How to Win Euromillions According to Math

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Last updated on March 21, 2024

Are you curious about how to win Euromillions? If so, stop using statistics and start using combinatorial mathematics and probability theory to understand how balls behave in a random draw.

From understanding the odds to selecting the best combinations, we will explore valuable insights into the science of making intelligent choices while clearing up some common myths and superstitions.

Ready to elevate your Euromillions strategy with math? If so, let’s begin.

Ebook image: how to win Euromillions according to Math

The Odds of Winning The Euromillions

Knowing how to win Euromillions requires understanding the game’s challenges. The National Lottery 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.

From another perspective, you have 139.8 million attempts to win the jackpot, playing one ticket for each draw. Then, if you purchase 100 tickets every week, you have 1.4 million weeks or 27,000 years to hit the jackpot.

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.

In short, my first lottery tip on how to win Euromillions is to 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, losing nth times raises this number to the power of n. For example, the probability that you lose 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, this 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 is very challenging, let alone winning the jackpot. So don’t believe if someone says you can profit from the Euromillions game by frequently winning small prizes.3

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.4

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.

Now, that begs the question: How do you win Euromillions when numbers and combinations have an equal probability of winning in a truly random game?

Well, here’s the answer.

The only way to increase your chances of winning is to buy more tickets. However, buying more tickets is useless if you’re making the wrong choices.5

If you want to win Euromillions, you must know how to make informed choices and be intelligent for most of the draws. Let me explain.

Follow the behavior of a random lottery game

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 every other number.

This combination is a bad idea and a waste of time and money.

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. That’s because the probability is fairly distributed between odd and even numbers. A random lottery game will not favor the even numbers or vice versa.

I don’t know about you, but I advise Euromillions players to choose numbers in a way that closely follows how winning lottery combinations are typically drawn.

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

However, if asked if they will buy ten tickets using the previously mentioned combinations, none will take the risk.

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.6

Your gut feeling should manifest your calculated knowledge about the game.7,8,9

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

Having a strong mathematical conviction for choosing or avoiding certain lines would be best.

Fortunately, this random behavior of a lottery game can be calculated mathematically to help you make informed choices. But to do this, you must use the right mathematical tools. Read on: How to Win the Lottery According to Math

That said, don’t rely on statistical analysis.

Shifting strategies from statistics to combinatorics and probability.

Statistical analysis is not ideally suited for Euromillions because of its finite structure.

We don’t use the tools of statistics when finite elements are involved because this 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 a lottery game are probability problems to solve rather than statistical ones.

So, we can ask, “What is the probability that the next combination will be 10-12-14-16-18?

We can rephrase this question into:

What is the probability of a combination composed of purely low numbers and all numbers are even?

We use combinatorial mathematics and probability theory to understand the behavior of lottery balls in a random setting. These two mathematical tools are essential in calculating the many possible outcomes of the game, offering valuable information for making informed choices. Read on: The Winning Lottery Formula Using Math

In the context of the Euromillions game, this information is represented using the success-to-failure ratio.

Success-to-Failure Ratio: Understanding the Dynamics of Success and Failure

As a Euromillions player, you don’t have the power to change the underlying probability, and you cannot beat the odds of the Euromillions game. But you have the power to know 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.

Odds and probability are two different terms, and they are not mathematically equivalent.10,11

What is the difference?

Probability refers to the measurement that an event will likely occur. We measure the likelihood by using the formula:

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

Meanwhile, odds compare the number of ways an event can succeed and the number of ways it can fail. To get the odds, we use this formula instead:

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

The difference is that probability is the measurement of chance, while odds describe the ratio of success to failure.

odds are the ratio between success and failure. This is an important ratio when learning how to win Euromillions

In simple terms, the difference between odds and probability can be described in the following way:

Probability = Chance

Odds = Advantage

You cannot control the probability or beat the game’s odds. But at least you can choose better odds that will be most favorable to you.

So, the mathematical strategy is in the act of choosing better odds.

Let’s consider the combination 2-4-6-8-10. This combination consists of 5 even numbers with no odd numbers. It belongs to the 0-odd-5-even group.

There are 53,130 ways to combine five even numbers in a 5/50 game format.

Therefore, we calculate the odds of a 5-even combination in the following way:

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

This means that a 5-even combination will give you 2 or 3 favorable shots of winning in 100 attempts, playing the Euromillions game.

As you can see, a combination such as 2-4-6-8-10 offers a very low success-to-failure ratio.

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

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

Simply put, a 3-odd-2-even combination will give you 33 favorable shots in 100 attempts.

If we compare the two classes of combinations, we can see a big difference:

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

The way to explain the table above is that if you play the 0-odd-5-even combination, then expect that you have 2 million ways to fail, and thereby you have less opportunity to win.

On the other hand, if you play a more balanced combination, such as a 3-odd-2-even, you have more favorable shots to win.

Because there are more 3-odd-2-even combinations in the Euromillions game than 5-even combinations, lotto draws tend to pick combinations from this dominant group.

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 success-to-failure ratio.12

In a random event such as the Euromillions game, making an intelligent choice requires understanding varying success-to-failure ratios.

It’s all about getting more favorable shots.

Your goal is to win the lottery, and the first thing you should know when playing Euromillions is to know your success-to-failure ratio. You cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you have the power to make informed choices. Even choosing not to play lotto is a strategy by itself if you think the odds don’t go in your favor.

These varying success-to-failure 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.13

Let’s peek at the past Euromillions results and see how the game follows the probability dictate.

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

The results of each lottery draw are random, but when you look at many draws over time, the game follows a consistent trend. This is due to the law of large numbers, which means that the more draws you have, the more the results match what’s probabilistically expected. This shows that the Euromillions game follows the rules of probability theory.

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.

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

Thanks to the power of combinatorial math and probability theory.14,15

You don’t need statistical analysis of the 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.

The problem is that two different questions may provide contradictory answers.

This contradiction happens because combinatorial and probability calculations are complex and need a proper methodology for an accurate conclusion.

For example, not all combinations in the 3-odd-2-even group have a favorable success-to-failure ratio. The combination 1-2-3-4-5 is one such example.

Understanding the nature of a random lottery game, we know that 1-2-3-4-5 cannot have a favorable success-to-failure ratio. Thus, we recommend avoiding this combination.

We must perform combinatorial mathematics and probability calculations correctly to achieve accurate results.

Lotterycodex uses the following sets for Euromillions to accurately describe the fair distribution of probabilities across the number field.

knowing how to win 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.

Generated by Lotterycodex calculator

Based on Lotterycodex calculations, only two of 56 combinatorial compositions are dominant groups that will give the most favorable success-to-failure ratios.

We use templates to represent the compositions of each group. This simplifies the process of number selection for Euromillions players.

Euromillions are divided into three combinatorial groups:

To learn how to win 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 very straightforward. Use patterns #1 and #2 and get the best shot possible.

If you want to know the compositions of these templates, check our Lotterycodex calculator.

How To Win Euromillions Using Lotterycodex Templates

Remember that purchasing multiple tickets is the only way to increase your odds of winning. However, employing a lottery wheel instead of randomly buying tickets could improve this strategy. A lottery wheel, rooted in mathematical principles, is designed to trap the winning numbers strategically. This advantage is not achievable by buying tickets randomly. Discover more here: Lottery Wheel: A Clever Mathematical Strategy That Works.

We developed the Lotterycodex calculator as an advanced lottery wheeling system. This system distinguishes groups with varying success-to-failure ratios, helping you make informed number selection choices. Learn more about this technique: Lottery Calculator: A Mathematical Guide Beyond Number Selection.

We recommend using templates #1 or #2 to get the best shot at winning the Euromillions game. These two templates are the dominant groups that will give you the most favorable success-to-failure ratio.

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:

Generated by Lotterycodex calculator

It’s not easy to win the 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 about twice in 5000 draws, as indicated by template #55.

A lot of Euromillions players are doing it all wrong. Don’t be one of them.

If you hate math, you can use a Lotterycodex calculator to avoid manual calculations.16 But not all calculators are equal. You have to use a calculator that puts combinatorics and probability theory together in one system.17

Remember, the lottery is just entertainment. Please understand that lottery addiction can affect your life negatively in many ways.18

You must play with the proper attitude and a lottery game plan.19 Save money for your entertainment, and please play the lottery responsibly.20

Share Your Tips for Playing 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:

How do you play EuroMillions?

The basic rule of the EuroMillions lottery involves selecting five main numbers from 1 to 50 and two Lucky Stars from 1 to 12. To win the jackpot, a player’s chosen numbers must match all numbers drawn, including both main numbers and Lucky Stars.

Can statistics predict EuroMillions winning numbers?

Statistics cannot reliably predict the next winning numbers in Euromillions due to the random nature of the lottery draw. Each number has an equal chance of being selected in any given draw. Therefore, while statistical analysis can provide insights into past draws, it does not influence or predict future outcomes. The randomness inherent in the lottery draw means that all numbers, regardless of previous draws, have the same probability of being drawn next.

How do odds differ from probability?

In the context of the lottery, the difference between odds and probability is significant. Probability refers to the likelihood of a specific outcome occurring. It’s expressed as a ratio of the number of favorable outcomes to the total number of possible outcomes. In contrast, odds compare the chances of success to the chances of failure. It’s the ratio of the number of ways an event can occur to the number of ways it cannot. In lotteries like Euromillions, understanding this distinction is crucial for players who apply mathematical principles to their strategies.

What’s the best strategy to boost Euromillion winning odds?

The best strategy to increase your chances of winning in Euromillions is to buy more tickets. But buying multiple tickets can be useless if you’re not making informed choices. That’s why I suggest using combinatorial mathematics and probability theory when learning how to win Euromillions. This involves understanding the composition of number combinations and choosing those with the best success-to-failure ratio. While no strategy can guarantee a win due to the lottery’s random nature, this approach allows for more informed and mathematically sound choices, potentially giving you more favorable shots.

How can you predict the exact winning numbers in Euromillions?

It is not possible to predict the exact winning numbers in Euromillions. The lottery is designed to be completely random. This randomness means that all numbers have an equal probability of being drawn, regardless of the numbers drawn in the past or any patterns observed. Therefore, while players can use strategies to improve their chances, accurately predicting the winning numbers is not feasible.

Thank you for reading :)

Additional Resources

  1. Breakdown of the Euromillions odds    []
  2. All You Need to Know About Euromillions    []
  3. The Truth About Winning Small Prizes in the Lottery    []
  4. 10 Lottery Strategy Myths Debunked    []
  5. Why Buying Hundreds of Lotto Tickets Can Be Useless    []
  6. Introduction to the basic concepts of probability theory    []
  7. When to Trust Your Gut    []
  8. Developing Your Intuition For Math    []
  9. Do The Math, Then Burn The Math and Go With Your Gut    []
  10. Odds and Probability Explained in the Context of a Lottery Game    []
  11. What is the difference between odds and probability?    []
  12. The Lotto Secret: Three Math Strategies for Winning Revealed    []
  13. Law of Large Numbers    []
  14. Probability Theory    []
  15. Combinatorics    []
  16. Lottery Calculator: A Mathematical Guide Beyond Number Selection    []
  17. A Lottery Number Generator That Works    []
  18. Lottery Addiction – Signs, Dangers, and Where To Get Help    []
  19. The Lottery Game Plan    []
  20. Play The Lottery Responsibly    []

23 comments

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

  • 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.

  • 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 ?

    • 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.

    • 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.

  • 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.

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

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

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