## The Odd-Even Patterns Based On The Actual EuroMillions Results

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

In this case, we want to know the frequency of each odd-even pattern. To take things up a notch, we will compare our calculation against the actual results of the EuroMillions.

There are 1,276 draws in EuroMillions from April 16, 2004, to February 4, 2020. Therefore, we calculate the expected frequency by multiplying the probability by 1,276 draws.

Expected Frequency = Probability X 1,276

In the case of 3-odd-2-even with the probability of 0.3256621797655230, the expected frequency will be 416.

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

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 probability principle.

- 3-odd-2-even is expected to appear 416 times – it occurred 461 times in the real draw.
- 4-odd-1-even is projected to appear 190 times – it appeared in 184 times in the actual draw.
- 0-odd-5-even is supposed to be drawn 32 times – it was drawn 31 times in the real draw.

Thanks to the power of probability. And you don’t need statistical analysis of the historical results to do such high-accuracy and high-precision prediction.

## Combinatorial Patterns in EuroMillions

Let me describe a mathematical method that will catapult you to Euro Million’s success. Deep within the finite sets of EuroMillions numbers are combinatorial patterns that should tell you the best combinations to play and the worst ones to avoid.

The image above describes the complete randomness of a lottery game. It shows that the lotteries are made up of independent random draws that, when put together with time, exhibit a mathematically deterministic behavior given the law of large numbers. See The Visual Analysis of a True Random Lottery with Deterministic Outcome

Let me clarify that we don’t need statistics to determine the best combinations in a lottery game. Statistics is not the right tool to analyze a lottery game.

So if statistical analysis will not provide the best clue, what will?

Well, since the lottery has a finite structure, any question that we ask is a combinatorial and probability problem to solve rather than statistical.

So instead of statistics, we need the concept of combinatorics and probability theory. These two mathematical tools will help predict the general outcome of the EuroMillions game from the perspective of the law of large numbers.

This prediction is possible because a truly random lottery follows the dictate of probability.

Again, we can explain this better from the context of combinatorial patterns.

For example, we can ask:

“What is the probability that the next winning numbers will be 1-2-3-4-5?”

To solve this question combinatorially, we can rephrase the question this way:

“What is the probability that the next winning numbers will be three-odds and two-even numbers?”

Can you see it? Composition matters.

And the composition of a combination is best described using a combinatorial pattern. You can look at combinatorial patterns in many different ways. There are simple patterns and there are Lotterycodex patterns.

We will talk about Lotterycodex patterns later (you don’t want to miss this section).

Let’s discuss the simple ones first.

## The Huge Difference Between Odds and Probability

Odds and probability are two different terms with two different equations. The difference between the two can be best describe when we study the composition of combinations.

As a lotto 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 choices and make the right decision based on those choices.

And making the right choice is possible when you know the difference between odds and probability.

What is the difference?

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

We normally expressed the results of this formula in percentage.

Now, to get the odds, we use this formula instead:

What you get from this formula is a ratio.

So the difference is that the probability is the measurement of chance while the odds are the ratio of success to failure.

In layman’s term, the difference between odds and probability can be described in the following way:

Probability = Chance

Odds = Advantage

That is, you cannot control the probability and you cannot beat the odds, but at least you can choose the best odds and get the best ratio of success to failure.

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

In the Euromillions game, there are 53,130 ways you can combine 5 numbers that are all even numbers and no odd numbers.

Therefore we calculate the odds of a 0-odd-5-even in the following way:

Odds of 5-even-0-odd = 53,130 / 2,065,630

This means that 2-4-6-8-10 and all similar combinations under the group of 0-odd-5-even will give you 2 or 3 opportunities to match the winning combinations for every 100 attempts that you play the Euromillions game.

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

In comparison, you will have a better ratio of success when you pick a more balanced odd and even numbers.

Let’s prove that.

There are 690,000 ways you can combine numbers of type 3-odd-2-even. If we calculate the odds, we get:

Odds of 3-odd-2-even = 690,000 / 1,428,760

In simple terms, a 3-odd-2-even combination will give you the opportunity to match the winning numbers 32 to 33 times in every 100 attempts that you play the Euromillions game.

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

0-odd-5-even VS 3-odd-2-even

0-odd-5-even | 3-odd-2-even |

2 to 3 opportunities to match the winning numbers in every 100 draws | 32 to 33 opportunities to match the winning numbers in every 100 draws |

The worst ratio of success | The best ratio of success |

The worst choice | An intelligent choice |

In a random event like the Euromillions game, making an intelligent choice requires mathematical strategy. We calculate all the possible choices and finally make an intelligent choice.

Remember this: As a EuroMillions player, your objective is to get a better ratio of success to failure. Know all the possible choices and make an intelligent choice.

I explained the details of this mathematical strategy in my article The Lottery and the Winning Formula of Combinatorial Math and Probability Theory.

But to give you a gist of how to make an intelligent choice, let’s dig deeper through these combinatorial patterns below.