Lotterycodex Mathematics Meets The Lottery

How to Win the Irish Lottery 6/47 According to Math


People have been using hot numbers since ancient time believing that when a number is appearing more frequently, it is bound to appear more often in the next draws. This belief is contrary to the Mathematical Principles of probability.

Today I am going to discuss with you the Mathematical method to play the Lottery. Not many people are using this with the Irish Lottery. Let’s start off with a discussion of the odds of winning in Irish Lottery and how we can improve our chances of winning the Irish Lottery from a mathematical point of view.

how to win the Irish Lottery 6/47 according to mathematics

The Odds Of Winning The Irish Lottery

The rule of Irish Lotto 6/47 is to pick six numbers from 1 to 47. Using the Binomial Coefficient formula, we will come up with:

n = 47 numbers

r = 6 combinations

47C6 = 10,737,573 total possible combinations

So the odds of winning in the Irish Lottery is 1 to 10.7 million. The odds are not favorable for you, and I can say, you have a better chance of being elected leader in your local area than winning the Irish Lotto.

Winning the jackpot in the Irish Lottery is hard.  However, if you steer clear of the many strategy myths in the lottery and start playing Mathematically, you can improve your chances of winning.

We have to look at the numbers differently. The key is in the pattern. In short, you have to select the number pattern that will give you the best probability of winning.

Let’s discuss how we can do that in the Irish Lottery from a Mathematical standpoint.

The Odd-Even Patterns In The Irish Lottery

Focusing on a better odd-even pattern when you select numbers can drastically improve your probability of winning. Here is the complete list of odd-even patterns in the Irish Lottery with the corresponding probability:

Patterns Combinations Probability
3-odd-3-even 3584504 0.33382813788553500
4-odd-2-even 2688378 0.25037110341415100
2-odd-4-even 2443980 0.22761009401286500
5-odd-1-even 977592 0.09104403760514600
1-odd-5-even 807576 0.07521029193468580
6-odd-0-even 134596 0.01253504865578100
6-even-0-odd 100947 0.00940128649183573
10,737,573 100%

For simplicity, I divided the above patterns into three groups:

Best Patterns Fair Patterns Bad Patterns
3-odd-3-even 4-odd-2-even 5-odd-1-even
2-odd-4-even 1-odd-5-even

From the table above, it’s the 3-odd-3-even that has the best probability. As an Irish Lottery player, you should focus your strategy only with the best and nothing else.

Let me prove mathematically.

The Odd-Even Patterns From The Actual Irish Lottery Results

There are 155 draws in the Irish Lottery from September 5, 2015, to March 01, 2017. We will compare our Probability estimation with the actual results, and there should be no big difference between the expected frequency and the actual.

We determine the expected frequency by multiplying the Probability by 155 draws.

Expected Frequency = Probability x 155

Therefore for the 3-odd-3-even pattern, the expected frequency will be 52.

Expected Frequency = 0.33382813788553500 x 155
= 51.7433613723 or 52

If we do the same computation with the rest of the patterns, we will arrive at the following table below:

Patterns Expected frequency in 155 draws Actual frequency in 155 draws
3-odd-3-even 52 53
4-odd-2-even 39 42
2-odd-4-even 35 37
1-odd-5-even 12 10
5-odd-1-even 14 9
6-odd-0-even 2 1
6-even-0-odd 1 3
155 155

Probability estimation compared to actual Irish Lottery 6-47 results

As you can see from the table above, the expected frequency and actual frequency are very close which prove that Lottery behaves in a predictable pattern. And this is the power of Mathematics. We can determine the patterns that will perform best in the lottery. Thanks to Probability.

  • The 3-odd-3-even pattern is expected to appear 51 times. It occurred 53 times in the actual draw.
  • The 2-odd-4-even pattern is expected to appear 35 times. It occurred 37 times in the actual draw.
  • The 6-odd-no-even pattern is expected to appear two times. It occurred once in the actual draw.

In the Irish Lottery, it is the 3-odd-3-even pattern that stands out. Now, it’s important to understand that the expected value and the actual value may not necessarily be exact.

Probability is the Mathematical tool we use to estimate how likely an event will occur. For example. If we want to know in advance the outcome of Irish Lottery in 1000 draws, we use Probability.

If P(pt) = is the probability of pattern pt,


Expected frequency = P(pt) x 1000 draws

Therefore, if we are to predict the outcome of the odd and even patterns, we know it will always be the 3-odd-3-even that will stand out.

Patterns Probability Expected Frequency in 1000 draws
3-odd-3-even 0.33382813788553500 334
4-odd-2-even 0.25037110341415100 250
2-odd-4-even 0.22761009401286500 228
5-odd-1-even 0.09104403760514600 91
1-odd-5-even 0.07521029193468580 75
6-odd-0-even 0.01253504865578100 13
6-even-0-odd 0.00940128649183573 9

As an Irish Lottery player, you should pick the pattern with the best probability. That’s how mathematics can help. However, like any other lottery, the Irish Lottery is not about just Odd and Even. Deep within the 47 numbers, there are layers of complex patterns that can help you improve your chances of winning the Irish jackpot.

So now, let’s go deeper into the advanced patterns.

The Winning Number Patterns In Irish Lottery

For simplicity sake, I divided the patterns into three groups.

Group Patterns Number of Patterns
Best group Patterns #1, #2, #3 3
Fair group Patterns #4 to #49 46
Bad group Patterns #50 to #210 161
210 total patterns

Even though you can still play the fair group, I always recommend to stay with the best group and avoid the rest of the patterns. So as an Irish Lottery player, you should focus on only three patterns. They are patterns #1, #2, and #3.

There are 210 patterns in Irish lotto, but let’s take a look at some of them in the table below:

Patterns Probability Expected Occurrence
#1 0.0301744165 3x in every 100 draws
#2 0.0301744165 3x in every 100 draws
#3 0.0301744165 3x in every 100 draws
#180 0.0004380878 4x in every 10,000 draws
#185 0.0002346899 2x in every 10,000 draws
#198 0.0001173450 Once in every 10,000 draws

Like I said, focus on just the first three patterns #1, #2, and #3. The problem, the majority of the Irish lottery players are playing blindly.

Players should understand that there are patterns in Irish Lottery that will never be a winning combination in any draw. For example, the table below shows the worst patterns that you should avoid.

Patterns Probability Expected Occurrence
#205 0.0000469380 4x in every 100,000 draws
#206 0.0000195575 2x in every 100,000 draws
#207 0.0000195575 2x in every 100,000 draws
#208 0.0000195575 2x in every 100,000 draws
#209 0.0000078230 8x in every 1,000,000 draws
#210 0.0000026077 3x in every 1,000,000 draws

See the complete list.

If you are playing the Irish Lottery without knowing your patterns, what’s the guarantee you are not incidentally playing the bad ones? With the help of Probability, an Irish Lottery player gets two main advantages:

1. Save money
2. More probability of winning

Math is a very reliable tool. It’s how Science meets the lottery.

How To Win The Irish Lottery

For all the Irish Lottery players, I recommend the following strategies:

  1. Avoid the 5-odd-1-even, 1-odd-5-even, 6-odd-0-even, and 6-even-0-odd combinations
  2. Focus on high probability patterns especially on patterns #1, #2, and #3 (see the complete list at the lottery analysis section)

Now, here’s the most important thing. The lottery is truly a random game. Using math cannot help you beat the odds.  But you can use a properly crafted lottery game plan to improve your chances of winning.

Not even the best math guy in the world can beat the odds of the Irish lottery. But you can improve the way you play using probability theory.  For this reason, you are advised to play responsibly.

With proper attitude, lottery addiction problem could be prevented.

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Lotterycodex Mathematics Meets The Lottery

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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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