Lotterycodex Mathematics Meets The Lottery

How to Win the Lottery and Win Sooner According to Math


The lottery consists of too many lousy combinations that players should not be using at all. In fact, I can almost guarantee 90% of lotto players around the world are doing it all wrong (and you are probably one of them. I hope not).

So, let’s talk about math and see how to win the lottery sooner.

Number Patterns in the Lottery

A winning lottery strategy is primarily all about “number patterns.”

Let me explain.

In the lottery, millions of number combinations will never appear in any draw no matter how many times you play them. For example, the 1-2-3-4-5-6 has never occurred in the history of the lottery.

But you probably heard from the media and the internet that any number combination is as likely to occur as any other.  The Law of Large Numbers or LLN states that each number in the lottery has an equal chance of getting drawn.

This particular law in math explains why hot numbers and cold numbers don’t work in the lottery.  See my post on lottery strategies that don’t work.

However, the Law of Large Numbers doesn’t apply when numbers are combined.  We will prove that when we get to the actual mathematical reasoning.

So, when you combine numbers, you form a pattern.  Examples are:

  • 2 low and 4 high numbers
  • 3 low and 3 high numbers
  • 4 odd and 2 even numbers
  • 3 odd and 3 even numbers

The popular 1-2-3-4-5-6 is a classic example of a combination that belongs to the 6-low-0-high pattern.

These patterns play a significant role in your playing strategy.

And indeed, the wrong choice of number pattern makes a significant impact.

The bad, the worst, and the best number patterns

Let’s go back to the infamous 1-2-3-4-5-6.

According to a report by TheGuardian, about 10,000 people are playing this number combo every draw. A massive number of players that will bring home about £400 each should this combo indeed happen to occur in a draw.

But apart from sharing the prize. I guess the biggest picture here is that people are not aware that bad patterns exist in the lottery.

Want more specific examples?

Here are other combinations that are theoretically bad based on their patterns:

  • 1-3-4-6-7-9
  • 12-13-14-27-28-36
  • 20-27-34-41-48-55
  • 13-14-36-37-42-43
  • 04-15-26-37-48-59
  • 11-14-16-19-27-29
  • 08-22-34-38-42-44
  • 05-19-21-33-47-49

OK. There are millions of these bad number combos in the lottery. But, it’s not possible to list them all here.

But the main point I want to get across to you is simple. If you have been picking numbers randomly without much thought on the pattern, you are doing it all wrong.

In fact, you may have been wasting your money on too many bad number combinations your whole life. And that’s precisely the reason why you are not winning the lottery.

A graph showing why majority of lotto players do not win by playing number combinations that almost never appear in the lottery. Mathematics can be helpful guide on how to win the lottery.

It’s straightforward.  Bad patterns exist.  And to be honest with you, some of them are notably worst.

Luckily for you, the best ones are there ready for picking.

But how do we know which pattern is the best to play in the lottery?

The answer is probability theory.

So then, let’s talk about probability theory in great details.

How probability theory works in the lottery

Probability is a branch of mathematics that deals with measuring the likelihood of an event’s occurrence. The expression of measurement is between 0 and 1. The 0 indicates impossibility and 1 means certainty.

Probability is calculated by the following formula:

P(A) = Number of favorable outcomes to A / Total number of outcomes

To get the probability, we need to divide the number of favorable outcomes by the total number of outcomes.

But how do we get the favorable outcomes and the total number of outcomes?

We use binomial coefficients formula invented by an Italian Polymath Girolamo Cardano:

nCr = n! / r!(n-r)!

Now, let’s apply probability in a lottery game.

First, we need to know the rules of the game. For example, in U.S. Powerball, you pick 5 numbers from 1 to 69. In UK Lotto, you choose 6 from 1 to 59. In some lottery systems, the game requires you to pick 6 from 1 to 49.

Probability analysis differs from each lottery format.  So U.S. Mega Millions 5/70 have different probability calculations from the Powerball 5/69.

I am telling you this, so you know that there’s no one-size-fits-all calculation in a lottery.

For illustrative purposes, I will use the popular Lotto 649 system.

Let’s start with a simple low/high number patterns.

Low-High Number Patterns

In a lotto 649 format, you pick 6 numbers from 1 to 49. So a lotto 649 game has the following number sets:

Low numbers = {1, 2, 3, 4, 5, ... 25}

High numbers = {26, 37, 38, 39, 40, ... 49}

Now, let’s compare the probability of two number patterns 6-low-0-high and 3-low-3-high.

Based on the probability formula, we get the following values:

  1. The total playable combinations in a lotto 649 system = 13,983,816
  2. Favorable combinations that you can produce out of 6-low-0-high number pattern = 177,100
  3. Favorable combinations that you can produce out of 3-low-3-high number pattern = 4,655,200



= 177,100/13,983,816 

= 0.01266464032

= 4,655,200/13,983,816 

= 0.33289911709

What do these numbers mean from a lotto player’s perspective?

It means that 6-low-0-high pattern has only 1% chance of occurring.

And the 3-low-3-high pattern has 33% chance of occurring.

So that explains why 1-2-3-4-5-6 is never a good bet according to math.

In other words, probability theory suggests the following:

  1. Do not play 6-low-0-high number pattern
  2. Choose to play 3-low-3-high number pattern

Do you want to see the complete probability picture?

Here’s the complete probability table for a lotto 649 low/high number patterns.

Combination Pattern Probability Percentage
0-low-6-high 0.0096251266 1%
1-low-5-high 0.0759878419 8%
2-low-4-high 0.2279635258 23%
3-low-3-high 0.3328991171 33%
4-low-2-high 0.2496743378 25%
5-low-1-high 0.0911854103 9%
6-low-0-high 0.0126646403 1%

Of course, as a lottery player, your objective is to have fun (apart from winning). And selecting numbers is part of the entertainment experience. So why not, choose numbers based on a pattern with a high probability of occurring in a draw?

You see.  Probability theory is your no-nonsense guide to play the lottery.  It tells you 2 essential pieces of information:

  1. Number patterns that you should avoid at all cost
  2. The best number patterns that you should focus on

Of course, how do you want to play the lottery is up to you.

For me, wasting money on lousy number pattern doesn’t make sense, does it?

Odd-Even Number Patterns

This time, we will not only calculate the probability but also estimate the number of times a particular pattern will occur in a given number of draws.

I will use Euromillions 5/50 matrix here.

In Euromillions, you pick five numbers from 1 to 50.  This lotto system has the following number sets:

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

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

So, there are 25 odd and 25 even numbers.

Let’s try to answer some simple questions, to begin with:

  1. How many times will the 5-odd-0-even pattern occur in 100 draws?
  2. How many times will the 3-odd-2-even number pattern occur in 100 draws?

We do the problem-solving in 3 steps:

First, we calculate binomial coefficients.  Next, we compute the probability value.  Lastly, we multiply the probability value by the number of draws.

Here is how we do it:


= 690,000 / 2,118,760

= 0.32566217976

= 0.32566217976 * 100

= 32.566217976

= or 33 times

= 53,130 / 2,118,760

= 0.025075987841945

= 0.025075987841945 * 100

= 2.50759878419

= or 3 times

So there.  The answers to the previous questions are:

  • 5-odd-0-even pattern occurs approximately 3 times in 100 draws.
  • 3-odd-2-even number occurs approximately 33 times in 100 draws.

Based on our probability calculation above, it suggests that 3-odd-2-even is better than 5-odd-0-even.

You see? That’s how probability works to guide you on how to win the lottery.

Now. It doesn’t tell us precisely how a pattern will occur.

But probability is a helpful guide that shows you what works, so you only spend your money when it matters.

Well, they say the proof is in the pudding. So, let’s put our probability calculation to the test.

Probability versus the actual lottery results

Let’s see how Euromillions behaved over time in real 970 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 Value

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)
= 970 x 0.3256621797655230

= 315.892314373 

= or 316

So let me show you the complete estimation table.

Patterns Probability Estimated frequency in 970 draws
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 how estimation matches exceptionally close to the actual data.

Below is the comparison between the 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. This bar graph teaches that probability can be used to predict the Euro Millions. The probability formula will guide you how to win the lottery game.

Read: Winning The Euromillions 5/50 According To Math

Looking at the probability analysis table above, you can see that the estimation is very close to the actual lottery results. That is the power of probability.

Now, remember that probability concept applies to all random games.

You can use the same probability formula to determine the best number pattern in any lottery systems in the world.

Let’s take a look at the probability analysis for other popular lottery systems 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

This is an example of how to win the lottery with the help of probability theory. This is a bar graph showing the probability estimation compared to actual results of the TattsLotto 6/45 game. It tells you that the TattsLotto 6/45 can be predicted using probability theory. Apparently, probability can guide you on how to win at Tattslotto 6/45 lotto system.

Read: Winning 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

This bar graph shows the probability estimation compared to actual lottery results of the Eurojackpot 5/50. It shows how to predict the Euro Jackpot using probability theory. Probability theory remains the only tool to guide players on how to win the lottery.

Read: Winning 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 51.74 53
4-odd-2-even 38.81 42
2-odd-4-even 35.28 37
1-odd-and-5-even 11.66 10
5-odd-1-even 14.11 9
6-odd 1.94 1
6-even 1.46 3
155 155

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

A bar graph comparing probability estimation and the actual Irish Lottery 6-47 results. This probability concept guides players on how to win the lottery.

Read: Winning The Irish Lottery 6/47 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.

This is a bar graph comparing probability estimation of the U.S. Powerball with the actual results. The graph proves that probability theory can be a useful guide on how to win the lottery and it can be applied too on Powerball.

Read: Winning 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

A UK Lotto bar graph showing the comparison between probability estimation and the actual results. The bar graph proves that probability formula is a useful guide on how to win the UK Lotto.

Read: Winning The UK Lotto 6/59 According To Math

The complete list of all these lottery analyses is available at the lottery analysis section.  I have covered every lottery systems in the world.  Choose your favorite lottery and implement what works for you.

Odds and Probability

Now, let me tell you that “odds” and “probability” are two different mathematical terms in much the same way as “accuracy, ” and “precision” are two different words.

Knowing the difference between the two is also important.

Let me explain.

Let’s say an event A has a 25% chances of occurring.


The probability of event A is 1/4

The odds in favor of event A is 1/3

This example is just a simple illustration for you to understand the difference.

But when the number of events gets bigger such as in the lottery, the odds make a big impact.

From a statistical science point of view, there is “only one way” to win the grand prize. And there are 292 million ways to lose. So no matter what strategy you use to play the lottery, the ratio of winning and losing doesn’t change.

For instance, player A uses some strategy, and player B just picks numbers at random.  Therefore, the odds in favor of winning the grand prize are:

Player A = Only 1 way to win and 292 million ways to lose

Player B = Only 1 way to win and 292 million ways to lose

See.  No matter how the two play differently, the odds for both players are just the same.

But, one thing is certain.

Using probability theory, you have the power to know the likely outcome of the lottery.  And that’s how it guides you to choose numbers that are more likely to occur.

On the lottery analysis page, you will see all the bad, the worst and the best number patterns in the lottery.

How to predict the lottery

Imagine. You have access to some paranormal information.

Say, some magical creature who knows prior knowledge about the next draw. It can tell you when to play and what numbers to occur in the lottery.  So you win. Over. And over. And over.

What a beautiful life it’s going to be. Isn’t it.  You can even feed the entire world.

Sadly, this paranormal creature only exists in movies and fiction novels.

The odds of the lottery is the toughest to beat.

For example in the U.S. Powerball, only one will be picked to get the grand prize out of 292 million possible combinations.

It’s the type of odds that no system in the world can reverse engineer. And surely not by your favorite psychic guy next door.

So until this magical thing is possible, probability theory remains the only tool for lottery players to rely on.

As the evidence unfolds from our probability study, we have proven that the lottery behaves in a predictable pattern.

Therefore, you can predict the lottery (to an extent).

How do we do that?

We use advanced lottery patterns.

Advanced Number Patterns

You must know that there is more to number patterns than meets the eye.

Knowing the basic low-high and odd-even numbers barely scratch the surface.

If you study the winning numbers of the lottery intensely, you will discover deep layers of advanced patterns that could be the key to your lottery success.

For instance, there are 462 patterns found in the U.S. Powerball.  A total of 210 patterns for Canada Lotto 649.  And exactly 56 advanced patterns for Fantasy 5 Lotto.

The number of advanced patterns depends on the format of the lottery, and we have covered the complete list on the lottery analysis page.

These advanced number patterns play a big role in lottery prediction.

For example in U.S. Mega Millions, pattern #671 is calculated to occur once in every 100,000 draws.  But lottery players keep playing this number pattern.  I know because the press says they do.

In Tattslotto 645, pattern #198 is calculated to occur 8x in 100,000 draws.  But many insist on playing this pattern instead of a better one which occurs 3x in 100 draws.

In a 5/35 lotto system, one can choose to play a number pattern that occurs 7x in every 100 draws.  But lotto players keep on using pattern #55 which only occur 3x in 10,000 draws.

I mean why waste your money on number patterns that occur once in a blue moon?

But understandably, many lottery players are playing blindly.  They are not aware of the pattern from which they base their number selection process.

It’s high time that you know your number pattern.

Discussion of these advanced lottery patterns is available on the lottery analysis page.

One last note

Just because math can help you pick good numbers doesn’t mean you can play the lottery all you want haphazardly.

A better approach to lottery playing requires proper mindset.

You have to understand that the lottery is still a random game and no one can manipulate that. Not even the best math prodigy in the world can do that.

Winning only comes after a long streak of losses.

Therefore, you have to play the lottery using the money that you can afford to lose. Afterall, the lottery is just entertainment.

Anyone playing without a proper attitude can be at risk of lottery addiction.

Therefore, a lottery game plan is necessary to prevent any adverse consequences that lottery playing may bring to your life


Leave a Reply

  • I feel like your analysis is being applied incorrectly, for example, if you had a bag 100 black marbles (with numbers on them) and 1 white marbles. And someone is going to take one marble out of the bag each time, and your job is to guess the exact marble and One person has strategy to guess one of the 100 black marbles randomly and another person has strategy to guess only the white marble every time. The odds of either them guessing correctly is exactly the same from what I see. It’s basically that patterns that are more likely to happen just have more combos in them inherently thus it’s harder to actually Get the exact match given the lottery has that pattern. Does that make sense?

    • I understand your point my dear friend, and I respect your opinion.

      But I don’t think you get my point.

      Let me explain.

      If we talk about odds, I am 100% all agree with you. The odds in favor of guessing the exact marble correctly in your example are just the same. So there’s no point arguing on that since we have the same belief.

      The problem. I am not discussing “odds.” The main topic of my analysis is about “probability.”

      Odds and probability are two different terms. They are not mathematically equivalent.

      I explained the difference here: Odds, Probability, and The Lottery.

      So since you posted your comment, I have updated this post to emphasize the difference between the two.

      Now, going back to guessing the “exact” marble correctly from your example. I think you are taking it out of context.

      Let me set one thing straight here: This article is not about predicting the “exact” combination in the lottery. No one can do that. Not even by the most talented math prodigy in the world.

      I try to delve into the practical use of probability theory to determine what works in the lottery from the context of “number patterns.”

      And I made that premise numerous times all throughout the content.

      My objective is to help players focus on the winning patterns rather than wasting money on lousy combinations.

      People are not aware. Lottery players just pick numbers at random without having any thought on the patterns.

      Let’s take a lotto system such as a 5/35 format:

      Say we have two patterns: Pattern A and pattern B.

      Pattern A is 5-odd-0-even with a probability of 0.026392961876833 or 3% chance of occurring in a draw.

      Pattern B is 3-odd-2-even with a probability of 0.34185169669041 or 34% chance of occurring in a draw.

      As you see, pattern B has a better probability of occurring in a draw.

      But of course, the odds are just the same.

      Because in a 5/35 lotto system, there is only one way to win the grand prize. And there are 324,631 ways to lose.

      The same holds true in any lottery system.

      So odds don’t change, whether or not some strategy is involved.

      Story short, you cannot beat the odds of the lottery. But you can pick numbers based on a pattern that exhibits a high probability of occurring.

      I hope you understand the difference.

      And thank you for sharing your thoughts.

Lotterycodex Mathematics Meets The Lottery

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Edvin Hiltner

I get a good grasp of mathematical theory 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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