How to Use Math to Increase Your Chances of Winning the Lottery


I can almost guarantee 99% of lotto players always pick the wrong combination each draw. And you are probably one of them.

First off, before we proceed, if you want to jump quickly into the heart of what we are doing here, then go straight to the lottery analysis section where you will discover the bad, the worst, and the best number combinations in the lottery.

However, if you want to engage yourself deeply into the nitty-gritty aspect of combinatorics and probability theory, then proceed below.

In the lottery, millions of number combinations will never appear in any draw no matter how many times you play them. For example, the 1-2-3-4-5 or 1-2-3-4-5-6 has never appeared in the history of the lottery.  And any number combination that follows similar pattern will never appear in the lottery according to Math.  I will prove it in this article.

Here are some combinations almost identical to 1-2-3-4-5-6:

  • 2-3-4-5-6-7
  • 3-4-5-6-7-8
  • 4-5-6-7-8-9
  • 1-3-5-7-9
  • 2-4-6-8-9
  • 3-4-6-7-8

And here are some combinations of similar patterns:

  • 12-13-14-17-18-19
  • 20-23-25-27-28-29
  • 33-35-36-37-38-39
  • 40-42-45-48-49

The chances of these number patterns are meager that they will not occur in the lottery, never. Definitely, not in your lifetime or your grandsons’ or granddaughters’ lifetime.

Let me tell you the bad news, the lottery has millions of bad number combinations, and if you play the lottery, you may have been wasting your money on these bad numbers your whole life.

Why? The best way to explain this is through Mathematical reasoning. The 1-2-3-4-5-6 and those identical combinations belong to a number pattern that has the least likelihood of appearing.

See the likelihood of their occurrences in 6 ball lottery games below:

Lottery Possible Occurrence of 1-2-3-4-5-6 and those with identical number pattern
UK Lotto 2 times in 1,000,000 draws
Irish Lottery 7x in 1,000,000 draws
Tattslotto once in 100,000 draws
Any lotto 6/49 game 6 times in 1,000,000 draws

And here is the likelihood of them occurring in 5 ball lottery games:

Lottery Possible Occurrence of 1-2-3-4-5 or those with identical number pattern
US Powerball once in 100,000 draws
Euromillions 5 times in 100,000 draws
US Mega Millions 7x in 1,000,000 draws
Eurojackpot 5 times in 100,000 draws

The tables show that the likelihood of the 1-2-3-4-5 or the 1-2-3-4-5-6 appearing in a lottery draw is almost “impossible.”

How do I know? I use a Mathematical tool called the Probability Formula. That is how Science meets the Lottery. In fact using the same Mathematical tool, you can learn to play the lottery with better odds of winning.

However, the majority of lottery players do not know how to play. People keep on playing the wrong pattern. Below is a graphic representation of why the majority of players do not win the lottery.

A graph showing why majority of lotto players do not win by playing number combinations that never appear in the lottery.

Many players are unaware of the number patterns that simply don’t have any chances in the lottery, and they have been wasting money on these useless combinations their whole life. To know what number combination works in the lottery, we need to study and apply the Probability theory.

Let’s discuss now how probability works in the lottery.

The Probability Theory and the Lottery

One way to find out if a number combination has any chance of getting drawn in a lottery is through the use of probability theory. Let me start this discussion with a simple example of 9 black marbles and 40 white marbles. If you blindfold someone and ask to pick a marble, what color do you think will get picked on the first try?

It doesn’t require someone to be more mathematically inclined to know that white is the answer. It is because the probability is more likely leaning towards the white marbles.

However, we deserve a better explanation than just mere assumption.  What is the point of using math if we don’t compute?  So let’s start computing.  The table below will show you the probability of each color getting picked in a random event:

Marbles Probability
Black 9/49
White 40/49

The table above shows that you pick black marbles 18.37% of the time while you pick white 81.63% of the time.

In layman’s term, the probability means:

You get approximately 18 black marbles in every 100 draws.

You get approximately 82 white marbles in every 100 draws.

Using this simple black and white marbles, you will see how Probability principle works in Mathematics.

Of course, the above example is far from how the real lottery works. So let’s take this marble example up a notch.

What is the chance of picking six black marbles?
What is the chance of picking six white marbles?

Now, the problem gets a little bit complex, but at least it is closer to how the lottery works. So, let’s group black and white marbles into the following sets:

Black marbles = {1,2,3,4,5,6,7,8,9}

White marbles = {10,11,12,13,...,49}

We can come up with many different possibilities:

Pattern Sample combination
6 Black 1-2-3-4-5-6
5 Black + 1 white 1-2-4-5-9-38
4 Black + 2 White 2-3-7-8-26-42
3 Black + 3 White 1-3-9-11-20-48
2 Black + 4 White 4-8-14-31-43
1 Black + 5 White 6-12-23-39-40-44
6 White 10-12-23-39-40-49

Our next objective is to determine the number of favorable combinations for each pattern. Such objective can be performed using Binomial Coefficient:

nCr = n! / r!(n-r)!

Therefore, we can complete the following table below:

Pattern Favorable Combinations
6 black marbles 84
5 black marbles + 1 white 5,040
4 black marbles + 2 white 98,280
3 black marbles + 3 white marbles 829,920
2 black marbles + 4 white marbles 3,290,040
1 black marbles + 5 white marbles 5,922,072
6 white marbles 3,838,380

Now we have enough data to compute the likelihood of an event to happen. In our case, we are looking for the likelihood of six black marbles to appear versus that of the six white marbles. We do this using the Probability Formula.

P(A) = Number of favorable outcomes / total number of possible outcomes


P(6 black marbles) = 84 / 13,983,816

= 0.00000600694 or 0.000600694%

P(6 white marbles) = 3,838,380 / 13,983,816

= 0.27448730732 or 27.448730732%

So now, we can answer our previous questions:

Pattern Probability
What is the chance of picking six black marbles? 0.000600694%
What is the chance of picking six white marbles? 27.45%

Or in Layman’s term, we get:

Pattern Occurrence
Six black marbles 6 times in every 1,000,000 draws
Six white marbles 27 times in every 100 draws

From the table above, we can see 1-2-3-4-5-6 which represents one of the six black marbles will not likely happen during a draw. In short, almost “impossible.”

Isn’t this the same reason 1,2,3,4,5,6 doesn’t appear yet in the history of the lottery? It is. Too sad, according to the report by the DailyMail, about 10,000 people play this combo every week. Mathematically, this is just – “waste of money.”

But contrary to popular belief, 1-2-3-4-5-6 is not the worst combination in the Lottery. In a lotto 6/45 game, the worst is 40-41-42-43-44-45. However, whether it’s the worst or just one of the useless combinations, the idea remains, you should never play them. Plain and simple.

In probability, you have the power to know what combinations to avoid.

Probability Knows the Bad, the Worst, and the Best Combinations In The Lottery

So many lottery myths exist and from this point on, let me debunk the popular belief that each number combination has an equal probability of getting drawn. It’s not true, and I will prove it to you if you continue to read.

The equal probability exists on individual numbers. However, the probability differs when numbers are combined together. In short, each combination in the lottery has different chances. There will be combination patterns that will appear more frequently than others.

Below are some examples of bad number combinations in the lottery:


I can list millions of these, and we will run out of space. If you have been playing the lottery, you could have been falling into one of these bad combinations and their similar variations. You get the gist, but we will get to that later.

Now, let’s talk about probability analysis as we apply it in a real-world lottery.

Odd and Even Number Combination Pattern in the Lottery

To apply Probability in a real-world lottery game, first, we need to know the rules of the game. For example, in U.S. Powerball, you pick five numbers from 1 to 69. In UK Lotto, you pick six numbers from 1 to 59. In some lottery systems, the game requires you to pick six numbers from 1 to 49.

Probability analysis differs from each lottery format. For the sake of discussion, I will use Euromillions here and then I will use the Actual lottery results to prove my Probability computation. Then, progressively, we will go ahead with other popular lotteries.

In Euromillions, you pick five numbers from 1 to 50. With this lotto format, we come up with the following number sets:

Odd numbers = {1,3,5,7,9,11,...,49}

Even numbers = {2,4,6,8,10,...,50}

In Euromillions, there are 25 odd and 25 even numbers. Below are examples of number combinations using the odd and even pattern:

Pattern Sample Combination
2-odd-3-even 4-12-5-24-17
3-odd-2-even 9-22-31-44-49
All-odd 9-13-21-43-47
All-even 4-14-22-36-50

The following table will show you the complete list of possible patterns and the corresponding probability:

Patterns Probability
3-odd-2-even 0.3256621797655230
3-even-2-odd 0.3256621797655230
1-odd-4-even 0.1492618323925310
1-even-4-odd 0.1492618323925310
5-odd 0.0250759878419453
5-even 0.0250759878419453

Now with the above table, we now have enough data to determine how Euromillions behave over time in Euromillions actual draws from April 16, 2004, to February 28, 2017.

Using the probability formula, we can determine the estimated frequency for each of the Odd and Even number pattern in Euromillion’s 970 total draws:

Estimated frequency = 970 X Probability

In the case of 3-odd-and-2-even, we multiply 0.3256621797655230 by 970 draws.

Therefore, we get:

Estimated frequency (3 odd and 2 even) = 315.892314373 or 316

So let’s recreate the complete table and this time, I include an additional column for estimated frequency.

Patterns Probability Estimated Frequency
3-odd-2-even 0.3256621797655230 316
3-even-2-odd 0.3256621797655230 316
1-odd-4-even 0.1492618323925310 145
1-even-4-odd 0.1492618323925310 145
5-odd 0.0250759878419453 24
5-even 0.0250759878419453 24
1 970

Now, right before your own eyes, I’ll prove to you that our estimation matches extremely close to the actual data. Below is the comparison between theoretical estimation and the actual frequency from the actual Euromillions 5/50 results.

The Actual Results of the Euromillions 5/50

Patterns Estimated Frequency
in 970 Draws
Actual Frequency
in 970 Draws
3-odd-2-even 316 354
3-even-2-odd 316 291
1-odd-4-even 145 140
1-even-4-odd 145 140
5-even 24 25
5-odd 24 20
970 970

A total of 970 draws from April 16, 2004, to February 28, 2017

Probability estimation compared to actual Euromillions 970 draws

Read: How To Win The Euromillions 5/50 According To Math

Looking at the probability analysis table above, you can see that the estimation is very close with the actual lottery results.  That is the power of probability.  So, with all these probability discussions, we can come up with some conclusions, but perhaps the most important takeaway is this:

Playing with the wrong pattern is just a “waste of money.”

From the words of the late Gail Howard:

That which is MOST POSSIBLE happens MOST OFTEN.
That which is LEAST POSSIBLE happens LEAST OFTEN.

But hang on, how many Euromillions players are mindful of the number patterns when they pick numbers? Very few.  Now that you know how probability can be used to determine the worst patterns in the lottery, let’s take a look at now the results of my probability analysis for other popular lotteries below.

The Actual Results of the Australian TattsLotto 6/45

Pattern Estimated Frequency
in 582 Draws
Actual Frequency
in 582 Draws
3- odd-and-3-even 194.88 187
4-odd-and-2-even 146.16 154
2-odd-and-4-even 132.24 143
5-odd-and-1-even 52.90 50
1-odd-and-5-even 43.28 39
6-odd 7.21 5
6-even 5.33 4
582 582

A total of 582 draws from January 7, 2006, to March 04, 2017

Probability estimation compared to actual results of the TattsLotto 6/47

Read: How To Win The TattsLotto 6/45 According To Math

The Actual Results of the EuroJackpot 5/50

Pattern Estimated 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 6 11
5-odd 6 2
258 258

A total of 258 draws from March 23, 2012, to March 03, 2017

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

Read: How To Win The Eurojackpot 5/50 According To Math

The Actual Results of the Irish Lottery 6/47

Patterns Estimated frequency
in 155 draws
Actual frequency
in 155 draws
3-odd-3-even 51.7433613723 53
4-odd-2-even 38.8075210292 42
2-odd-4-even 35.279564572 37
1-odd-and-5-even 11.6575952499 10
5-odd-1-even 14.1118258288 9
6-odd 1.94293254165 1
6-even 1.45719940623 3
155 155

A total of 155 draws from September 5, 2015, to March 01, 2017

Probability estimation compared to actual Irish Lottery 6-47 results

Read: How To Win The Irish Lottery 6/47 According To Math

The Actual Results of the U.S. Mega Millions 5/75

Patterns Estimated frequency
in 353 draws
Actual frequency
in 353 draws
3-odd-2-even 115 128
2-odd-3-even 112 98
4-odd-1-even 56 58
1-odd-4-even 51 53
5-odd 10 8
5-even 9 8
353 353

A total of 353 draws from October 22, 2013, to March 07, 2017

Probability estimation compared to actual U.S. Megamillions 5-75 results

Read: How To Win The US Mega Millions 5/75 According To Math

The Actual Results of the U.S. Powerball 5/69

Patterns Estimated frequency
in 146 draws
Actual frequency
in 146 draws
3-odd-2-even 48 42
2-odd-3-even 46 43
4-odd-1-even 23 27
1-odd-4-even 21 30
5-odd 4 2
5-even 4 2
146 146

A total of 146 Draws from October 7, 2015, to March 04, 2017.

Probability estimation compared to actual results of the U.S. Powerball

Read: How To Win The US Powerball 5/69 According To Math

The Actual Results of the UK Lotto 6/59

Patterns Estimated frequency
in 147 draws
Actual frequency
in 147 draws
3-odd-3-even 48 44
4-odd-2-even 36 42
2-odd-4-even 34 36
5-odd-1-even 13 10
1-odd-5-even 12 10
6-odd 2 4
6-even 2 1
147 147

A total of 147 Draws from October 10, 2015, to March 08, 2017

Probability estimation compared to the actual results of the UK lotto 6/59

Read: How To Win The UK Lotto 6/59 According To Math

The complete list of all these lottery analyses is available for free at the lottery analysis section. Choose your favorite lottery and implement what works the next time you play. Everything is calculated for you.

The Lottery can be Predicted to an Extent

As the evidence unfolds from our study of the odd and even numbers in the Lottery, we can say that the lottery behaves in a predictable pattern. Therefore, the lottery could be predicted to an extent, according to Math.

But the lottery is not all about odd and even numbers. There is more to the lottery than meets the eye. If you study the winning numbers of the lottery very deeply, you will discover winning patterns that could be the key to your lottery success.

Now, let’s talk about a better strategy.

The Geometry of Chance

One school of thought tells us that a sure-fire way to win the lottery is to buy all the tickets. Right? Correct. However, it’s not practically feasible, and no one with the right mind will do it.

If you remember, at the beginning of the article I made mention of number combinations that are destined not to appear in any draw. Using these number combination is a waste of money.

From the mathematical perspective, the way to increase your chances of winning a big jackpot is to play the number pattern that carries the best probability.

How do we know the best and the worst number patterns in the lottery?

I use the method proposed by Renato Gianella from his study called The Geometry of Chance. I am going to talk about the Geometry Of Chance in a separate article. In this article, I’ll show you how I use The Geometry of Chance to determine best numbers so that your chances are more leaning on the winning side.

For example, there are 2 million playable number combinations in Euromillions 5/50. Using Gianella’s method, we can reduce this number into 196 manageable templates. From these templates, I use Probability formula to determine the best, the fair and the worst number patterns to play. Let’s take a look at the patterns below:

The Best Patterns The Fair Patterns The Worst Patterns
Pattern #1 Pattern #2 to #86 Pattern #87 to #196

There are 196 patterns in Euromillions, and only one is the best.

In Mathematics, once we get the probability we have the power to predict how likely an event will perform over time. So let’s pick some of these patterns from The Euromillions 5/50.

Pattern Probability
#1 0.0424776756
#20 0.0169910702
#89 0.0025486605
#119 0.0019114954
#196 0.0000594687

I know the numbers sound dull. Doesn’t it? Let me convert those probability numbers in layman’s term.

Pattern Occurrence
#1 4x in every 100 draws
#20 2x in every 100 draws
#89 2x in every 1,000 draws
#119 2x in every 1,000 draws
#196 5x in every 100,000 draws

So obviously it is pattern #1 that stands out. If you always pick numbers based on patterns #89,#119, and #196, you will never win the lottery. Guaranteed!

Let me prove it.

We can use probability to determine the expected frequency of any pattern over a period. I will use the formula below:

Expected Frequency = Probability X The number of draws

This time, let’s take things up a notch. Let’s use the Actual Euromillions Results to compare our computations with the real draws. To prove that Math works, here is the table to show the comparison:

The Actual Results of the Euromillions 5/50

Pattern Expected Frequency
in 983 Draws
Actual Frequency
in 983 Draws
Pattern #1 42 42
Pattern #20 17 16
Pattern #89 3 2
Pattern #119 2 2
Pattern #196 0 0

A Total of 983 draws from April 16, 2004, to April 14, 2017

Expected frequency versus actual results of the Euromillions 5/50

Once again, Mathematics is a useful tool to measure how the Euromillions behaves. The same Probability principle applies in all the lottery systems in the world.

Inside the lottery analysis section, you will see the complete list of probability analysis where you see the best, the bad and the worst number combinations in your favorite lottery. Access to the lottery analysis section is free for all.

My Fearless Predictions of the Lottery

Like I have told you earlier, we can predict the lottery to an extent. The following formula is what we use:

Estimated Frequency = Probability X The number of draws

Therefore, if we want to predict how many times pattern #1 and pattern #196 will appear in 2000 draws, this is what we get:

Estimated Frequency (pattern #1)

= 0.0424776756 x 2000

= 84.9553512  (or approximately 85 times in 2000 draws)
Estimated Frequency (pattern #196)

= 0.0000594687 x 2000

= 0.1189374 (or no appearance at all)

Notice the huge difference between the two patterns.

My recommendations for all players of Euromillions 5/50

  • Focus on Pattern #1.
  • Avoid the rest of the patterns.

Below are my recommendations for other lotteries:

Lottery Recommended Patterns Patterns to Avoid
U.S. Powerball 5/69 Patterns #1,#2,#3,#4,#5,#6 Patterns #7 to #462
Australian TattsLotto 6/45 Patterns #1,#2,#3 Patterns #4 to #210
Irish Lotto 6/47 Patterns #1,#2,#3 Patterns #4 to #210
U.S. Mega Millions 5/75 Patterns #1,#2,#3,#4,#5,#6 Patterns #7 to #792
EuroJackpot 5/50 Pattern #1 Pattern #2 to #196
UK Lotto 6/59 Pattern #1 Patterns #2 to 462

Get your  free access to the lottery analysis section now

Conclusion: How to Win the Lottery

True, it’s not easy to win the lottery. No one can reverse engineer the random nature of the lottery. But you can play better. With the right strategy in place, you can increase your chances of winning the lottery. That’s where Mathematics comes to help.

Here are my recommendations:

  1. Avoid the bad odd-even patterns especially the all-odd and the all-even numbers.
  2. Focus on number patterns that have the best probability.

Check the lottery analysis section now.

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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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