we ask about the lottery must be a combinatorial and probability problem to solve.

However, combinatorial and probability calculations are complex and require proper methodology. If not done properly, analysis can only yield contradictory conclusions.

For example, 1-2-3-4-5 has a balanced mix of odd and even numbers, but notice that numbers are all low numbers. Therefore, it has poor composition. According to probability theory, a truly random draw distributes the probability across the entire number field.

Therefore, we must combine odd/even and low/high numbers into a single analysis.

We use the Lotterycodex sets below for Euromillions to accurately describe the fair distribution of probabilities across the entire number field.

knowing how to win the Euromillions requires proper combinatorial and probability calculations. These are the four sets of numbers to ensure fair distribution of probabilities across the number field of Euromillions. The sets are LOW-ODD, LOW-EVEN, HIGH-ODD, and HIGH-EVEN.

Read The Winning Lottery Formula Using Math

We extract different combinatorial compositions based on these sets and organize them into templates. This simplifies the number selection process.

Probabilistically speaking, only two of these templates will dominate the Euromillions draw over time.

To learn how to win the Euromillions, you must familiarize yourself with these Lotterycodex templates. Templates #1, and #2 are the dominant groups in this lottery game.

Generated by Lotterycodex calculator

The table above is straightforward. Patterns #1 and #2 are the most dominant groups in the game. You should play with these two templates if you want the best shots.

Predicting Euromillions

Use the calculator below and see a visual graph of how the Euromillions game will behave over time:



How To Win Euromillions Using Lotterycodex

Remember that purchasing multiple tickets is the only way to increase your odds of winning. There are two ways you can do such a strategy. Either use a lottery wheel or buy randomly chosen numbers.

A lottery wheel can trap the winning numbers strategically. This advantage is not achievable by buying tickets randomly.

Lotterycodex developed a lottery calculator as an advanced lottery wheeling system. This system distinguishes groups with varying frequency ratios, helping you make informed choices.

We recommend using templates #1 or #2 to get the best shot at winning the Euromillions game. According to the law of large numbers, these two templates will continue dominating as more lottery draws occur.

Look at the following prediction table below:

Template #1 dominates the Euromillions game overtime as more draws take place. Template #1 occurs 7 times, 138 times, and 345 times in 100, 2000 and 5000 draws respectively. While template #55 occurs only once in 2000 draws and only twice in 5000 draws.

Generated by Lotterycodex calculator

It’s not easy to win Euromillions. But based on this table, making an informed choice is easy. As a lottery player, you don’t want to spend your money on a group of combinations that will only occur twice in 5000 draws, as indicated by template #55.

But how do you know you’re not playing template #55?

Many Euromillions players are unaware of it. You can’t fix something you don’t know exists.

Realize that your likelihood of winning is not different from that of any other player. However, armed with mathematical insights about the game, you get more favorable shots for most draws if you play long enough.

Use that piece of mathematical information to your advantage.

If you hate math, use a Lotterycodex calculator to avoid manual calculations.

Remember, the lottery is just entertainment. If you get addicted to it, it can affect your life negatively in many ways.

Playing with the proper attitude and a lottery game plan would be best.

Save money for your entertainment, and please play the lottery responsibly.

Unlock Lottery Success with Proven Math-Based and Data-Driven Insights

Access Lotterycodex now!

Share Your Tips on How to Win Euromillions

Do you know how to win Euromillions? Please share your thoughts. I invite you to join the conversation. Here are some questions you might want to review for further discussion:

Thank you for reading 🙂

Explore more:

References

  1. Breakdown of the Euromillions odds    []
  2. All You Need to Know About Euromillions    []
  3. When to Trust Your Gut    []
  4. Introduction to the basic concepts of probability theory    []
  5. Do The Math, Then Burn The Math and Go With Your Gut    []
  6. What is the difference between odds and probability?    []
  7. Law of Large Numbers    []
  8. Combinatorics    []
  9. Probability Theory    []

25 thoughts on “How to Win Euromillions According to Math”

  1. Can we make an app for calculate the 3odd 2 even? That it just gives the user only 3odd 2 even conbinations?

  2. Useful and well explained.
    I would like to join a syndicate to play euromillions and improve the probabilities of winning.
    Thank you

  3. Why is it when I do the euro million,which ever number I pick Camelot pick the next number ie no 7 camelot picks number 8 if I pick 3 Camelot picks 4.this is definitely a fixed game.

  4. My own concern is “ Why is it that it’s the older people that mostly win the lottery
    2) Why must it be Up North always or far outside London
    3) Have seen people who have been playing for 10 years and more that has never win nothing
    4) is lottery a scam or is it real ?

  5. I too belive it is a scam. We checked online and found most winners were white and not many people of colour who also play the lottery regularly and in the Uk its mainly people up north and not Londoners. Do the research yourself if you dont believe me.

  6. Thank you for a most fantastic read, I was very impressed by your mathematics and equations.
    I used to pick the most overdue numbers , but never won .but reading your article I am now going to try the three odd two even number system.
    I do also try the hotpick (select three numbers ) to win.
    Does playing hot pick where you select few number make winning harder ? I would be fascinated to know.

  7. Very interesting, for all the years I played, I have been a total failure, so opted for lucky dips no joy there either.

  8. Do these probability theory and combinatorics patterns also apply in 6-digit game? Here in the Philippines, we have 5 6-digit lottery games namely 6/42, 6/45, 6/49, 6/55 and 6/58. Over two months ago, a 6/55 lotto draw had 433 winners with a jackpot of more than 200 million pesos (more than 4 million dollars) which to many like myself find it unbelievable or doubtful but turned out to be true or legit. It was a multiple of 9. The winning number was 9, 18, 24, 30, 36 and 42. It begun exactly with the lucky 9 number. How was that probable or indeed superstitious? Thanks.

  9. Hi OLA and Barry; all these lottery things you observed are dictated by probability. Most winners are old people because most lotto players are older people. The same holds that if more white people are playing, then by the law of large numbers, more white players win. It is that simple.

  10. There are millions of people in the uk and all the other countries that are in the euro why don’t they make the prizes smaller it would be better with prizes of £500,000 if you can’t survive on that you must stupid or greedy most people who win many millions end up getting divorced or unhappy or on drug’s because they don’t know how to handle large amounts of money £500,000 is enough for anyone in the world to survive on and why not put the price of a ticket down to £1 it’s just a cash cow thanks

  11. This is very interesting, Edvin. I always realised intuitively that it must be right to have your 5 numbers spread evenly across the low & high number sets, and across odds & evens. I’m not sure why this is, but I can definitely see that it makes sense in a gut-wise way. That’s why we never see combinations like 2,4,6,8,10, or 27, 29, 31, 33, 35.

  12. I’m a UK citizen and can play Euromillions quite easily but if I was to be abroad in Europe I cannot play the Euromillions as for some reason the rules layed down by the National lottery say I can’t because I don’t live in that European country I am in , yet Europeans can freely play it.
    Is that fair ?
    Also the prize money increases on a rollover but when you look at the amount of players both in the UK and Europe it doesn’t add up and somebody is making a vast amount of money.
    I don’t know why it is but I can tell my wife that it is going to rollover and I can also tell her when it’s going to be won and also the winners are mainly European people and not the UK.
    It’s the same with lotto , prize money for winning the jackpot on a Saturday night if you are a single winner is about 3.8 million pounds.
    If this rolls over to the following Wednesday the jackpot will pay to a single winner 4 million pounds , that’s an increase of 200k yet if it didn’t roll over to the Wednesday the prize money for a single winner is 2 million pounds , so where has the 1.8 million pounds disappeared to.
    It seems like the whole country is being conned.

  13. I play the lottery every week picking random numbers but i have never won an significant amount usually less than a fiver at very long intervals , i have tried different ways of picking numbers even going back to the fist draw ever on euro millions and trying to work out possibilities. So now i will try your lottery codex for euromillions and also work out my own from the information you have given me thank you Les.

  14. If lottery is completely random why haven’t 10 or 50 or 100 or a thousand people shared the jackpot in all the years it’s been running?

  15. The odds of winning the EuroMillions jackpot are 1 in 139.8 million, therefore you and everyone else have the same likelihood of winning. So, if 139.8 million players participate in the EuroMillions game today, there might be one winner tonight which is expected on average. However, it’s also possible to have multiple winners or no winner at all, because we cannot predict the outcome of a truly random draw. As the number of players increases, the possibility of splitting the jackpot increases. But given the odds, the chance that thousands of people sharing the jackpot is extremely low, though not impossible.

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