Probability & the Lottery

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Copyright Š 2018 by Edvin Hiltner – All Rights Reserved

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Probability and the Lottery in Layman's Term Do you know why you keep losing the lottery?

You probably keep doing the wrong thing and you don't even know it. Truth be told, you can't fix something you don't know exists.

Let me cut through the chase.

The belief that all combinations in the lottery have an equal chance of coming up should end up once and for all. Because the truth is, number combinations don't have equal probability.

And you probably keep playing combinations with very low probability.

What's the evidence?

Well, I guess the best evidence is to show you a couple of calculations then use the actual lottery draws to prove my calculation.

Let me start off by discussing the difference between a number and a combination.

The Difference Between a Number and a Combination Knowing the difference between the two plays an important role in your search for lotto strategy that works.

A number refers to an individual ball in the lottery. A combination, on the other hand, is a selection of numbers that when combined form a specific characteristic.

For example, 3-15-27-39-41-49 is a combination of all odd numbers.

The table below shows some examples of combinations.

So what’s the difference?

For a lottery player like you who aims at the biggest prize, the difference is huge.

What represents a number?

A number possesses equal probability as any other number in the lottery

What represents a combination?

A combination exhibits different probability depending on its characteristics

To put it simply, whatever number you pick in the lottery doesn’t matter. In fact, you can pick any number you like. Yes, including those numbers that you consider are unlucky (if any).

How you combine numbers is what makes the biggest factor in your winning chances.

For example, a combination which consists of all even numbers can only occur once in 100 draws while a balanced odd and even combination can occur 33 times in 100 draws.

If we want to know how these two combinations will occur in 1000 draws, we only need to multiply the number of draws by their corresponding probability.

Numbers don't lie.

A wrong combination leads to a waste of money.

While the right choice of combination leads to a good shot at the lottery.

Thanks to probability theory because we have the means to know which is which.

So Why Don't Combinations Exhibit Equal Probability?

Let me explain with the use of two simple types of marbles in a jar. The yellow and the red color marbles represent the types of combinations in the lottery.

As you see, the yellow marbles outnumbered the five red marbles.

Probability explains that when you randomly pick a marble from a jar with your eyes closed, you will more likely get a yellow one.

Your second and third pick will be more likely yellow marbles again because the probability leans towards the yellow marbles getting picked more often than the red ones.

In mathematics, we express the probability of the two types of marbles in the following ways: P(yellow) = 95/100 or 95% P(red) = 5/100 or 05% Assuming we reset the number of marbles in each trial, the yellow marbles will get picked 95 times in every 100 draws. Then the black marbles will only get picked 5x in every 100 draws.

The same probability principle rules in a random game such as the lottery.

Let me give you some theoretical proofs in the next pages that in fact combinations in the lottery exhibit different probabilities.

Odd/Even Combinations Let's group 49 numbers in two sets.

Odd Numbers 1,3,5,7,9,11,13,15,17,1 9,21,23,25,27,29,31,3 3,35,37,39,41,43,45,4 7,49 Even Numbers 2,4,6,8,10,12,14,16,18 ,20,22,24,26,28,30, 32,34,36,38,40,42,44, 46,48

We have 25 odd numbers and 24 even numbers.

The two sets represent the 49 balls of a lotto 6/49 game.

Out of these 2 sets, we can produce the following types of combinations:

Each odd/even pattern holds a certain number of possible combinations. The sum of all these combinations equals to 13,983,816 which represents all the combinations in a lotto 6/49 game. And the sum of all their probabilities should equal to 1.

From the table, above we see that it's the 3 odd and 3 even pattern that exhibits the best probability of getting drawn in a lotto 6/49 game. This type of combination is expected to occur 33 times in 100 draws.

And accordingly, those combinations which consist of either all even or all odd numbers are the worst combinations.

Noticeably, those combinations which consist of either 1 even or 1 odd are the middle types which go in between the best and the worst. Use of these types of combinations is up to your own judgment.

The following tables below should guide all lotto 6/49 players what combinations to play in a lotto 6/49 draw.

Recommended Combinations

Middle Type Combinations

Combinations to Avoid

Actual Lottery Results Versus Theoretical Calculation I have shown that combinations don't have an equal chance of getting drawn from a theoretical point of view.

Now, let's prove it by comparing our calculation with the actual lottery results.

As I said, we use probability to measure how likely a combination will occur in a given number of draws. So by multiplying probability value by a certain number of draws, we get the expected frequency of any type of combination in that given number of draws.

Expected frequency = Probability x number of draws And to prove that our theoretical calculation is correct, the expected frequency should closely match with the actual frequency.

Australian Saturday Lotto 664 draws from January 7, 2006 to September 29, 2018

Source: How To Win the Tattslotto 6/45 Can you notice the close match between expected frequency and actual frequency?

Take note that probability is simply a guide. Don't expect that values will always match exactly as estimated (though this happens a lot of times) Of course, this probability analysis does not only apply to the Australian lottery. In fact, probability theory applies to all lottery systems.

And as you see, the above table proves that number combinations don't have equal probability.

Let's move on to another lottery systems to further prove my point.

U.S Powerball 309 draws from October 7, 2015 to September 29, 2018

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

If you are noticing it, both theoretical probability and the actual lottery results agree that combinations have different probabilities. And we can prove it again and again. The succeeding tables below should speak for themselves.

Euro Millions 1,135 draws from April 16, 2004 to September 28, 2018

Source: How to Win the Euro Millions 5/50

Euro Jackpot 340 draws from March 23, 2012 to September 28, 2018

Source: How to Win the Euro Jackpot 5/50

Irish Lotto 320 draws from September 5, 2015 to September 29, 2018

Source: How to Win The Irish Lotto 6/47

U.S. Mega Millions 96 total draws From October 31, 2017 to September 28, 2018

Source: How to Win the U.S. Mega Millions 5/70 Note: Our analysis of the U.S. Mega Millions must start on October 31, 2017 because this is the date when lottery officials started to implement the 5/70 format.

UK Lottery 309 draws from October 10, 2015 to September 29, 2018

Source: How to Win the UK Lotto 6/59

Low/High Combinations

Aside from odd and even, numbers can be grouped into low and high. Let's group 49 numbers in two sets:

Low Numbers 1,2,3,4,5,6,7,8,9,10,11,12 ,13,14,15,16,17,18,19,20, 21,22,23,24,25

High Numbers 26,27,28,29,30,31,32,33 ,34,35,36,37,38,39,40,4 1,42,43,44,45,46,47,48, 49

Out of these two sets, our probability analysis shows that winning numbers tend to be evenly distributed in the entire number field as the majority of the winning combinations consist of 3 numbers from the low set and 3 numbers from the high set.

Similarly, players are encouraged to stay away from a combination which consists of purely low numbers or purely high numbers. This approach alone will make your lotto strategy a lot better.

Below are the tables showing all the types of combinations we can produce from the two sets of low and high numbers.

Recommended Combinations

Middle Type Combinations

Patterns to Avoid

Actual Lottery Results Versus Theoretical Calculation

Again, both theoretical calculation and the actual lottery results agree that some combinations perform better than others.

Let's take a look at the actual lottery draws again to prove our calculations:

Australian Saturday Lotto 664 draws from January 7, 2006 to September 29, 2018

U.S Powerball 309 draws from October 7, 2015 to September 29, 2018

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

Euro Millions 1,135 draws from April 16, 2004 to September 28, 2018

Euro Jackpot 340 draws from March 23, 2012 to September 28, 2018

Irish Lotto 320 draws from September 5, 2015 to September 29, 2018

U.S. Mega Millions 96 draws from October 31, 2017 to September 28, 2018

Note: Our analysis of the U.S. Mega Millions must start on October 31, 2017 because this is the date when lottery officials started to implement the 5/70 format.

UK Lottery 309 draws from October 10, 2015 to September 29, 2018

The Best and the Worst Combinations

Probability analysis can be problematic and quite confusing.

For example, a combination such as 1-2-3-4-5-6 consists of 3-odd-and-3even numbers and therefore according to our odd/even analysis, such combination is considered one of the best ones.

But we know it’s not true because conversely from our low/high analysis, a combination that is made of purely low numbers possesses a very poor probability.

Confusing isn’t it?

Evidently, odd/even or low/high analysis are not the best solution to determine the best and the worst.

There should be better way to know.

Fortunately, there is a solution. The solution is discussed in details in the free lottery guide section of Lotterycodex.com As I said, it's free to access the lottery guide section so don't forget to pay a visit and discover the best number combination that will give you the best shot possible at winning the lottery.

Conclusion: Number Combinations Exhibit Different Probabilities Our analyses above will show you that the lottery, in fact, has biases towards certain combinations.

Your combination should put you closer to matching all the winning numbers.

In this case, you would rather choose a combination that will likely occur 33 times in 100 draws rather than a combination that can only occur once.

As a lottery player who aims at the jackpot, you don’t want to bet on a combination with very poor probability. After all, you want the best shot possible. Don’t you?

But playing the lottery is more than just odd/eve or low/high.

Deep within the finite number structure of the lottery are layers of advanced and discrete number patterns that will give you the key solution to winning.

If you want a short introduction to the mathematical method of winning, I highly recommend to you this article: How to Win the Lottery According to Math. It's the best article to begin with for all lottery players who want to win the lottery soon.

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