Lotterycodex Mathematics Meets The Lottery

How to Win the Euromillions 5/50 According to Math


If you are like the majority of the Euromillions players who pick numbers randomly or by quick pick, you are wasting money. Truth be told, there are worst number combinations in Euromillions that will never appear in any draw.

Many lotto players have this idea of using birth dates of their sons and daughters, select dates in their life like anniversaries, lucky numbers, horoscope numbers, and even hot numbers, etc., etc. That makes me think, 80 to 90% of Euromillions players are doing it wrong.

I recommend you start playing the Euromillions with the use of Math. You will never play the Euromillions the same way again, once you understand the mathematical method of playing the lottery. Let’s begin.

how to win the Euromillions 5/50 according to Math

The Odds of Winning The Euromillions

The National Lottery Euromillions game is a 5/50 lottery format. So the rule is to pick five numbers from 1 to 50. We compute the total combinations by using the Binomial Coefficient formula.


n = 50 numbers

r = 5 combinations

50C5 = 2,118,760

So now we know that there are 2 million possible ways to combine numbers in Euromillions. In simple terms, the odds are said to be 1 to 2 million. However, to win the jackpot, you are required to match the lucky stars so that the actual odds now become 1 to 116.5 million chances.

If you think about your odds, you have a better chance of becoming the next Prime Minister of U.K. In short; it is tough to win in the Euromillions.

The Euromillions lottery is a random game. The same holds true for all the lottery systems in the world. You cannot predict the next Euromillions winning numbers. So how do we beat the odds of the Euromillions?

You cannot beat the odds of Euro Millions.  But you can improve your probability of winning.

The solution is to look at the Euromillions number patterns in a different perspective. Let’s first discuss the odd-even patterns.

The Odd-Even Patterns In the Euromillions

Mathematically, odd-even patterns do have an impact on your chances of winning. The table below shows the complete odd-even patterns in Euromillions with their corresponding probability:

Patterns Probability Calculus
3-odd-2-even 0.3256621797655230 32.5662179766%
3-even-2-odd 0.3256621797655230 32.5662179766%
1-odd-4-even 0.1492618323925310 14.9261832393%
1-even-4-odd 0.1492618323925310 14.9261832393%
5-odd-0-even 0.0250759878419453 2.5075987842%
5-even-0-odd 0.0250759878419453 2.5075987842%
1 100%

The table shows that the first two are the best ones to play in Euromillions. I further divide the patterns into three groups:

Best Patterns Fair Patterns Bad Patterns
3-odd-2-even 1-odd-4-even All-even-numbers
2-odd-3-even 1-even-4-odd All-odd-numbers

Based on the table above, I recommend playing either the 3-odd-2-even or the 2-odd-3-even pattern. Let’s peek at the past Euromillions results and see how I came up with such conclusions.

The Odd-Even Patterns Based On The Actual Euromillions Results

Remember that in the list of the odd-even patterns above, we also included the probability. We use the Probability value to determine how likely an event will happen in a given period.

In this case, we would like to estimate the frequency of each odd-even pattern. To take things up a notch, we will compare the estimated frequency of each odd-even pattern against the actual in Euromillions.

There are 970 draws in Euromillions from April 16, 2004, to February 28, 2017. Therefore, we estimate the frequency by multiplying Probability by 970 draws.

Expected Frequency = Probability X 970

In the case of 3-odd-2-even with the Probability of 0.3256621797655230, the expected frequency will be 316.

Expected Frequency(3-odd-2-even) 
= 0.3256621797655230 x 970 = 315.892314373
or 316

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

Pattern Expected Frequency in 970 draws Actual Frequency in 970 draws
3-odd-2-even 316 354
2-odd-3-even 316 291
4-odd-1-even 145 140
1-odd-4-even 145 140
All-even 24 25
All-odd 24 20

If we compare the expected frequency with the actual frequency, you will see that values are very close.

Probability estimation compared to actual Euromillions 970 draws

The comparison between expected frequency and actual frequency shows no big difference which proves that Euromillions behaves in a predictable pattern. We use Mathematics to determine trending patterns.

  • 3-odd-2-even is expected to appear 315x – it occurred 354 times in the real draw.
  • 4-odd-1-even is projected to appear 140x – it appeared in 144 times in the actual draw.
  • 0-odd-5-even is supposed to be drawn 24x – it was drawn 25 times in the real draw.

Thanks to the predictive power of Probability.

Naturally, the expected frequency and the actual frequency will not always match exactly, but I hope you are getting the power of Probability to predict the lottery (to an extent).

For example, if we want to know in advance the outcome of Euromillions after 2000 draws, we use this formula below:

If P(pt) = is the probability of pattern pt,


P(pt) x 2000 draws = the number of times this pattern is estimated to occur in 2000 draws.

If we are to predict the outcome of all the odd-even patterns, we will come up with the following table below:

Pattern Probability Estimated Occurrence in 2000 draws
3-odd-2-even 0.3256621797655230 651 times
2-odd-3-even 0.3256621797655230 651 times
4-odd-1-even 0.1492618323925310 299 times
4-even-1-odd 0.1492618323925310 299 times
All-odd 0.0250759878419453 50 times
All-even 0.0250759878419453 50 times

As a smart Euromillions player, you don’t want to waste your money on patterns with low probability. That is the power of probability as we apply it in Euromillions and any lottery system in the world. Let’s discuss now more complex and better patterns.

The Best Number Pattern In Euromillions

Renato Gianella proved that not all number combinations have equal chances of occurring in the lottery in his study The Geometry Of Chance. I have conducted studies of the lottery based on Gianella’s probability method, and here I will show the best pattern to play in Euromillions.

Of course, like I always do, I will prove everything using the actual Euromillions draw.

For simplicity sake, I have divided Euromillions patterns into three groups.

Group Patterns Number of patterns
Best group #1 1
Fair group From #2 to #86 85
Bad group From # 87 to #196 110
196 total patterns

Based on these groups, you have an idea now that pattern #1 is the best one to play in Euromillions. To illustrate this further, the pattern #1 has a probability of 0.0424776756 which means this one occurs approximately 4x in every 100 draws.

To illustrate this further, the pattern #1 has a probability of 0.0424776756 which means this one occurs approximately 4x in every 100 draws. While pattern #170 has a probability of 0.0005663690 which means it is expected to occur only once in 2,000 draws.

Pattern Probability Expected occurrence
#1 0.0424776756 4x in every 100 draws
#170 0.0005663690 Once in 2,000 draws

If you want to play Euromillions to win, then pick your numbers based on pattern #1 and stay away from pattern #170. In fact, my recommendation is to avoid the rest of the patterns and simply focus your energy on pattern #1 only.

The problem, almost 90% of the lotto players, do not know the worst combinations that will put their money down the drain. For example, here are the worst combinations in Euromillions:

Pattern Probability Expected Occurrence
#166 0.0005946875 Once in 1,600 draws
#182 0.0005097321 Once in 2,000 draws
#186 0.0003964583 Once in 2,500 draws
#190 0.0001189375 Once in 10,000 draws
#194 0.0000991146 Once in 10,000 draws
#196 0.0000594687 Once in 16,600 draws

View the complete list of these patterns. Access to the private section is absolutely free.

If you are playing blindly, there’s no guarantee you are not falling into one of these worst patterns in Euromillions. So I propose to use Probability analysis when you play the Euromillions for two reasons:

1. You save money
2. You improve your chances of winning

This is how Mathematics meets the lottery. Let me show you the proof.

Theoretical Analysis Versus Actual Euromillions Results

Below is the comparison between the expected frequency and the actual frequency for each of the pattern in Euromillions. The data covers the real 970 draws of the Euromillions from April 16, 2004, to February 28, 2017.

Pattern Probability Expected Frequency in 970 draws Actual Frequency in 970 draws
#1 0.0424776756 41 41
#2 0.0212388378 21 16
#3 0.0212388378 21 22
#4 0.0212388378 21 21
#5 0.0212388378 21 21
#102 0.0021238838 2 2
#103 0.0021238838 2 2
#104 0.0021238838 2 3
#105 0.0021238838 2 1
#106 0.0021238838 2 1
#186 0.0003964583 0 1
#187 0.0005946875 0 0
#188 0.0005097321 0 0
#189 0.0003964583 0 0
#190 0.0001189375 0 0

See the complete list

As you see, the expected frequency is very close to the actual frequency.

Knowing your number pattern has an impact on your chances of winning as the difference between #1 and #190 is so huge. You don’t want to take it for granted. The truth is, pattern #1 will always appear the best.

How To Play Euromillions To Win

To play the Euromillions with greater chances of winning, follow these strategies:

  1. Avoid the all-odd-number, and all-even-number combinations
  2. Focus on pattern #1 and avoid the rest

But remember, the lottery is just an entertainment. Please understand that lottery addiction can affect your life negatively in many ways. Using a mathematical approach is not a surefire thing to beat the odds of the lottery. Nothing or no one can beat the lottery.

The odds of the lottery doesn’t change.  But you can improve your chances of winning through probability theory.  However, you have to play with the proper attitude and with a proper lottery game plan. Please play the lottery responsibly.

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Lotterycodex Mathematics Meets The Lottery

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Edvin Hiltner

I study maths. I get a good grasp of it through persistent learning. I get my inspirations from the works of Gerolamo Cardano and Renato Gianella in the fields of Combinatorics and Probability theory.

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