Lottery Calculator: A Mathematical Guide Beyond Number Selection


Last updated on April 5, 2024

What is the best lottery calculator? It’s the one that makes you an intelligent lotto player.

Some calculators only compute your chances of winning. Some lottery tools offer suggestions derived from statistical analysis (even if statistics is not the right tool for lottery games).

This article explains why some calculators don’t work and what you should use.

Let’s dig in.

The Fallacy Of A Statistics-Based Lottery Calculator

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

You don’t need statistics to help pick numbers.

Why? Because the lottery has a finite structure.

In statistics, we use sample datasets; sometimes, they call it sample population. This sample dataset is necessary when our knowledge of given facts is limited. Conversely, when a finite quantity is involved, we have adequate knowledge of the composition of a lottery game. Therefore, a sample dataset is unnecessary.

For example, the 5/39 Lotto game has 19 even numbers and 20 odd numbers. A 5/70 game comprises 35 low and 35 high numbers.

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

That’s why we created Lotterycodex calculators based on combinatorial and probability principles, avoiding statistics altogether.1

Numbers and Combinations Are Not The Same Words

Each number is equally likely. This means there are no “hot” or “cold” numbers.

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

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

This probability concept has been proven repeatedly throughout the lottery’s history. 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.

the pie graph shows that all numbers have the same probability. A lottery calculator must recognize that all numbers are equally likely.

Whether you’re playing the Mega Millions,2 Powerball,3 Fantasy 5,4 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 help lotto players make informed choices when all numbers have the same probability?

The secret lies in the fact that combinations are not created equally.

You don’t win a lottery jackpot with just a number. You have to put numbers together to purchase a ticket.

So, unlike numbers, combinations have varying compositions.

Of course, like numbers, all combinations have equal probability because there is only one way to win the jackpot.

The probability of winning the jackpot = 1 divided by all the possible combinations in the lottery. A lottery calculator must use this formula in conjunction with the odds formula to provide comprehensive information about the behavior of a truly random lottery game.

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.

I ask, “Will you buy a ticket with 5-10-15-20-25-30 on it?”

You will probably say “no way” because part of you screams and tells you it’s not a sensible choice.

That’s how gut feeling takes over logical reasoning.

But why? Why worry when you believe all combinations are equally likely?

Are you ready to give up math when your gut feels much stronger?

See, it doesn’t make sense.

You have to put your trust in a mathematical strategy.

So, let’s discuss how using a lottery calculator can help you be more confident in every decision you make when playing the lottery.

A Lottery Calculator Must Recognize The Difference Between Odds And Probability

Understand that odds and probability are two different terms, and they are not mathematically equivalent.5

While probability measures the likelihood, odds describe the ratio of success to failure.

Probability = Chance

odds = advantage

You cannot manipulate the probability. You cannot beat the odds. But at least you can choose the odds that work for you.

This is how we use math to make intelligent decisions.

Lottery Calculator Must Provide Success-To-Failure Ratios

Now that you know the difference between odds and probability, it’s easy to see that a mathematical strategy is in the act of choosing better odds.

Therefore, a true lottery calculator should help you calculate all the possible outcomes and make an informed decision based on the success-to-failure ratio that works for you.6

Lucky for you, varying success-to-failure ratios exist because combinations have varying compositions.

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

2-3-4-34-35-36Two sets of consecutive numbers.
5-6-39-40-46-47Three sets of consecutive numbers.
7-12-23-38-41-46No consecutive numbers.

Let me explain why composition is such an important part of your strategy.

For example, in a lotto 6/49 game, there are 134,596 ways to combine pure six even numbers and 13,849,220 other ways. Hence, we can calculate the success-to-failure ratio of this composition using the odds formula:

Odds_favor(6-even) = 134,596/13,983,816 = 1/103

In 104 attempts, you get one favorable shot, and in 103 ways, you don’t get favorable shots.

You don’t want to wait 104 draws to get one favorable shot as a lotto player.

That’s how the success-to-failure ratio helps you make informed choices.

Your goal is to win the lottery, and the first thing you should know when playing is your success-to-failure ratio. You cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you have the power to make informed choices. Even choosing not to play is a strategy by itself.

A lottery calculator must be able to calculate all the possible choices in your game and then help you make informed choices.

You cannot change the underlying probability.

You cannot beat the odds.

But you can choose your odds based on the information suggested by the success-to-failure ratio.

A Lottery Calculator Must Be Able To Make Probability Prediction

The lottery is truly random.

In simple terms, it’s not easy to win the lottery. I will not 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. Our probability calculation won’t make sense if something disturbs the lottery’s randomness.

The law of large numbers or LLN shows 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.7

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

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

The US Powerball 5/69
from October 7, 2015, to March 16, 2024
(Total of 1,008 draws)

The graph was updated March 16, 2024. This graph shows that theoretical calculations closely match with the actual results of the Powerball Game. 3-low-2-high is expected to occur 329 times. In actual it occurred 326 times. This indicates that a lottery game is subordinate to the dictate of probability theory. A lottery calculator must be able  to make such predictions.

Note: Our analysis of the US Powerball must start on October 7, 2015, when lottery officials began implementing the 5/69 format.

The Mega Millions 5/70
from October 31, 2017, to March 8, 2024
(Total of 628 draws)

The graph was updated March 8, 2024. In this graph of the Mega Millions, the 2-odd-3-even group is expected to occur 202 times. In the actual results, it occurred 209 times.

Note: Our analysis of the Mega Millions must start on October 31, 2017, because this was when lottery officials changed the format to the current 5/70 game.8

The bar graphs above show that the mathematical prediction matches the lotto results. It’s solid proof that the lottery follows the dictate of probability.

Probability Calculation Applies to All Lottery Systems

Yes, all lottery systems follow the same probability principle 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 March 15, 2024
(Total of 728 draws)

The graph was updated March 15, 2024. In this graph of the Euro Jackpot's 503 draws from 2012 to 2021, the 1-odd-4-even group is expected to occur 109 times. In the actual results, the group occurred 114 times.

The Euro Millions 5/50
from April 16, 2004, to March 15, 2024
(Total of 1,705 draws)

The graph was updated March 15, 2024. In this graph of the Euro Millions's 1,705 draws from 2004 to 2024, the 1-odd-4-even group is calculated to occur 254 times. In the actual results, the group occurred 260 times.

The Irish Lotto 6/47
from September 5, 2015, to March 16, 2024
(Total of 890 draws)

The graph was updated March 16, 2024. In this graph of the Irish Lotto's 890 draws from 2015 to 2024, the 4-odd-2-even group is calculated to occur 223 times. In the actual results, the group occurred 227 times.

The Tattslotto 6/45 Game
from January 7, 2006, to March 16, 2024
(Total of 949 draws)

The graph was updated March 16, 2024. In this graph of the Tattslotto's 949 draws from 2006 to 2024, the 1-odd-5-even group is calculated to occur 71 times. In the actual results, the group occurred 74 times.

The UK Lotto 6/59 Game
from October 10, 2015, to March 16, 2024
(Total of 876 draws)

The graph was updated March 16, 2024. In this graph of the UK Lotto's 876 draws from 2015 to 2024, the 4-odd-2-even group is calculated to occur 216 times. In the actual results, the group occurred 233 times.

As a lotto player, you must pick your combination from the group that dominates lottery draws.

But wait, if you think that odd-even and low-high numbers are the answer to the lottery hack you have been waiting for, wait until you see what the Lotterycodex calculator can do to help you better.

Lottery Calculator Based On Lotterycodex Analysis

Odd-even and low-high, as two separate probability analyses, can be problematic. They provide conflicting conclusions.

For example, a combination such as 1-2-3-4-5 is considered dominant according to odd/even analysis.

Conversely, a combination comprised purely of low numbers possesses an inferior success-to-failure ratio.

Therefore, there should be a better method by which we calculate all the possibilities of a lottery game and give you more accurate information.

And here is where Lotterycodex analysis comes in handy.

Lotterycodex combines odd/even and low/high sets into a single analysis.

To execute such an analysis, we need to group the lottery’s number field using the following steps:

Step one, we divide the total number of balls into low and high numbers. For example, if your lottery has 40 balls, your low half must be from 1 to 20. Then, your high half must be from 21 to 40.

Step two, we divide the low numbers into odd and even sets.

Step three, we divide the high numbers into odd and even sets.

We designate a color for each set to make things much easier visually.

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

Lotterycodex calculator divides the number field into four sets namely LOW-ODD, LOW-EVEN, HIGH-ODD, and HIGH-EVEN. This lottery calculator ensures the balance spread of probability across the entire number field.

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

The Lotterycodex calculator use the same sets of numbers for all lottery games. The only difference is the size of the number field. The sets will always be four sets.

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

No matter what the format of a lottery game, the number field is always divided into four sets.

Those four sets, represented by four colors, are all we need to determine all the combinatorial compositions that comprise a particular lottery game.

In the calculation process, we use probability theory to separate the dominant, the occasional, and the rare groups.

Below are examples of how Lotterycodex separates combinatorial groups based on the success-to-failure ratio. Each lottery format has different calculations.

The Lotterycodex analysis for the 5/69 game indicates only one dominant combinatorial group with the name template #1

Generated by Lotterycodex Calculator

As a lottery player, you must ensure that you bet on the dominant group to get the best shot possible. In Lotterycodex, we describe these groups using templates. Dominant templates give you more favorable shots.

You don’t want to wait and play 1000 times to get one favorable shot. Do you?

Here’s another Lotterycodex analysis for a 6/49 lottery game:

The Lotterycodex analysis for the 6/49 game is dominated by templates #1, #2, and #3.

Generated by Lotterycodex Calculator

And here’s another analysis for a 4/30 game:

In 4/30 lottery game, template #1 is the only dominant group.

Generated by Lotterycodex Calculator

Whatever your lottery game is, use the right Lotterycodex calculator.

As you can see, knowledge is power.

When you know the group that will give the best shot possible, you get this particular advantage. You have removed the blind spot that crippled 99% of the lotto players.

Use this lottery calculator to save you from the complexity of calculation. Especially if you hate math, you will be glad to have one for yourself.

How to Pick Lotto Combinations

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.

It would be best if you had a tool based on mathematical logic, which has been tested and proven repeatedly since the probability formula was discovered in 1654 by Blaise Pascal and Pierre de Fermat.

All the calculators designed by Lotterycodex give you the power to make informed choices using the success-to-failure ratio. These calculators can benefit lotto syndicates tremendously9. Each calculator comes with a program that allows you to generate a list of combinations, making it easy for you to pick.10

Of course, take some time to learn the complexity of computing probability to enrich your mind.11 Enrich your knowledge of probability and combinatorics and how they work.

But aside from using a lottery calculator, you should also steer clear of the many lotto strategy myths12 that have been going around for centuries.13

Learn more lottery tips14 as much as possible and take action with a proper lotto game plan15 and do it consistently.

Questions and Answers

What is the key limitation of statistics-based lottery calculators?

The key limitation of statistics-based lottery calculators is their overemphasis on historical draw data. They often focus on the frequency of individual numbers being drawn in the past, assuming that past trends can predict future outcomes. This approach overlooks that lotteries are random and each draw is independent.

What differentiates lottery numbers from combinations?

In the lottery context, numbers and combinations represent distinct ideas. Each number corresponds to an individual lottery ball. However, a single number isn’t enough to purchase a lottery ticket. Conversely, a combination is a specific grouping of these numbers that forms a valid ticket and offers a probabilistic chance of winning a prize. Combinations have varying compositions and success-to-failure ratios.

Why is understanding odds vs. probability crucial in lottery strategy?

Understanding the difference between odds and probability is crucial in lottery strategy because it helps players evaluate the options when selecting numbers. Odds refer to the likelihood of winning versus losing, whereas probability measures the likelihood of a specific outcome. Recognizing this distinction helps make more informed decisions about which combinations to choose, as different combinations have varying success-to-failure ratios. This understanding is key to developing a more effective lottery strategy.

What is the success-to-failure ratio’s role in a lottery game?

The success-to-failure ratio in the lottery plays a vital role in informing players about the relative chances of different combinations. It compares the number of ways you get favorable shots to the number of ways you will fail. This ratio helps players understand which combinations are more likely to dominate a lottery game over time, guiding them in making more informed choices when selecting numbers.

What is Lotterycodex’s unique approach as a lottery wheel?

All Lotterycodex calculators give you the power to make informed choices using the success-to-failure ratio. They come with a lottery wheel that separates those groups that will dominate the lottery draw as the number of draws increases according to the law of large numbers.

Additional Resources

  1. The Winning Lottery Formula Using Math    []
  2. How to Win the Mega Millions    []
  3. How to Win Powerball    []
  4. How to Win Fantasy 5    []
  5. Odds, Probability, and the Lottery    []
  6. The Lotto Secret: Three Math Strategies for Winning Revealed    []
  7. Law of Large Numbers    []
  8. How to win the Mega Millions 5/70 game according to math    []
  9. Lottery Syndicate and the Mathematical Advantage You Don’t Want to Miss    []
  10. A Lottery Number Generator That Works    []
  11. Probability Theory    []
  12. Top 10 Lottery Strategy Myths Debunked (Perhaps You’re Doing #4 or #10)    []
  13. How to Win the Lottery    []
  14. Lottery Tips: What Works and What Doesn’t    []
  15. The Lottery Game Plan    []


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