Lottery Can Be Predicted To An Extent According To Math

By Jesse Veluz | Last Updated June 7, 2016

Losing the lottery, especially when the jackpot gets as big as the Powerball’s $1.5B record jackpot, can be devastating. However, if you’ve been playing the lottery for a long time now and kept losing, what makes you think you’ll win this time?

Jesse Veluz


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Lottery formula - lottery predictions with the use of probability analysis and binomial coefficients

The lottery is random by nature, but as far as mathematics is concerned, it can be predicted to an extent.

Firstly, it is important that I introduce some basic mathematical concepts to you. This will be your foundations in understanding the rest of this article’s content.

But don’t worry! You don’t need a math degree to understand anything here.

Let’s start…

The Two Math Formulas That All Lottery Players Should Be Thankful For

Firstly the binomial coefficients formula or nCr the combination formula.

This is the formula used to compute for the number of possible combinations in a given set.

The formula will be expressed as:

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

The second, is the P(A) the probability formula.

This formula is used to compute for how likely an event is to happen. In this case, the formula will be used to compute for the probability of a certain set of numbers appearance in a lottery.

The formula will be expressed as:

P(event) = No. of Favorable Outcomes / Total No. of Possible Outcomes

The two formulas previously listed above are essential to understand the odds of winning in various different lotteries in the world.

Let’s take one example:

The 6/47 Irish Lottery Game

n = 47, r = 6

Total no. of combinations

nCr = (47/6)(46/5)(45/4)(44/3)(43/2)(42/1)
= 10,737,573

If A represents one of the combinations, then:

P(A) = 1/10,737,573
= 0.0000000931309151518691

As you can see the odds of winning are 1 in 10,737,573.

Considering the astronomical odds of winning, you are likely thinking it is impossible to win.

But, hang on, there’s more to the lottery than meets the eye.

The Problem With Classical Approach To Lottery Strategy

As we have seen from our previous computation above, the odds are truly astronomical. In fact, winning the Irish Lottery with odds of 1 in 10,737,573 is less likely to happen than get hit by lightning.

In the Mega Millions, the odds or winning are 1 in 259 million.

In Powerball, your odds of winning are a staggering 1 in 292 million.

The chances are so slim so that your chances of becoming the next president of the United States are better.

Of course, in probability, if you do not play the lottery, your chances of winning will then be reduced to zero or “impossible”.

So this is the problem with playing the lottery in a classical approach. Players are always looking at the odds based on individual combination.

You won’t win the lottery if you keep looking at the lottery one-sidedly.

Fortunately, there is hope.

“All lottery players must stop focusing on the odds one-sidedly.”

By digging deeply into how the lottery works, you will find certain observable patterns that will give you the key on how to win the lottery.

Certainly, this calls for looking at lottery playing in a different way.

Key Takeaway:

“All lottery players must stop focusing on the odds one-sidedly. By digging deeper into how lottery works, you will find certain observable patterns that will give you the key to the winning formula. Certainly, this calls for looking at lottery playing in a different way.”

So if looking at the lottery one-sidedly does not help you win, then what does?

Enter Gianella’s Template.

Gianella’s Template – How To Win The Lottery Using Modern Approach

Renato Gianella is a Brazilian mathematician who published a study called the Geometry of Chance in 2013. 1

Gianella recommends players to play the lottery with combinations of numbers based on a “template” with greater likelihood of winning.

To illustrate how Gianella’s Template works, he grouped numbers into different colors like the one below:


Lottery color guide - 1 to 10 belongs to yellow, 10 to 19 belongs to cyan, 20 to 29 belongs to gray, 30 to 39 belongs to green, 40 to 49 belongs to magenta, 50 to 59 belongs to olive, 60 to 69 belongs to red and 70 to 75 belongs to blue group.

Using the colored group of numbers above, we can produce many different patterns like the ones below:



In Gianella’s study, using these templates show that patterns do not have the same chances of winning.  Therefore, in order to win the lottery, you must play the lottery using patterns that have higher probability of getting drawn.

Let me say that again, “combinations that have higher probability of winning”.

By picking numbers based on those winning patterns, you are improving your odds.

In application of Gianella’s theory by Lottometrix on popular lotteries, they confirmed Gianella’s theory that not all combinations have equal chances of getting drawn.  People at Lottometrix have sorted the patterns according to their probabilities.  The ones on the top being the best of them all while patterns at the end of the list are considered the worst. 2

The “worst” patterns are the ones people should avoid at all cost because it is unlikely for them to appear in a thousand years to come.

Key Takeaway

In order to win the lottery, you must play the lottery using patterns that have higher probabilities of getting drawn.

Now that we know that the best way to play the lottery is by choosing the best patterns rather than just simply picking numbers at random, let’s discuss now how to determine these precious patterns.

How Do We Identify The Best Patterns In Lottery

We use math.

A complete description of the method is describe in this article titled How To Win The Lottery According To Math. 3

To apply math in lottery, first we get the probability of each pattern based on the two formulas we have discussed above.  Then, we multiply the probability with the number of total draws to get its expected frequency or in simple terms, the “estimated occurrence” of the pattern.

According to The Law Of Large Numbers, the average of the results obtained from a large number of trials should be closed to the expected value, and will tend to become closer as more trials are performed to infinity. 4, 5


Therefore, to prove that our recommendation of playing the lottery based on patterns is correct, our estimation should be close to the actual results, given a sufficiently large number of data from actual lottery draws.

So without further ado, let’s go to the confirmation part of this article.

Enter actual lottery results.

The Empirical Proof Reflected on Big Lotteries

We can proceed with computing for each possibility, but probability will always be a means to put a solid number on our expectations scientifically and mathematically. It’s merely a guide on how events will turn out eventually.

So let’s see how our expectations match with actual lottery results.

Lottometrix have studied 7 of the most popular lotteries in the world.  These include Powerball, Mega Millions, Australian Saturday Lotto, Irish Lotto, Euro Millions, Euro Jackpot and UK Lotto.

Take a look at some examples of computations from these lotteries. The results should prove the closeness of estimation from actual lottery results.

Australian Lottery

Analysis Period: June 2, 1990 to June 11, 2016
Period Covered 26 years
Total Draws 2,160 draws
Pattern Probability Expected Frequency Actual Occurrence
Pattern 1 0.0298340344 64 62
Pattern 2 0.0223755258 48 49
Pattern 3 0.0149170172 32 32
Pattern 4 0.0134253155 29 27
Pattern 5 0.0119336137 26 25
Pattern 6 0.0111877629 24 21
Pattern 7 0.0089502103 19 20
Pattern 8 0.0082872318 18 19
Pattern 9 0.0074585086 16 15
Pattern 10 0.0066297854 14 17
Other patterns…
Total 1 2,160 2,160


As you can see from the table of Australian lottery results of 2160 draws, the column “Expected Frequency” and “Actual Occurrence” matches extremely close.

The column “Expected Frequency” shows our estimation of how many times the pattern will appear.

The column “Actual Occurrence” shows the actual appearance of the pattern in actual lottery draws.

We estimated pattern 1 to occur about 64 times in 2160 draws.  The actual lottery results show 62.

Pattern 2 is estimated to appear about 48 times in 2160 draws.  The actual draws show 49.

The rest of the patterns show similar accuracy in estimation and actual appearances.

Therefore, this proves that lottery patterns exhibit different probabilities and the probability of each pattern is instrumental in predicting how many times it will appear in a given number of draws.

The table shows that if you are to select the best patterns to play in the lottery, you would pick “pattern 1”.  However, there are 210 patterns in Australian lottery, it’s impossible to list down  all the patterns.

The complete list of these Australian lottery patterns with their corresponding computations is freely accessible in Lottometrix website.

Now let’s see the other patterns from other lotteries.

The Euro Millions

Analysis Period April 16, 2004 to June 17, 2016
Period Covered 12 years
Total Draws 899 draws
Pattern Probability Expected Frequency Actual Occurrence
Pattern 1 0.0424776756 38 36
Pattern 2 0.0212388378 19 19
Pattern 3 0.0191149540 17 17
Pattern 4 0.0169910702 15 12
Pattern 5 0.0095574770 9 8
Pattern 6 0.0095574770 9 9
Pattern 7 0.0086017293 8 6
Pattern 8 0.0076459816 7 6
Pattern 9 0.0056636901 5 4
Pattern 10 0.0047197417 4 4
Other patterns…
Total 1 899 899


Similar to the table above, the estimations from the expected frequency tab matches extremely close with actual occurrences or values under the observed frequency tab. This, again, shows that probability can, indeed, pose as an accurate guide in predicting how a lottery behaves.

Again, from the table above, it shows that if you are to select the best patterns to play in the Euro Millions, you would pick pattern 1.  However, there are 195 patterns in Euro Millions. What you see on the table above are just samples of patterns.

Now that we’ve proven that the lottery exhibits observable patterns wherein each pattern has different probabilities, this gives us a way to predict how the lottery behaves on a sufficiently large number of lottery draws.

Lottometrix Predictions On Popular Lotteries

Powerball was recently changed its matrix to accommodate bigger jackpots on October 7, 2015.

Irish Lottery changed its matrix just last year, September 3 of 2015

UK lottery changed its matrix on October 10, 2015

Since, we know that measuring the probability is an accurate tool for identifying the best patterns in a lottery,   we can use the same probability analysis to predict how the lottery behaves in the future.

Let’s go first with the new Powerball 5/69 Lottery game.

Which pattern are you going to play? Pattern 1 or Pattern 10?

I’m guessing by now, you would say pattern 1.

The question now is, how do you know which pattern you’re playing?

Lottometrix team has analyzed 7 of the most popular lotteries and you can now see all these patterns for free when you visit their website.

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