How to Win Irish Lotto According to Math

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Last updated on March 22, 2024

Want to learn how to win the Irish Lotto? If so, say goodbye to your statistical analysis. Use combinatorics and probability theory to choose numbers. Math can be difficult, but don’t worry; a calculator can bring this potent tactic to you on a silver platter.

First, we will discuss the Irish lottery game’s mechanics and challenges. Knowledge is crucial so we can make smarter choices rather than picking numbers randomly or believing in today’s horoscope.

Ultimately, you will learn a lottery strategy based on what is mathematically achievable within the game’s framework.

Let’s dive right in.

how to win Irish Lotto 6/47 according to mathematics

The Odds of Winning the Irish Lottery

To know the odds of winning the jackpot, we need to know the number of distinct playable combinations out of picking six numbers from 47 balls. It’s possible using the combination formula:

You read this formula by saying “n choose r”. This is the formula for computing the total number of possible combinations of r objects from n set of objects. For example, you can find the number of combinations in a 6/42 game by substituting 6 to r and 42 to n.

Let n = 47 and r = 6, the probability of winning the Irish Lottery jackpot is 1 in 10.7 million (10,737,573).

When you buy two tickets, your probability of winning technically improves to 1 in 5,368,787. The odds are still unfavorable, and you have a better chance of being elected leader in your community than winning the Irish Lottery.

Of course, winning the jackpot prize isn’t the only possibility. You can also win more likely lower-tier prizes if you don’t match all six numbers.

Based on the official odds and prizes schedule, the overall odds of winning any prize are 1 in 29.1 Therefore, the probability of an individual ticket not winning is approximately 0.9655. Consequently, the probability that you lose nth times is this number raised to the power of n.

P(losing nth times) = 0.9655n

Achieving a 50/50 shot at winning any prize may require the purchase of approximately 20 tickets. However, this is no assurance of success. To attain a 99.99% certainty of winning a prize, buying about 262 tickets may be required. We calculate this using the P(winning any prize) being the complementary of P(losing).

P(winning any prize) = 1 – 0.9655262 tickets

Understand that this 99.99% guarantee leans towards winning the lowest-tier prize. Winning typically involves a match of two balls and one bonus ball, resulting in a €3.00 win.

Securing minor prizes in the Irish Lottery proves to be very challenging, let alone bagging the jackpot. So please don’t subscribe to the belief that you can profit from the lottery. You can’t.2

Be Mathematical When Playing Irish Lotto

Winning the jackpot in the Irish Lottery is not easy. If there’s only one tip to win the Irish Lotto, it’s buying more tickets.

However, buying more tickets is useless if you’re not choosing numbers sensibly.

Look at this combination:

10-11-12-14-16-18

Notice that each number in this sequence belongs to the 10s group, meaning they all start with the digit 1. Additionally, this combination predominantly consists of even numbers. Furthermore, the numbers are arranged sequentially but skip every other number.

Not only is this combination a poor choice, but it is also a waste of time and money.

According to probability theory, a truly random lottery game spreads the probability fairly across the entire number field.

Therefore, a winning combination of purely even numbers and all numbers belonging to only one group is rare.

As an Irish lotto player, the last thing you want to do is to bet your money on this rarity. To get the best shot possible, you must play your game the way a random lottery game picks winning combinations most of the time.

Gut feeling and mathematical logic

Most people believe that all combinations have an equal chance of winning. However, most people don’t trust their math.

Take a look at the following combinations:

2-4-6-8-10-12all even numbers
1-10-11-12-20-21exclusive use of digits 1 and 2, excessive use of consecutive numbers
1-11-12-20-21-22-exclusive use of digits 1 and 2, excessive use of consecutive numbers
1-7-17-27-37-47numbers predominantly ending in seven
10-15-20-25-30-35numbers are in multiples of five

Let me ask, “Are you willing to buy five tickets with these previously mentioned combinations?

I have asked other lottery players; surprisingly, none will take the risk.

Even if most people strongly believe that all combinations have an equal chance of winning, their intuition screams and says, “These combinations cannot be right.”3

Gut feelings take over.4

I don’t know about you, but I don’t think intuition is enough.5

When playing the lottery, you should make informed choices based on calculated guesses supporting your gut feeling. This reasoning strategy is important when learning how to win the Irish Lotto.

For example, many lotto gurus recommend avoiding 1-2-3-4-5 to avoid splitting your jackpot prize since many players use the same combination to play lottery games.

It does make sense, but mathematically speaking, that is not the real reason why you avoid certain combinations when buying lotto tickets. Read more: How to Win the Lottery According to Math

Statistics will not help.

Statistics is not the right tool for lottery games.6

A lottery game is finite. We don’t use statistical analysis when dealing with a finite game because we have sufficient data to infer the game’s composition.

In the context of the lottery game, we use combinatorial mathematics and probability theory to understand how balls behave in a random game.7,8 These two mathematical tools help calculate all possible outcomes of the Irish Lotto game and reveal information that will help us make intelligent choices when playing the lottery. Read on: The Winning Lottery Formula Using Math

Lottery players get this information in the form of a success-to-failure ratio.

Understanding Irish Lotto’s Success-to-Failure Ratios

In a truly random game, two things stay the same no matter what you do. First, you cannot manipulate the underlying probability. Second, you cannot beat the odds of a lottery game.

This inherent randomness of the game ensures fairness so that numbers and combinations have equal chance.

So now, How do you make smart choices when all the numbers and combinations have the same chance of winning?

The key is understanding the concept of the success-to-failure ratio. This ratio will guide you on how to win the Irish Lotto.9

Let me explain.

In random lottery games, “odds” and “probability” are two different terms.10 They are not mathematically equivalent.11

Probability is expressed as:

P(success) = all favorable events / all possible outcomes

So, P(failure) is complementary to P(success):

P(failure) = 1 – P(success)

The probability formula calculates how likely an event is to happen, while odds compare the number of ways an event can succeed and the number of ways it can fail.12

Odds = P(success) / P(failure)

So, odds provide a clearer picture of your advantage. In Lotterycodex, we call this success-to-failure ratio.

A lottery strategy exists because not all combinations are created the same way. Combinations have varying compositions and exhibit different success-to-failure ratios.

Making Informed Choices Using Success-to-Failure Ratios

To master the concept of success-to-failure ratio, we have to compare two combinatorial groups.

There are 134,596 ways to combine six numbers using a 6-even composition. This group will give you only one favorable shot to match the winning combination and 105 ways to fail.

There are 4,655,200 ways to combine numbers using the 3-odd-3-even composition. This group will give you 33 favorable shots in every 100 draws. Hence, this group is a better choice.

Let’s compare the two groups side by side.

This table compares the 0-odd-6-even vs 3-odd-3-even groups. The 0-odd-6-even group has 1:105 success-to-failure ratio. The 3-odd-3-even has 1:2 ratio.

Based on the comparison table above, you should avoid the 6-even group due to its unfavorable ratio of 1:105. This ratio indicates that out of 106 draws, you get only one favorable shot, and the remaining 105 are unfavorable.

As an Irish Lotto player, you don’t want to spend your money on 106 draws to get one favorable shot.

Lottery Game’s Subordination to the Law of Large Numbers

Each lottery draw is independently random. However, if you observe many draws together, you’ll notice that the Irish Lotto game follows a deterministic behavior. This is possible because of the law of large numbers, which states that with more and more draws, the outcomes align closely with what’s likely to happen according to probability.13

The image of randomness shows streaks and clusters.
The image above indicates streaks and clusters in a genuinely random lottery game. This behavior could give hints about how to play the lottery more strategically and make smarter decisions. Read “A Truly Random Lottery with a Deterministic Outcome.”

The Irish Lottery had 890 draws from September 5, 2015, to March 16, 2024. The comparison table below should show an agreement between theoretical estimation and actual results.

We determine the expected frequency by multiplying the probability by 890 draws.

Expected Frequency = Probability x 890

Therefore, for the 3-odd-3-even, the expected frequency will be 297.

Expected Frequency = 0.33382813788553500 x 890 = 297

If we do the same computation for the rest of the compositions, we will arrive at the following table and comparison graph below:

Bar graph updated as of March 16, 2024. This is the Irish Lotto odd-even anaysis with 890 draws. The graph shows apparent agreement between predicted frequency and actual draws.

As you can see from the table and the accompanying graph, the expected frequency and the actual frequency are very close. Knowing the relationship of probabilistic prediction to the actual draws helps you learn how to win the Irish Lotto.

This is the power of mathematics. Thanks to probability, we can determine the likely behavior of the game over many draws.

It’s important to understand that the prediction and the actual value may not necessarily be exact. However, the probability can serve as an accurate guide on what to expect.

The Irish Lottery Using Lotterycodex

Combinatorial and Probability analysis is a complex process. Without proper methodology, you may get contradicting conclusions.

For example, we show you that the 3-odd-3-even group dominates the 6/47 game. However, not all combinations with a 3-odd-3-even composition have a favorable success-to-failure ratio.

The combination 1-2-3-4-5-6 belongs to the 3-odd-3-even group, but based on its composition, it cannot have a favorable success-to-failure ratio. A truly random lottery fairly spreads the probability between low and high numbers.

So, precision and accuracy are important when dealing with combinatorial and probability analysis.

To accurately represent the lottery’s random behavior, we must consider sets of numbers that spread the probability fairly across the entire number field, putting odd/even numbers and low/high numbers in one combinatorial calculation.

Lotterycodex puts the number field of the Irish Lottery into four sets, as shown below:

Lotterycodex uses four sets as basis for its calculations of the 6/47 game. The four sets are LOW-ODD, LOW-EVEN, HIGH-ODD, and HIGH-EVEN.

Generated by Lotterycodex calculator

These number sets fairly distribute the probability across the entire number field. The results of the Lotterycodex analysis will allow you to see the likely behavior of the Irish Lottery draws over time according to the law of large numbers.

Lotterycodex categorizes compositions into templates. These templates are then classified as dominant, occasional, or rare, as illustrated in the table below:

Lotterycodex categorizes the Irish Lottery game into dominant, occasional, and uncommon.

Generated by Lotterycodex Calculator

Remember, matching the right composition doesn’t automatically make you an Irish Lottery winner. These templates can be a helpful guide, especially if you’re not a fan of math and prefer to avoid complex manual calculations with large numbers. Read on: The Winning Lottery Formula Using Math

How to Win Irish Lotto

If you want a better chance of winning the Irish Lotto game, buying more tickets helps. However, using a lottery wheel could make this strategy even better than buying tickets randomly. A lottery wheel is a strategic way to trap winning numbers. You cannot achieve this strategic trapping method by simply buying tickets randomly. To learn more, check out “Lottery Wheel: A Clever Mathematical Strategy That Works.”

We created the Lotterycodex calculator as a powerful lottery wheel. It helps you determine which groups of combinations dominate the Irish Lottery’s draw, helping you choose numbers wisely. Read Lottery Calculator: A Mathematical Guide Beyond Number Selection.

Using Lotterycodex templates, always choose the success-to-failure ratio that will favor you. These templates are #1, #2, and #3.

The table below reveals how Lotterycodex predicts the likely behavior of the game according to the law of large numbers.

If you're looking for tips on how to win Irish Lotto, you should familiarize yourself with these Lotterycodex templates. The Irish Lottery consists of different combinatorial groups called templates with varying ratios of success to failures. This image shows that templates #1 dominated the lottery draws over time and will continue to dominate as more draws take place.

Generated by Lotterycodex Calculator

Lotterycodex’s predictions, laid out in tables, provide insights into the game’s likely trend based on the law of large numbers. The templates, sorted by success-to-failure ratios, allow players to make informed choices. If you’re not a fan of doing complex calculations manually, especially involving probabilities and combinations of large numbers, these templates simplify this process.

What Are Your Thoughts About the Irish Lotto Game?

Do you know how to win the Irish Lotto? Share your thoughts. Add value to the conversation. Here are some questions for you to review:

How can math help in selecting Irish Lotto numbers?

The recommended mathematical strategies for choosing Irish Lotto numbers include combinatorics and probability theory. Combinatorics helps understand the possible combinations that can be formed from the lottery’s number set, while probability theory assesses the success-to-failure ratio. These concepts help make more informed choices rather than relying on random selection, luck, or superstition-based methods. However, it’s important to remember that lottery outcomes are still unpredictable.

What are the odds of winning the Irish Lottery jackpot?

For the Irish Lotto, players pick six numbers from 1 to 47. The odds of getting all six numbers correct and winning the jackpot are 1 in 10,737,573.

Does purchasing more Irish lotto tickets boost winning odds?

Buying more Irish lotto tickets mathematically increases the chances of winning. However, buying more tickets is useless if you’re not making informed choices. It’s also important to know your success-to-failure ratio when selecting numbers, and this ratio can be calculated using combinatorial mathematics and probability theory.

What is a common mistake in selecting Irish Lotto numbers?

A common mistake in selecting Irish Lotto numbers is choosing combinations randomly without understanding the associated success-to-failure ratio. This approach is not only expensive but also a waste of time. As an Irish Lotto player, your job is to aim for more favorable shots, and understanding this success-to-failure ratio will help you make informed choices when playing the lottery.

How do odds differ from probability in the context of the Irish Lotto?

In the context of the Irish Lotto, odds and probability represent different concepts. Probability is the measure of how likely an event is to occur. For example, the probability of winning the jackpot is calculated based on the total number of possible number combinations. On the other hand, odds compare the likelihood of winning against losing. It’s a ratio of the number of ways to get favorable shots to the number of ways you get unfavorable shots. Both concepts are crucial in understanding the chances in lottery games but are calculated and interpreted differently.

What role does the law of large numbers play in the Irish Lottery?

In the context of the Irish Lottery, the Law of Large Numbers suggests that as more lottery draws occur, the actual outcomes will align more closely with the expected probability distributions. Over a large number of draws, the frequency of each combinatorial group being drawn should approximate its mathematical probability. Since combinatorial groups have varying success-to-failure ratios, certain groups will dominate the Irish lottery draws and continue to do so as more drawing events occur. This law highlights that while individual draws are random, the overall trend over many draws will reflect the underlying probabilities.

Thank you for reading.

Additional Resources

  1. Irish Lotto Odds of Winning    []
  2. The Truth About Winning Small Prizes in the Lottery    []
  3. When to Trust Your Gut    []
  4. Developing Your Intuition For Math    []
  5. Do The Math, Then Burn The Math and Go With Your Gut    []
  6. A Truly Random Lottery with a Deterministic Outcome    []
  7. Combinatorics    []
  8. Probability Theory    []
  9. The Lotto Secret: Three Math Strategies for Winning Revealed    []
  10. What is the difference between odds and probability?    []
  11. Odds and Probability Explained in the Context of a Lottery Game    []
  12. Probability    []
  13. Law of Large Numbers    []

2 comments

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  • I think the irish lotto is 6 numbers and a bonus, so that would be pick 7 from 47, which would affect your calculations. Not certain, so might be wrong.

    • The Irish Lotto game is a 6/47 game. The bonus number provides additional layers of winning opportunity but only six numbers are required to win the jackpot prize. The rule of the game is to pick 6 numbers from 47.

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