Lotterycodex Mathematics Meets The Lottery

How to Win the Eurojackpot 5/50 According to Math


You can improve your chances in the Eurojackpot if you know how math works in the lottery.

The EuroJackpot’s 5/50 game can produce a total of 2,118,760 combinations. However, winning the jackpot requires you to match two additional numbers, which makes the overall odds to 1 in 95 million.

The probability is terrible that you have a better chance of becoming the next elected leader in your town. And many players still don’t get it. Rather than relying on a scientific approach, many players stick to lottery playing methods that don’t work.

Fortunately, if you look deeply into how number combination works, there’s a way to improve the probability of winning the Eurojackpot. In this article, I will explain to you the mathematical method that will help improve your chances of winning.

how to win the Eurojackpot 5/50 according to mathematics

The Odds of Winning in Eurojackpot 5/50

The National Lottery Eurojackpot game is a 5/50 lottery game. So the rule is to pick five numbers from 1 to 50.  It is tough to win Eurojackpot because the odds of winning is one in 95 million.

Like I always say, the lottery is a random game. No one can predict the next winning combinations. However, Math offers an ingenious solution. You cannot predict, but undoubtedly, you can improve your chances.

The main reason why you are not winning the Eurojackpot is that you play with the wrong number pattern. Let’s talk about these Eurojackpot patterns now.

The Odd-Even Patterns In Eurojackpot

Mathematically, the odd and even numbers play a vital role in your chances of winning.  Pick the wrong odd-even pattern, and you are leaving the money on the table.

To illustrate, the table below shows the complete odd-even patterns 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 first two patterns are the best ones to play in Eurojackpot. I divide these 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 Eurojackpot players to focus on the best ones and avoid the rest. In Eurojackpot, the best odd-even patterns are 3-odd-2-even and 2-odd-3-even.  Then, the bad patterns are just waste of time and money.

Let’s prove this mathematically.

Odd-Even Patterns From The Actual Eurojackpot Results

In this section, I will compare the theoretical analysis with the actual lottery results of the Eurojackpot. My mathematical estimation should match closely with the actual lottery results. Otherwise, we will all end up here with the belief that winning the lottery is pure luck.
First, we need to compute the expected frequency of each pattern; we use the following formula:

Expected frequency = Probability X number of draws

There are 258 draws in Eurojackpot from March 23, 2012, to March 03, 2017. So in the case of 3-odd-2-even, we multiply 0.3256621797655230 by 258 draws.

Therefore, we get:

Expected frequency (3odd-2even) 
= 0.3256621797655230 x 258 
= 84.0208423795 or 84

We round up the numbers, so the final answer is 84.

Using the same computation for the rest of the odd-even patterns, we come up with the completed comparison table below:

Pattern Expected Frequency in 258 draws Actual Frequency in 258 draws
3-odd-2-even 84 97
2-odd-3-even 84 65
4-odd-1-even 39 47
1-odd-4-even 39 36
5-even-0-odd 6 11
5-odd-0-even 6 2

Probability estimation compared to actual lottery results of the Eurojackpot 5/50

As we can see, the comparison between expected frequency and actual frequency shows no big difference which proves that the lottery behaves in a particular trend.

Pure math shows that the best odd-even pattern to play in Eurojackpot is either 3odd-2even or 3even-2odd. The actual Eurojackpot results prove that Math works. Thanks to Probability. In fact, we use Probability to predict the lottery (to an extent)

For example, if we want to know in advance the outcome of Eurojackpot after 1000 draws, we use this formula below:

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


P(pt) x 1000 draws is the number of times pt is estimated to occur in 1000 draws.

If we continue to use the same formula for the rest of the patterns, we will come up with the following Eurojackpot predictions:

Pattern Probability Estimated Frequency in 1000 draws
3-odd-2-even 0.3256621797655230 326 times
2-odd-3-even 0.3256621797655230 326 times
4-odd-1-even 0.1492618323925310 149 times
4-even-1-odd 0.1492618323925310 149 times
5-odd-0-even 0.0250759878419453 25 times
5-even-0-odd 0.0250759878419453 25 times

The difference between the best and the worst patterns is huge. That is the basic idea of why I propose Math to play the Eurojackpot or any lottery system in the world. Because with probability, you know how to play Eurojackpot with a better chance of winning. But hang on, we can go deeper than just odd-even patterns.

Let me introduce to you now a better lottery pattern that will put your playing strategy to the next level.

The Best Number Pattern In EuroJackpot

Contrary to common belief, not all number combinations have the same probability of occurring in a lottery draw.

I took the chance to study The Geometry Of Chance proposed by Renato Gianella in 7 of the most popular lotteries in the world. The comparison between theoretical analysis versus the actual results of the lottery proves that Math is a powerful tool to predict the number patterns that will dominate the lottery.

In this article, I will show you the exact pattern in Eurojackpot that you should be playing to improve your chances of winning. Like I always do, I prove everything by comparing my analysis with the actual results.

The Eurojackpot patterns are divided into three groups.

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

From the table, there is only one best pattern in Eurojackpot, and that is pattern #1.

Let’s see the difference between the best and the worst pattern in Eurojackpot. Pattern #1 has a probability of 0.0424776756 which means this pattern occurs approximately 4x in every 100 draws. On the other hand, pattern #196 has a probability of 0.0000594687 which means this pattern is expected to occur five times in every 100,000 draws.

Pattern #1 has a probability of 0.0424776756 which means this pattern occurs approximately 4x in every 100 draws. On the other hand, pattern #196 has a probability of 0.0000594687 which means this pattern is expected to occur five times in every 100,000 draws.

On the other hand, pattern #196 has a probability of 0.0000594687 which means this pattern is expected to occur five times in every 100,000 draws.

Pattern Probability Expected occurrence
#1 0.0424776756 4x in every 100 draws
#196 0.0000594687 5x in every 100,000 draws

View the complete list.

If you want to play Eurojackpot to win, you would rather choose to play Pattern #1 and avoid pattern #196. In fact, I recommend to focus only on Pattern #1 and avoid the rest.

My analysis of the Eurojackpot shows there are 110 bad patterns that all lotto players must avoid at all cost.  Here are some examples of the worst patterns in Eurojackpot.

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

If you continue to play the Eurojackpot Lottery blindly, you will continue to fall into one of these bad patterns and waste money. But I guess you want to see the proof so let’s revisit the past Eurojackpot winning numbers.

Theoretical Probability Versus Actual Eurojackpot Results

Below is the comparison between probability estimation and the actual lottery results. The data are taken from the actual 258 draws of Eurojackpot from March 23, 2012, to March 03, 2017.

Pattern Probability Expected Frequency in 258 draws Actual Frequency in 258 draws
#1 0.0424776756 11 11
#2 0.0212388378 5 3
#3 0.0212388378 5 5
#4 0.0212388378 5 5
#5 0.0212388378 5 8
#102 0.0021238838 1 1
#103 0.0021238838 1 0
#104 0.0021238838 1 0
#105 0.0021238838 1 1
#106 0.0021238838 1 1
#186 0.0003964583 0 0
#187 0.0005946875 0 0
#188 0.0005097321 0 0
#189 0.0003964583 0 0
#196 0.0000594687 0 0

See the complete list

Knowing the number pattern you play has an impact on your chances of winning.  From the table above, you see that the expected frequency matches very closely to the actual occurrence. You don’t want to waste your money on pattern #196. Do you?

But most importantly, the table guides you on what number combination to play in the Eurojackpot.  You don’t want to waste your money on pattern #196. Do you?

Access to the lottery analysis section is free so so just check the Eurojackpot and pick what works for you.

How To Play Eurojackpot To Win

Play the Eurojackpot with greater chances of winning. Follow my recommendations below:

  1. Avoid the 0-odd-5-even and 0-even-5-odd combinations
  2. Focus on number patterns with high probability especially Pattern #1.

As always, just because you can use math to increase your chances of winning the Euro Jackpot, doesn’t mean winning is a surefire thing. Winning big jackpot comes only after a long streak of bad lucks so play the lottery with the proper attitude and with a proper game plan to prevent lottery addiction.

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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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