lottery probability calculator excel

Please verify you are a human

Access to this page has been denied because we believe you are using automation tools to browse the website.

This may happen as a result of the following:

  • Javascript is disabled or blocked by an extension (ad blockers for example)
  • Your browser does not support cookies

Please make sure that Javascript and cookies are enabled on your browser and that you are not blocking them from loading.

Reference ID: #6e53ea20-62e8-11eb-ba90-c93a6fa9bca3

Please verify you are a human Access to this page has been denied because we believe you are using automation tools to browse the website. This may happen as a result of the following:

Lottery Calculator: Knowing the Best Lotto Combinations Without a Math Degree

Last updated on January 27, 2021

To win the lottery, you need a lottery calculator that will help you make an intelligent decision. You need a tool that will allow you to see all the possible choices and finally help you make the right choice. And unfortunately, using a simple lottery wheel just doesn’t make the cut.

Calculators for the lottery are not created equally.

Some calculators only compute your chances of winning. And some calculating tools offer you suggestions derived from statistical analysis (even if statistics is not the right tool for the job).

So what is the best calculator for the lottery? It’s the calculator that is based on proven principles of combinatorial mathematics and probability theory.

To help you understand, let me show you why some calculators don’t work and what you should be using.

Table of Contents

The Wrong Application of Statistics

For centuries, the lotto playing public fumble around this belief that statistical analysis could help because they think that the past results will give them a clue on what numbers to pick. I think this belief must be corrected once and for all.

We only apply statistics when something is unknown, so we use a sample set to make some calculations. More often, the results proved to be inaccurate, especially when a sample set is not large enough to make any conclusive computation.

Truth be told, you don’t need statistics to determine the best lotto combinations.

Why? Because the lottery has a “finite structure” that requires logical analysis rather than statistical. When a finite quantity of numbers is involved, we have adequate knowledge of the composition of the whole population.

In other words, in the lottery, a sample dataset is not necessary. For example, we know that there are 19 even numbers and 20 odd numbers in the 5/39 Lotto game. We know that a 5/70 game is composed of 35 low-numbers and 35 high-numbers.

Based on our existing knowledge of the lotto game, any question is, therefore, a probability and combinatorial problem to solve.

That’s exactly what the Lotterycodex calculator does for you. It calculates all the possible choices in a lotto game and finally separates the best and the worst group using the principle of combinatorics and probability theory. 1 , 2 , 3

Now let me give you a little bit of intro to how this mathematical duo works in the lottery.

Understanding Some Lottery Lingo on the Road to Success

Each number is equally likely. Meaning, there are no “hot” or “cold” numbers.

If you believe that those numbers that occur more frequently are bound to happen more often in the future, then you’re not helping yourself.

The very reason we rely on mathematical calculations is to guide us not to make the wrong choices. In this article, I want to show you that building your playing strategy on the statistical frequency of each number is mathematically flawed.

For example, if you pick one ball from a bowl of 49 numbers, each number has 1/49 probability of getting drawn. If we do the experiment many times over, the results always accurately and precisely coincide with the calculation.

This probability concept has been proven over and over in the long history of the lottery. For example, the picture below describes the behavior of all the numbers in the Canada Lotto 6/49 game from 1982 to 2018. It shows that the lottery has no bias over certain numbers as lotto draws continue to get larger and larger.

And the same probability principle applies to all lottery systems.

Whether you’re playing the Mega Millions, or Powerball, or Fantasy 5, or the Set for Life game, the results are bound to follow the dictate of the probability theory.

Now, you’ll probably ask, how does Lotterycodex separate the best combinations from the worst ones when all numbers have the same probability?

The secret lies in the fact that numbers and combinations are two different terms. A number refers to the individual ball in the lottery, while a combination refers to how you put numbers together in a certain way.

And combinations are not created equally.

Don’t get me wrong. Like numbers, all combinations have equal probability because there is only one way to win the jackpot.

Theoretically, a straight sequential combination such as 1-2-3-4-5-6 is equally likely. The same holds for 2-4-6-8-10-12 or 5-10-15-20-25-30.

But if someone asks you, “will you spend your money on those combinations?

Probably not because you feel that it’s not going to make it in a lottery.

That’s how the gut feeling takes over logical reasoning. But why?

Why worry when you believe that the calculation is right?

But for some folk, they are ready to give up their math when the gut feeling is much stronger.

You see, the gut feeling doesn’t add up. You have to put your trust in a mathematical strategy. So let’s discuss how you can be more confident with your mathematical belief by knowing the difference between odds and probability.

The difference between odds and probability.

So if you want to play the lottery with the best shot possible, you have to understand that odds and probability are two different terms, and they are not mathematically equivalent. 4

While the probability is a measurement of likelihood, odds refer to the ratio of success to failure.

In other words, when we talk about our chance of winning, the underlying probability never changes. But that doesn’t mean that you have no control over your strategy because that’s exactly where odds come in handy.

As a lotto player, you want to make sure that you have a better advantage by choosing a better ratio of success to failure.

probability = chance (you cannot control this)

odds = advantage (you can choose a better ratio of success to failure)

This is how we use math to make an intelligent decision.

Always remember, that a true mathematical strategy helps you calculate all the possibilities and then make the right choice. And rest assured that you are not mathematically wrong for the majority of the time.

Let me reinforce my point by explaining odds and probability from the context of combinatorial groups or patterns.

A combination carries certain characteristics depending on its composition.

So while all combinations may have the same probability, you also have to look at the concept of combinatorial groups. 5 , 6 Combinations that share the same composition can be put together into combinatorial groups. And combinatorial groups don’t have equal probability.

The table below shows examples of how combinations may differ in characteristics.

Numbers are picked from only two groups (1’s group and 30’s group).

10’s group and 20’s group are not represented.

All number groups are represented.

You pick the wrong composition, and you already fail even before the draw begins.

For example, in a lotto 6/49 game, these combinatorial patterns have the following probabilities:

P(6-even-0-odd) = 0.0096251266464032

P(3-odds-3-evens) = 0.33289911709365

The difference is so simple.

A 6-even combination will give you the odds of 1 to 134,595 in favor of winning the jackpot, but this favorable advantage comes only once every 100 draws.

So if you play 2-4-6-8-10-12, then expect that your advantage of winning the jackpot comes every 100 draws. That expectation is way too long and expensive.

In comparison, there are 4,655,200 ways to combine numbers with a 3-odd-3-even pattern. If you play this pattern, 33 of 100 draws will put you in 1 to 4.6 million odds rather than 1 to 14 million. That’s the kind of advantage you might be willing to take since you have the opportunity to hit the jackpot every three draws.

Putting this in perspective, if you play 2-4-6-8-10-12, you are 99% wrong for the majority of the draws. Hence, you are wasting money for the majority of the time you play lotto.

So based on the calculated possibilities, here’s how you make an intelligent choice:

6-even-0-odd 3-odds-3-evens
A ratio of 1:100 A ratio of 33:100
This means that out of 100 attempts you play the lotto, you get only 1 opportunity to match the winning numbers. This means that out of 100 attempts you play the lotto, you get 33 opportunities to match the winning numbers.

That’s the basic idea of a mathematical strategy.

You cannot change the underlying probability.

You cannot beat the odds.

BUT, you have the power to choose your odds.

While you cannot predict the next winning combinations, you can use mathematics to make an intelligent decision for the majority of the draws.

Your goal is to win the lottery, and the first thing you should know before you play is to know the ratio of success to failure and choose the best one. You cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you have the power to know and make the right choice. Even choosing not to play is a strategy by itself.

So Lotterycodex exists to help you calculate all the possible choices in your game and then based on those possibilities, you make intelligent choices.

A lottery calculator is such an essential tool for every lotto player.

But, using the wrong calculator will not do any help. As I am explaining, you need the right calculator.

Let me show you what a lottery calculator must do to help you win the lottery:

A Lottery Calculator Must Generate a Balanced Low and High Numbers

As I have explained earlier, in a world of random chance, hot or cold numbers are nothing but myths.

In the same context, the lottery doesn’t care whether your numbers are lucky or unlucky. You don’t get the jackpot prize by matching a number. It’s only by matching all the numbers that you win the big prize.

So if we talk about strategizing your game, it’s how you combine the numbers that matter. Whether you love or hate specific numbers, it doesn’t matter. What matters is whether those numbers are combined in a way that will give you a better advantage.

Again, you should focus on choosing the group with the best ratio of success to failure.

When numbers are put together, they form a combination. So the question is just a matter of whether or not your combination possesses the characteristics of a winning combination. That is the question. Are you using a pattern with a better ratio of success to failure?

To illustrate, let’s take a look at low and high combinatorial patterns for the U.S. Powerball 5/69 game. 7

We can divide the numbers into low and high sets:

Based on those low-high sets, we can produce six combinatorial patterns for a Powerball game:

The U.S. Powerball 5/69 Game
Low and High Combinatorial Patterns

Total combinatorial patterns: 6
Total playable combinations: 11,238,513

Best combinations: 3-low-2-high, 2-low-3-high
Worst combinations: 0-low-5-high, 5-low-0-high

The table above shows that a combinatorial pattern of 5-low numbers with no high numbers occurs 2 to 3 times in 100 draws.

In comparison, a pattern which consists of balanced low and high numbers occurs 63 to 65 times in 100 draws combined.

Imagine all the 11 million combinations are put into six boxes. Where will you pick your combination?

I don’t know about you, but for me, I will pick the best ones.

Choosing a 3-low-2-high combination instead of a 5-low combination (e.g., 1-2-3-4-5) WILL NOT increase your chances of winning because all combinations are equally likely. You should avoid 1-2-3-4-5 because a 5-low-0-high pattern has fewer ways to win and more ways to fail. I recommend choosing 3-low-2-high because it offers the best ratio of success to failure.

As you see from the illustrations above, even though numbers have an equal likelihood of getting drawn, the probability varies when you consider combinatorial patterns.

A Lottery Calculator Should Generate a Balanced Odd and Even Numbers

Similarly, like low-high numbers, odd-even combinatorial patterns don’t have equal probability. You pick the wrong mix of odd and even combination, and the next jackpot winner is more likely not you.

Let’s use the U.S. Mega Millions 5/70 game. 8

We begin by separating numbers into two sets:

From the above number sets, we produce the following odd-even patterns for the Mega Millions below:

The U.S. Mega Millions 5/70 Game
Odd and Even Combinatorial Patterns

Total combinatorial patterns: 6
Total playable combinations: 12,103,014

Best combinations: 3-odd-2-even and 2-odd-3-even
Worst combinations: 5-odd-0-even, 0-odd-5-even

The table above shows that you should mix odd and even numbers in a balanced way as these types of combinations occur more or less 64 times in 100 draws combined.

Choosing a 3-odd-2-even combination instead of 5-even (e.g., 2-4-6-8-10) WILL NOT increase your chances of winning because all combinations have the same probability. The reason you shouldn’t choose 2-4-6-8-10 is that the 0-odd-5-even pattern has fewer ways to win and have more ways to fail. You should choose 3-odd-2-even because it gives you the best ratio of success to failure.

To get the best shot possible at winning the Mega Millions, you should pick your combinations from the best group.

If you want to win the lottery, where do you want to pick your combinations? I think you know the answer.

But how can we know all these combinatorial patterns work?

Well then, let’s prove it using the actual lottery results.

Let me introduce to you now the concept of the law of large numbers. In the next section, I will demonstrate to you how the lottery draws obey the dictate of probability.

The Probability Prediction and the Law of Large Numbers

The lottery is truly random.

In simple terms, it’s not easy to win the lottery. Sorry but I don’t want to give you false hope.

But despite its randomness, it follows the dictate of probability. Indeed, this total randomness is a requirement to make all probability calculations correct. If something is disturbing the randomness of the lottery, any probability calculation won’t make any sense.

The law of large numbers or LLN shows the proof that the results of the actual lottery draws are subordinate to the principle of probability.

Wikipedia defines LLN this way:

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer as more trials are performed. 9

In layman’s terms, this only means that each combinatorial pattern will occur more or less close to the frequency dictated by its probability. And the closeness in value will tend to become evident as the data gets larger and larger.

Lotterycodex studies show undeniable agreement between actual lotto results and probability prediction. The agreement between the actual draws and theoretical prediction proves that the lottery follows the dictate of probability from the perspective of the law of large numbers.

The U.S. Powerball 5/69
from October 7, 2015, to February 5, 2020
(Total of 449 draws)

Note: Our analysis of the U.S. Powerball must start on October 7, 2015, because this was the date when lottery officials began to implement the 5/69 format.

The Mega Millions 5/70
from October 31, 2017, to February 4, 2020
(Total of 237 draws)

Note: Our analysis of the Mega Millions must start on October 31, 2017, because this is the date when lottery officials change the format to the current 5/70 game. 10

The bar graphs above show that the mathematical prediction closely matches that of the actual lotto results. It’s solid proof that the lottery follows the dictate of probability no matter how random the lottery is.

Probability Calculation Applies to All Lottery Systems

Yes, all lottery systems follow the dictate of probability regardless of the format. Lotterycodex has conducted probability studies for some of the most popular lottery systems in the world, and below are some of the surprising results that should change the way you look at the lottery:

The Euro Jackpot 5/50
from March 23, 2012, to January 31, 2020
(Total of 410 draws) 11

The Euro Millions 5/50
from April 16, 2004, to February 4, 2020
(Total of 1,276 draws) 12

The Irish Lotto 6/47
from September 5, 2015, to February 5, 2020
(Total of 461 draws) 13

The Tattslotto 6/45 Game
from January 7, 2006, to February 1, 2020
(Total of 734 draws) 14

The UK Lotto 6/59 Game
from October 10, 2015, to February 5, 2020
(Total of 449 draws) 15

The lottery is random, but just because it’s random does not mean it has no bias. The bar graphs above are solid pieces of evidence that the lottery follows the dictate of probability.

As a lotto player who wants to win, you have to pick your combination from the right group that possesses the winning patterns that nearly all winning combinations have in common.

But wait, if you think that odd-even and low-high numbers are the answer to the lottery hack that you have been waiting for, well, wait until you see the concept of advanced combinatorial design.

Lotterycodex Calculator and the Advanced Combinatorial Design

Odd-even and low-high as two separate probability analyses can be problematic. They provide opposing viewpoints.

For example, a combination such as 1-2-3-4-5 is considered one of the best ones according to odd/even analysis.

But it’s not true because conversely, a combination that is purely made up of low numbers possesses an inferior probability according to low-high analysis.

Therefore, there should be a better method by which we can determine the types of combinations that will give you the best shot possible.

And here is where an advanced application of combinatorics comes to the rescue. That is, Lotterycodex put all factors together into one combinatorial equation.

Wait a minute. I hear someone’s asking. “Edvin, what do you mean by putting all factors together in one combinatorial equation?

Let me introduce you to a unique combinatorial design that will guide you along the way.

I need to explain the initial setup, so we get things right the first time.

The first step, we divide the total number of balls into two groups: Low and High numbers. For example, if your lottery has 40 balls, then your low half must be from 1 to 20. Then your high half must be from 21 to 40.

The second step, we divide the low numbers into odd and even numbers.

The third step, we do the same thing with high numbers.

To make things much easier visually, we designate a color for each group.

In a lottery with 49 balls, the division of numbers should look like the one below:

The table below should apply to a game with 35 balls:

And here is how it looks like for a game with 34 balls.

Those four sets represented by four colors are all we need to determine all the combinatorial patterns available for a particular lottery game.

In the process of calculation, we separate the best groups using the principle of probability theory. The unique sets are crucial if we want to predict the best composition with precision and accuracy—something that standard deviation and variance measure will not provide.

Lotterycodex is the only program of its kind that balances both low-high and odd-even combinations in one combinatorial calculator.

Below are examples of how Lotterycodex separates the best group of combinations from the worst ones. Each lottery format will have different calculations.

4/30 Lottery Format

5/69 Lottery Format

6/49 Lottery Format

As you can see, knowledge is power. When you know the group where to pick likely winners, you get this particular advantage. You have removed the blind spot that debilitates 99% of the lotto players.

Of course, you use a lottery calculator to save you from the complexity of calculation. Especially if you hate math, you will be glad to have one for yourself.

Why Use the Lotterycodex Calculator in the First Place?

It very important to understand the nifty concept of a mathematical strategy.

However, even if you know the mathematical methodologies involved, calculation tends to become an exhaustive and tedious task even for math prodigies out there. Even engineers and scientists need calculators too.

In the world of the lottery, there’s no one-size-fits-all calculation. The computation of combinatorics and probability differs from one lottery to another.

Therefore, first and foremost, you need to determine the format of your favorite lotto game and then choose the right lottery calculator that works best for that format.

With the right lottery calculator, you will never waste your money on useless combinations anymore. You will get this unique confidence that separates you from the 99% of lotto players who keep losing money on useless tickets.

If you are interested in getting access to the Lotterycodex calculator, you should start with this Free Guide: The Winning Lottery Formula Based on Combinatorics and Probability Theory

Knowledge is power. If you know how math works in the lottery, you have the best advantage to make your game a lot more fun.

However, like Uncle Ben said, with power comes great responsibility. So please use that power to play the lottery responsibly.

Spending money on a useless combination is an expensive exercise over time.

You really can’t afford not to invest in a probability calculator.

Spending your time and money on a combination that will not likely occur in one million draws is not fun.

If your goal is to win the lottery, you need the right tool that will allow you to see what group of combinations will give you the best advantage of winning.

You need a tool that is based on mathematical logic, which has been tested and proven over and over since probability formula was discovered in 1654 by Blaise Pascal and Pierre de Fermat.

All the calculators designed by Lotterycodex give you the power to know the best combinations in your chosen lottery, so you get the best shot possible. These calculators can benefit lotto syndicates tremendously 16 . Each calculator comes with a program that allows you to generate a list of combinations based on your chosen numbers. It’s an extraordinary number generator as it separates the worst type of combinations from the best ones. 17

Of course, take some time to learn the complexity of computing the probability to enrich your mind. 18 Enrich your knowledge of probability and combinatorics and how they work in tandem. 19

But aside from using a lottery calculator, you should also steer clear of the many lotto strategy myths that have been going around for centuries. 20 , 21

Learn more lottery tips 22 as much as possible and take action with a proper lotto game plan 23 and do it consistently.

Lottery Calculator: Knowing the Best Lotto Combinations Without a Math Degree Last updated on January 27, 2021 To win the lottery, you need a lottery calculator that will help you make an ]]>