Lotterycodex Mathematics Meets The Lottery

Top 10 Lottery Strategy Myths Debunked (Perhaps You’re Doing #4 or #10)


Despite what the experts are telling us, many players continue to devise a system to circumvent the odds of the lottery. The problem, many of these methods are based on misconceptions about how the lottery game works.

Here, in my opinion, are the top lottery strategy myths that lotto players should need to know.

1. You can pick better numbers by studying the past lottery results

In Mathematics, there are two kinds of random events: dependent and independent. In the lottery, every single draw is considered independent. It only means that the previous 100 draws will not affect the next draw.

It amazes me that many players would try to pick the most likely numbers based on the frequency in the last 100 draws. This approach is one example of people doing it all wrong.

The lottery doesn’t work on individual numbers. You have to pick five or six correct combinations to win the jackpot. So the player should be looking at combination pattern rather than the performance of individual numbers.

And if you focus on the combination pattern, you have the Math to back you up without laboring how the lottery performs in the past.

In Mathematics, it’s easy to determine the best combination patterns through the use of Binomial Coefficients and Probability formula. Let me give you an example:

What is the best combination of low and high numbers in the 6/49 lottery game?

If we divide the numbers into the following sets:

Low numbers = {1,2,3,4,5,6,…25}

High numbers = {26,27,28,29,30,…49}

Then, we will come up with the complete list of low-high combination patterns and their corresponding probability below:

Combination Pattern Probability Expected Occurrence in 100 draws
0-low-6-high 0.0096251266 1
1-low-5-high 0.0759878419 8
2-low-4-high 0.2279635258 23
3-low-3-high 0.3328991171 33
4-low-2-high 0.2496743378 25
5-low-1-high 0.0911854103 9
6-low-0-high 0.0126646403 1

The above table shows that the best patterns are 2-low-4-high, 3-low-3-high, and 4-low-2-high. Playing with the rest is just waste of money.

There is no need to check the past lotto statistics to build a similar conclusion. Although, in Lotterycodex, I use the past results because comparing mathematical estimation with the past actual lottery results is important to prove my point. This comparison helps the readers understand how Mathematical estimation works.

To see is to believe

I invite you to prove it yourself. Check any 6 number game lottery and go down the past 100 draws. Then tally the trending low-high pattern.

As always, probability doesn’t favor all-odd or all-even patterns.  It is always the 3-low-3-high pattern that will always dominate in a six-game lottery format.

Mathematics will not fail us. We can always see what’s working without looking at the past results.

Having said, that, I invite you to visit the lottery analysis section to see what works in the lottery based on the probability theory.  I have covered all lottery systems.  Chances are I have a detailed probability analysis for your local lottery system.

2. Every combination has the same probability

I heard and read them a lot. And this traditional belief must come to a stop.

Every one of us grew up and educated by the principle that each number has an equal chance of being drawn as any other number in the number field.  It’s true.  But that statement doesn’t apply when you combine numbers.

Let me clarify.

Single number and combination are two different terms in the lottery.

Every single number in the number field has the same probability of occurrence in a draw as any other.  It’s a mathematical fact.  I won’t argue on that issue.

But you don’t win the lottery by picking a single number.  That’s not how the lottery works.

You have to choose 5 or 6 numbers and match the winning combination to win the lottery.

However, when you combine numbers, the probability changes.

The probability of your combination depends on its structure.

Now to prevent confusion. Odds and probability are two different terms in mathematics.

Let me clarify that the entirety of this article talks about the “probability theory.”  In fact, the Lotterycodex, as a website deals with probability theory as one of the primary tools for lottery players.

Having clarified that, let’s proceed…

In my Mathematical studies of the lottery, I have discovered that number combinations in the lottery don’t have equal chances of getting drawn.

Some combinations will appear more often than others. And some combinations will never occur in the lottery (almost).

Let me illustrate that.

Let’s take a look at the low-high number patterns in a 6/49 lotto game once again:

Combination Pattern Theoretical Probability Expected Occurrence in 100 draws
0-low-6-high 0.0096251266 1 – the worst
1-low-5-high 0.0759878419 8
2-low-4-high 0.2279635258 23
3-low-3-high 0.3328991171 33 – the best
4-low-2-high 0.2496743378 25
5-low-1-high 0.0911854103 9
6-low-0-high 0.0126646403 1

As we can see from the table above, the difference between the best pattern and the worst pattern is huge. The 3-low-3-high combination pattern appears 33 times in 100 draws while the 6-low-0-high combination pattern appears only once in 100 draws.

The comparison between theoretical and actual lottery results reveal that all winning combinations in the lottery follow a deterministic pattern.

Putting this in perspective, this is similar to saying: 1-2-3-4-5-6 (all low numbers) will never be as good as 1-15-21-33-38-40 (3-low-and-3-high).

The probability is not equal.

This vast difference in probability answers why 1-2-3-4-5-6 has never occurred in the history of the lottery.

Want proof? Then, read further.

What you will see below are proofs that the actual lottery results agree with the probability theory.  The theoretical estimation closely matches with the actual results.

In Australian Tattslotto 6/45:

601 draws from January 7, 2006, to July 15, 2017.

Expected Occurrence
6-low-0-high 7 7
3-low-3-high 201 199

Read: How To Win The TattsLotto 6/45 According To Math

In U.S. Powerball 5/69:

A total of 175 draws.  Results statistics from October 7, 2015, to July 15, 2017.

Expected Occurrence
5-low-0-high 5 8
3-low-2-high 55 57

Read: How To Win The US Powerball 5/69 According To Math

In EuroMillions 5/50:

A total of 1009 draws.  Results statistics from April 16, 2004, to July 14, 2017.

Expected Occurrence
5-low-0-high 25 31
3-low-2-high 329 377

Read: How To Win The Euromillions 5/50 According To Math

In Irish Lottery 6/47:

A total of 194 draws. Results statistics from September 5, 2015, to July 15, 2017.

Expected Occurrence
6-low-0-high 2 2
3-low-3-high 65 72

Read: How To Win The Irish Lottery 6/47 According To Math

In EuroJackpot 5/50:

A total 277 draws.  Results statistics from March 23, 2012, to July 14, 2017.

Expected Occurrence
5-low-0-high 7 12
3-low-2-high 90 93

Read: How To Win The Eurojackpot 5/50 According To Math

In UK Lotto 6/59:

A total of 182 draws. Results statistics from October 10, 2015, to July 15, 2017.

Expected Occurrence
6-low-0-high 2 2
3-low-3-high 60 70

Read: How To Win The UK Lotto 6/59 According To Math

In U.S. Mega Millions:

A total of 390 draws. Results statistics from October 22, 2013, to July 14, 2017.

Expected Occurrence
5-low-0-high 11 10
3-low-2-high 127 135

Read: How To Win The US Mega Millions 5/75 According To Math

The above tables show that the difference between the best combination pattern and the worst combination pattern is huge. My probability studies of the lottery prove that combinations, depending on their patterns, don’t have equal probability. See my post: How To Win the Lottery Mathematically.

If those tables didn’t convince you that combinations have different probabilities, then I don’t know what does.

If you go to the lottery analysis section, you will see the bad, the worst and the best number patterns in your local lottery system.  Do not play the lottery until you know what works best for your game.

3. You cannot predict the lottery

The lottery is unpredictable alright.  But you can predict the lottery to an extent.

If you read myth #1 and #2, then you should know already that winning numbers follow a deterministic pattern.

In fact, you can tell how a pattern performs in a given number of draws. To do that, we multiply probability by the number of draws to get the estimation.

Let’s go back to my probability analysis of the Lotto 649 game regarding the low-high number pattern and see how lotto prediction is possible.

Combination Pattern Probability Expected Occurrence in 2000 draws
0-low-6-high 0.0096251266 19 – the worst
1-low-5-high 0.0759878419 152
2-low-4-high 0.2279635258 456
3-low-3-high 0.3328991171 666 – the best
4-low-2-high 0.2496743378 499
5-low-1-high 0.0911854103 182
6-low-0-high 0.0126646403 25

Read: Predicting The Lotto 649 Winning Numbers According To Math

I do not know you, but for me, I don’t see any reason why I would wager for All-6-high and All-6-low. Obviously, I don’t see any reason why anyone would avoid the 3-odd-3-even number pattern in the lottery.

Ultimately, the most important takeaway here is that you know what number pattern will dominate in 2000 draws.

If that is not a prediction, then, I don’t know what it is.

In the lottery analysis section, you will find a complete lotto prediction table for the most popular lottery systems played around the world.  Local lottery systems are included there as well.

4. Picking hot numbers give you more chances of winning

If you believe that playing with the most common winning lottery numbers will help you take the big jackpot home, then I’ve got some bad news for you.

In Probability theory, every number has an equal chance of getting drawn. For example, if a single number is expected to appear 100 times, then the rest are bound to occur more or less in the same frequency over a large number of trials.

As the number of draws takes place to infinity, the frequency of each number will tend to converge in the same theoretical probability. This theorem is The Law Of Large Numbers or LLN in mathematics.

In layman’s term, the LLN means that from the initial draws, there may be numbers that appear more frequently in the lottery but the rest of the numbers will eventually catch up soon as lottery draw continues to take place to infinity.

Given a large number of draws, the occurrence of each number in the lottery tends to be close to each other and getting closer and closer as more lottery draws take place.

Like I said earlier, in the lottery it is the combination that matters and not the individual numbers.

The rules of the game require you to combine 4, 5 or 6 correct numbers. So to have a better strategy, you are better off counting the most frequently appearing combination pattern than tracking the most frequently appearing numbers.

But like I said in myth #1, you don’t need to review 100 past results.  You have the power to know what will work in the lottery without statistics.  Get your pencil and paper and work it out mathematically.

Or just check out the complete list of the bad, the worst, and the best number patterns in the lottery here as everything is computed for you already and it’s available for free.  You just need to pick what works.

5. The number 13 is the unluckiest number in the Lottery

There are no lucky or unlucky numbers in the lottery. All numbers have the same theoretical probability, and therefore the only way to increase your chances is to understand how the lottery works from the Probability standpoint.

If you follow me, on myth #4, you should already know that the Law Of Large Numbers does not respect superstitious belief. Again, I would like to reinforce that it is not the individual numbers that matter in the lottery. It is hitting the right combination that matters.

But again, if you want to be lucky, then go to the lottery analysis section and follow the recommendation.  Lucky for you, you don’t need a degree in math to understand how it works.  Everything is computed already.  You just need to pick what applies to your local lottery system.

6. Prime numbers appear more frequently

Here is another case of making assumptions but failing to explain how things work from a mathematical perspective. Consistently, players always have this “performance-of-individual-numbers” mentality.

Here is the complete list of prime numbers used in the lottery:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

I reckon the number 97 is probably the last prime numbers in the lottery. I do not know any lottery that operates beyond 99. If any, let me know.

Now, did you notice that the number 2 is the only even prime from the list and that the rest are odd numbers? If you already read my article How To Win the lottery Mathematically, you will notice that the best probability is leaning towards the balanced mix of odd and even numbers.

Both theoretical estimation and the actual lottery results show that playing all-odd number pattern is not recommended at all. Simply put, playing with all-odd number pattern in the lottery is just waste of money.

Let’s take a look at the odd-even patterns in some of the most popular lotteries below:

The Euromillions 5/50 Results

970 draws from April 16, 2004, to February 28, 2017.

3 odd + 2 even 316 354
3 even + 2 odd 316 291
1 odd + 4 even 145 140
1 even + 4 odd 145 140
All 5 even 24 25
All 5 odd 24 20
970 970

Read: How To Win The Euromillions 5/50 According To Math

If you are seriously considering to win the jackpot, then choose to play both the 3-even-2-even or the 2-even-3-odd combination pattern.  The table shows that wagering for all prime numbers is not the best approach at all.

Let’s see how the odd-even pattern works in other lotteries.

The U.S. Powerball 5/69 Results

146 draws from October 7, 2015, to March 04, 2017.

3-odd-and-2-even 48 42
2-odd-and-3-even 46 43
4-odd-and-1-even 23 27
1-odd-and-4-even 21 30
5-odd-and-0-even 4 2
0-odd-and-5-even 4 2
146 146

Read: How To Win The US Powerball 5/69 According To Math

The TattsLotto 6/45 Lottery Results

582 draws from January 7, 2006, to March 04, 2017.

3-odd-and-3-even 194.88 187
4-odd-and-2-even 146.16 154
2-odd-and-4-even 132.24 143
5-odd-and-1-even 52.90 50
1-odd-and-5-even 43.28 39
6-odd-and-0-even 7.21 5
6-even-and-0-odd 5.33 4
582 582

Read: How To Win The TattsLotto 6/45 According To Math

I can list hundreds of these tables from different lottery systems and show you that winning numbers are composed of a balanced mix of odd and even numbers.

Suggested Homework

Go back to your favorite lottery’s past 100 results.  Tally the odd-even pattern and see what’s trending.

You will discover that number patterns exactly perform as determined by Mathematical theory:

All-even combination or all-odd (the worst)
3-even-3-odd combination (the best for a six-number game)
2-even-3-odd, and 3-even-2-odd (the best for a five-number game)

My recommendation: forget about prime numbers.  Before you play the lottery, be sure to visit the lottery analysis section and follow the recommendations.  You don’t need to calculate.  You just pick what applies to your lottery.

7. The better time to play is when the jackpot is big

When the prize is big, a horde of lottery fanatics will play, and the chances of sharing the big prize are therefore very high. Certainly, it doesn’t make sense to win the big jackpot and then only taking home just 1/3 of the money. It is just the equivalent of winning when the jackpot is less attractive. Isn’t it?

Sure, you can wait to play when the draw’s jackpot is at its highest to make the most out of your ticket but what is the guarantee that the prize is going up the next draw. In short, waiting is just pointless.

As soon as your savings are enough, go out and play.  Notice that I mentioned “savings.”  That’s is because I want you to play the lottery responsibly.  I am not suggesting that you play every draw.  You have to save money for your lottery entertainment.  You have to follow a game plan.  See my post: The Lottery Game Plan.

8. Birthdates, anniversaries, ages are poor numbers

Some experts tell players to avoid them. The probability of others using the same set of numbers as yours is very high. It’s not okay when you share your winnings with others because it reduces your take-home prize.

In my opinion, if those numbers are part of a lottery strategy, then it’s not bad at all. But, if you don’t know what you are doing, then, those numbers become useless.  Read what math says about using birth dates.

My recommendation: Pick the numbers based on the best pattern in your lottery system.  Don’t worry about other things (re dates, ages, etc.).  See The Lottery Analysis Section for more guidance on this.

9. Selecting your numbers using aesthetic pattern

The lottery is a random game. It knows no beauty. If you pick numbers based on pretty patterns like the ones below, then, don’t anticipate a victory party.

picking numbers in the lottery using pretty patterns

Do you think the patterns above will have any chance in the lottery? I understand that selecting numbers during a lotto play is hard.  But I highly recommend putting more effort into your number selection process.  It’s worth the effort.

Sure, Math is not everyone’s cup of tea. In which case, grab someone’s shoulder who knows their ways around Algebra.

Or you can just go to the lottery analysis section and see what works in your lotto game system. Nothing to calculate, just use the information to strategize and plan your attack in the lottery.

It seems to me that majority of the lotto players are clueless on how number system works during a random draw.

In fact, the Powerball website itself unknowingly reveals how 70% to 80% of players are doing it all wrong.

Want to know what this is?

Then read the next and the most critical misconception that you should understand and must avoid at all cost.

10. Quick pick machine gives you better chances of winning

I believe, the majority of quick pick machines installed in your local lottery shop are mainly producing numbers on a random algorithm. In my opinion, random selection is just playing the lottery without a strategy.

Some of you may know me already; I always advocate strategizing your game plan because that’s where FUN begins.  Number selection is part of the enjoyment.

I reckon quick pick machine doesn’t give you that much fun.

Hang on; I heard someone say…

But Edvin, most of the winners I heard from the news are coming out by quick pick machine. Does this not enough proof that quick pick machine works?

Short answer:

No. Many are winning by quick pick machine because the number of players who use it is higher than those who pick numbers by hand.

Long answer:

The number of players winning by quick pick machine is not the right gauge to prove that it can give you better chances of winning. Although, the lottery operators would love you to believe.

In the old Powerball FAQ section (January 2017 version)  once said this:

About 70% to 80% of purchases are computer picks. About 70% to 80% of winners are computer picks. Perhaps just one of those weird coincidences?

If we follow the official statement we found on the Powerball website, we get:

Probability(Quick pick) = 80% of winners / 80% of purchases

Probability(Player pick) = 20% of winners / 20% of purchases


Probability(quick pick) = Probability(player pick)

The official Powerball website only means that:

The chances of those who use quick pick machine and the chances of those who pick numbers by hand are just the same.

So for simplicity sake, let’s just assume hypothetically that there is 1 winner for every 292 million tickets so that we come up with a probability table below:

Selection Method Probability
P(quick pick) 0.000000003
P(player pick) 0.000000003

And assuming there are 30 billion total purchases in Powerball, therefore, we get:

0.000000003 x (80% of 30 billion) = 80% of winners are quick pick

0.000000003 x (20% of 30 billion) = 20% of winners are player pick

So there.  The same probability.

You may go back to the historical statistics to prove the calculation, but honestly, I reckon spending time with the past lottery results isn’t worth it. Again, you don’t need lottery statistics because math does not lie.

Perhaps, the main thing that you need to understand is that you don’t have control when you use the quick pick machine.

For one thing, a machine has no common sense to know what works in the lottery. It just picks numbers randomly for you without analyzing the numbers.

So with the variables being equal, you are better off selecting numbers by hand.

If you generate your numbers, then you have better control in improving the probability to your favor like what the MIT students did when they monopolized the Massachusetts Cash Winfall in 2005 and continued for seven years.

They took advantage of the lottery’s weakness and profited $8 million from it. The majority of these students majored in BS Mathematics.

Interestingly, they did not win the big jackpot but winning $8 million in seven years isn’t a joke. Is it?

They know better than anyone else.

How did they do it? Simple.

While others save time by using the quick pick machine, these MIT students were busy using their prodigious math skills filling out lotto slip oval to oval. By generating their numbers, they knew they could produce a broader range of better matches.  A quick pick machine is not capable of this approach.

How did this group monopolize the lottery? I discussed it in the lottery analysis section.  In that section, you can also check out the number generator I am dreaming of building as an alternative to the quick pick machine.

My two cents

What is the best way to win the lottery? Avoid what doesn’t work. Focus on what works.  Plain and simple.  You can waste money, or you can play smart. Your choice.  I hope that you find these lottery tips helpful.  Let me know your thoughts.

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Lotterycodex Mathematics Meets The Lottery

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Edvin Hiltner

I get a good grasp of mathematical theory 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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