How to Win the Lottery Math Algorithms (Complete Guide): Winning the lottery is a life changing moment. Get that good win and you’re good to go. But how do you win the lottery? Well, since a magic button is not available, math is still the only tool that can help. So if you want to hit the jackpot, you’re in luck, things are looking up.
But before we talk about the good news, let’s first talk about the bad news. Once you understand the roadblock to winning, it’s easy to come up with a sensible lottery strategy – one that works.
The Good News: Winning the Lottery According to the Math
Mathematically, you can increase your chances of winning.
The aforementioned, nobody will have prior knowledge of what will happen precisely in the next draw. Not even by a paranormal creature (if that also exists).
So when magic aid is not available, math is still the only excellent tool you can use to achieve lottery success.
I will reveal to you the many mathematical techniques that you can use to improve your ability to win. For the most part, we will deal a lot with the theory of probability and combinatorics.
With a little math and a little perseverance, you can play your game with the best shot possible.
Let me remind you that the calculations differ from lottery to lottery. For illustrative purposes, I’ll use the 6/49 lotto system for the most part.
By the way, in the free lottery guide, you will learn the complete formula for lottery success that will help you start your exciting journey on the right foot.
In the meantime, let me give you a brief introduction to some of the mathematical ways of playing the lottery one by one. (Of course we save the best method at the bottom so be sure to read the full article)
The Bad News
The lottery is really a random game. If we talk about randomness, it is unpredictable and you need perseverance, persistence and patience in order to win the jackpot.
Simply put, winning the lottery is not easy. That is why the lottery is considered a gambling activity.
how to win the lottery through the fortune teller. Even someone with paranormal power can’t predict the lottery
The odds in favor of winning the US Powerball 5/69 grand prize are between 1 million and 292 million.
At 5/70 Mega Millions, the odds are monumental at 302.6 million.
And the worst odds I’ve seen so far are the South African and Italian Superenalotto, where you choose from 90 numbers. Winning in this type of lottery format is the modern equivalent of wishing for a miracle.
Any statistician will tell you right away that your chances of winning the lottery are minuscule.
So many people say that the chance of being killed by a shark is much greater than that of winning the lottery.1 Of course, that’s not the whole truth. The truth, the probability that you will meet the shark is zero when you are not swimming in the ocean.
Similarly, in the lottery, you have to be in it to win it.
So, despite the huge odds, why do people play a lottery game?
One reason is the issue of availability bias. People think that winning seems very likely if they find out about recent lottery winners.
But how likely is it that you will win soon this year?
On average, it will take 292 million attempts to win the US Powerball. If you play 100 tickets each week, it will take 2,920,000 weeks. That corresponds to 56,154 years (if you ever lived that long). You see, the risk of losing your money is very high.
So don’t take the lottery too seriously. Play just for fun. And the lottery is fun and quite interesting as I will show you later.
how to win the lottery and have fun. It takes a lot of attitude, patience and perseverance to play and win.
The truth is, no one can beat the odds.
But like I said before, people play anyway.
Like children, adults also play.
So play now and then just for fun and try the “What if I win?” Taunt. That comes with that is not a bad idea at all.
However, some people think they have a smart solution to beat the lottery odds.
In fact, some people may go to great lengths to rig the lottery without success.
There will never be a perfect lottery trick to know past lottery results.
No machine can predict the exact combination of winning numbers in the lottery.
Sure, a supercomputer algorithm can be helpful in saving us from the tedious task of combinatorial calculations. But you definitely can’t predict the next winning numbers.
And lastly, no fortune teller or psychic next door can help you.
So how do you win the lottery?
Well the answer is to have a good sense of mathematical strategy. And that’s the good news.
Let’s talk about what you can do to improve your number picking strategy.
So, let’s start
Choose the Lottery with the Best Odds
If your goal is to win a big jackpot like the US Powerball or the US Mega Millions, you will have a hard time with your chances of winning.
You should go for a lottery that offers better odds even though it offers less jackpot. It’s easier to win that way.
Although the small lottery jackpot may not be too exciting, it is still an important one in making a difference in your life. It’s not like that?
But how do you know which one gives you the best odds?
The first factor is the numeric field. The smaller the number field, the better the odds. For example, a 42-ball lottery is better than a 49-ball lottery.
32 is better than 35 and 35 is better than 39. So of the three, 32 is the best. That simple
The second factor is the size of the pick. The smaller the size of the selection, the greater your chances of winning. For example, a pick-5 game is better than a pick-6 lottery game.
When you consider the two factors together, you get a better picture of the overall odds of the game.
A 6/42 lottery system is better than a 6/49 game.
Similarly, a 5/42 game is better than a 6/42 game.
And a 5/35 lottery system is easier to win than a 5/42 game.
The following table will give you an idea of the lottery odds.
Based on the table above, the 5/20 system gives you better odds.
Therefore, in your local lottery community, always choose a lottery system with fewer numbers.
But watch out for the extra ball. The extra ball can affect your chances of winning.
It takes many different names, depending on the games you are playing. For the US Powerball, it is called “Powerball”. In millions of euros, it is called a “lucky star”.
Some lottery systems take the extra ball from the same drum. For example, the Tattslotto system takes two supplementary numbers from the same drum, which makes this lottery favorable compared to the US Powerball or the US Mega Millions.
In the Irish lottery system, the supplementary numbers are taken from the same drum, making it an easy game like TattsLotto.
However, some lottery systems take the extra ball from a different drum. A system like this makes the lottery harder to win.
For example, the US Powerball allows you to choose 5 out of 69 numbers. If it weren’t for the extra red ball, his odds would have been one in 11 million. But because you need to match the red Powerball to win the grand prize by picking numbers from 1 to 26, your odds become one is 292 million.
How do we calculate the lottery odds?
To calculate the probabilities, we must first determine the number of possible combinations. To determine the total of possible combinations, we use the formula of binomial coefficients that we usually use in the field of statistics and probability.
We express binomial coefficients using the following formula:
Where:
n = The size of the numeric field
r = the size of the barb
Therefore, in a 6/49 lottery system, the total of possible combinations are:
n = 49
r = 6
Total combinations = 13,983,816
From that given value, determining the odds is as simple as separating the number of ways you win and the number of ways you lose.
Therefore, the odds in favor of winning the grand prize are expressed in:
Odds of winning the grand prize = 1 / (13,983,816 minus 1)
The formula means you have 1 way to win over 13,983,815 ways to lose.
The following table shows the odds of the most popular lotteries in the world.
From the table above, it is Trinidad / Tobago Cash Pot 5/20 with the lowest odds. This lottery is an excellent game to play if you live in Trinidad / Tobago.
On the other hand, it is the Italian Superenalotto with the most difficult odds to beat. The larger the number field in the lottery, the harder it is to win.
Of course, a lottery with a big jackpot is usually the hardest to win. It’s fun to imagine what it will be like to live with huge millions in your bank account. That is why people start with the lottery that pays the biggest prize.
I suggest you define what you want in life. How much is big enough is up to you.
Ultimately, you choose the lottery game that is not too difficult to win, but offers a jackpot that is big enough to change your life. There is no reason to rush. Start with the fruits that hang lower.
Don’t underestimate the power of a lottery system with a small jackpot. It is a great opportunity to win from a mathematical perspective.
You want to know how to win the lottery right? So choose your lottery game wisely.
Tip No. # 1: play a lottery system with better odds
Not all lotteries are the same. Some systems are a thousand times harder to win. And you don’t want those kinds of odds, no matter how big the jackpot is. Likewise, you don’t want a lottery game that is that easy to play if the prize isn’t big enough to change your life.
Remember that probabilities and probability are two different terms
Once and for all, let’s correct the most common misunderstanding that puts most lottery players at a disadvantage.
I always find myself everywhere where people say, “all combinations are equally likely.”
Of course, I agree.
There is no doubt that a 1-2-3-4-5-6 combination is just as likely as any six numbers you can pick from the top of your head. That’s because there is only one way to win a jackpot.
The same principle of probability applies to everyone else who selects numbers at random.
This probability formula works in theory. But as a lottery player, you cannot adopt such a one-sided calculation in practice. You have to move your numbers and see if your math can find an advantage.
To illustrate, look at the following numbers below:
2-4-6-8-10-12 (multiples of two)
5-10-15-20-25-30 (multiples of five)
20-21-22-23-24-25 (six consecutive numbers)
If I ask lottery players to spend their money on those combinations, do you think they will?
Some of them can, but most people never will.
And that’s because most people don’t trust their probability calculations.
Your instinct takes over.
But why?
If all combinations are equally likely, why be afraid to spend money on those combinations?
You see, a hunch is not an acceptable explanation.
If you really want to win the lottery, you must select your combination using strong mathematical reasoning.
When you have a solid mathematical foundation, you will always trust your calculations and never doubt your choices.
So what is this mathematical foundation that will help you get the best chance in the lottery?
Well it’s simple.
You have to understand the difference between PROBABILITIES and PROBABILITY. They are not mathematically equivalent.5
Let me show you the difference.
Probability is the measure of the probability of an event occurring. Mathematically, we express probability as:
Odds, as explained above, is the relationship between success and failure.
We can translate the above equations in the following simple terms:
Probability = chance
Odds = Advantage
Now, I hope you see the point.
While you have less control over your chances of winning, you have more control over your choice of odds.
In other words, careful choice of combination is about playing the lottery with a greater advantage.
And how do you calculate your advantage?
Well, look at the composition of the combination.
Let’s go back to the combination 2-4-6-8-10-12, notice that all these numbers are even numbers.
In a 6/49 game, there are only 134,596 ways that you can combine six numbers made up of purely even numbers.
At the right time, you have a lead of 1 to 134,596 to win the jackpot.
However, because there are 13 million combinations involved in the entire 6/49 game, you don’t know when that right time will be.
So mathematically, it means that you have 134,596 ways to match the winning combination with the 13,849,220 ways that you won’t.
From a layman’s point of view, it takes more than 100 draws before gaining a winning edge. And this combination choice is an expensive strategy.
Now consider a well balanced odd-even combination.
Combinations of 3 even and 3 odd
In a 6/49 game, there are 4,655,200 ways to combine six numbers with a composition of 3 pairs and 3 pairs.
That means that in every 3 draws, you have a chance to match the composition of the winning numbers. Thus, you approach the winning numbers with a ratio of 1 to 2.
As you can see, although all combinations have the same probability, these different combinations can be divided into combinatorial groups based on their composition. Each group exhibits a certain measure of advantage:
Note that the purpose of paying attention to the combinatorial pattern is to bring it closer to the winning numbers.
Winning the lottery is not easy. But if you choose to play the lottery with a better hit-or-miss ratio, you’re getting closer to winning the jackpot.
Tip # 2: Be less wrong
While all combinations are equally likely, combinations are not created equally. As much as possible, you want to look at the composition of your numbers to get a better success-to-failure ratio. Trusting a mathematical calculation is knowing how not to be mathematically wrong. Of course, it doesn’t necessarily increase your chances of winning, but you’re just doing your best to make less mistakes. That’s what we mean by getting the best possible shot. All of the Lotterycodex calculators are designed to help you achieve just that.
Be thankful that the lottery is truly random
Why do you have to be grateful?
This is because we can be 100% sure that any mathematical calculation we do is precise and exact according to the law of large numbers.
Any external force that disturbs the random nature of a lottery game will distort the validity of any probability calculations we make. We might as well throw away what we’ve learned from our math teachers.
Remember the rule. All random events are subordinate to the dictates of probability theory.
What does that mean?
It means that the lottery is “mathematically predictable” up to a point.
There are only two types of processes. The process is deterministic or random. If you combine the two then it becomes probabilistic.
That means you can calculate your options. And you will not be wrong mathematically because a random event like the lottery with finite possibilities, the actual results always agree with the mathematical prediction. (You will see the proof later)
Now, I’m not here to give you an illusion of control.
By saying that the lottery is mathematically predictable, that does not mean that we can predict the next winning numbers. You cannot predict the next winning numbers. Nobody can.
And well, the predictability of the lottery does not contribute to its profitability. The lottery is never a profitable exercise. It’s gambling, and you play just for fun, not for profit.
But with probability theory, we can plan a better game strategy based on the law of large numbers.
A truly random lottery suggests practical advice on how not to go wrong mathematically when trying to win the game.
The idea is simple. You can use probability theory to choose the best combination and be sure that you will get it right most of the time.
Here at Lotterycodex, we separate the combinations into combinatorial groups. Based on the different probability measures in each group, Lotterycodex can separate the best combinations from the worst.
And what makes math so fascinating is that any probability prediction we make agrees with the actual results. (I’ll show you the proof below)
It is not magic. It is the power of mathematics.
Fortunately, the principle of probability works in all lottery systems.
Below is an example of how applied probability theory can predict the 5/50 lottery game.
5/50 Lottery game
In a 5/50 lottery game, there are a total of 56 patterns. Two of these patterns exhibit the best probability.
Of course, the same probability principle works for all lottery systems. For other lottery systems, see the calculator page.
Since the lottery follows the dictate of probability, you can be sure that a mathematical prediction will always put you on the right track. These calculated choices are possible because the lottery is truly random.
Tip No. # 3: don’t play the lottery blind, follow the probability
Most lottery players think that since the lottery is truly random. No strategy will help you win the lottery. That is not true. On the contrary, the random nature of the lottery will give you an idea of how to play the lottery by applying the probability calculation.
Of course, we cannot predict the next winning combination, but we can predict the overall lottery result in a large number of draws.
With proper application of combinatorial mathematics and probability theory, you can separate the best combinations from the worst.
Fortunately, you don’t need a math degree to do all these complex calculations. Lotterycodex calculators are available to do the heavy lifting for you.
Play fewer giveaways to save more money so you can buy more tickets
Do you know what FOMO means?
It means “fear of missing something.”
And that’s the main reason why some people tried not to miss out on playing all the draws as much as possible.
I know.
FOMO is important because you are concerned that your numbers will go up if you don’t play.
True. That can happen. But most likely not.
The probability that your numbers will come up is approximately 1 in 292 million (if you play US Powerball).
So FOMO, when it comes to the lottery, it’s pure “irrational fear”.
Again, you need to understand the odds. If you play just one ticket per week, it will take you 5.6 million years to win. Therefore, winning may not happen to you in your life.
The best thing to do is save your money until you can buy more tickets.
More tickets will give you a better chance of winning. And that’s especially true when using the hedging principle. We’ll talk more about this coverage principle in the lottery wheels section below.
Let me briefly explain how more tickets work from a mathematical point of view.
By way of illustration, we will use the lotto 6/49 system. But regardless of the lottery format, the basic concept is the same.
If you buy a ticket, your chance of winning is 1 in 14 million.
So if you buy two tickets, then you double your chance of winning, which is 1 in 7 million.
As you purchase more tickets, the likelihood that you will win the jackpot will also improve.
So how could this work?
The way to explain this is through the use of probability theory.10
Earlier, I introduced you to the probability equation. Let me remind you of the basic formula:
Since there are 13,983,816 total combinations in a 6/49 lottery and there is only 1 favorable combination to win a jackpot, we calculate the probability as follows:
In probability theory, we measure probability between 0 and 1.
Usually we use a percentage to express the probability. But for the sake of the layman, we also use fractional presentation with rounded numbers for simplicity.
So, in a layman’s term, it’s 1 in 14 million possibilities.
When you buy two tickets, the probability becomes 2 / 13,983,816 or 1 in 7 million.
When you buy ten tickets, your probability of winning becomes 10 / 13,983,816 or 1 in 1.4 million.
And so.
In other words, more tickets equals more chances of winning.
As the probability approaches the value of one, your chances of winning also improve.
I hear someone ask, “Edvin, isn’t the probability of playing one ticket in ten separate drawings the same as playing ten tickets in one drawing?”
Of course, mathematically they are the same.
10 / 13,983,816 = 10 x (1 / 13,983,816)
However, playing a ticket in each draw will not allow you to use the power to cover. Hedging is such a powerful mathematical method in combinatorics that it can dramatically improve your chances of winning (see The lottery and winning formula according to mathematics for more information on combinatorics).
The following table will show you the probability of winning the jackpot based on the number of different tickets you play in a 6/49 lottery system.
Notice that in the first line, I put zero to indicate that if you don’t buy a lottery ticket, it is impossible to win.
On the other hand, if you play all 13,983,816 unique combinations, the probability of winning the lottery is safe.
Of course, buying all the tickets is something that cannot be achieved. Somewhere in the middle, you need to define how many tickets you can afford to buy.
And when I say afford, I mean the money you can afford to lose for the price of FUN. Remember, the lottery is a random game.
Let me remind you that even buying hundreds or thousands of tickets is not guaranteed to win the jackpot. Take it from a group of MIT students who played the Massachusetts Cash WinFall lottery for more than seven years. They had been buying up to 80% of the tickets and yet they did not win a single jackpot during their time.11,12
Nonetheless, the group had made a profit of around $ 8 million in a span of 7 years. His goal was quite simple. They were targeting the smaller prizes during the drawing.
Now the probability analysis differs for each lottery format. Therefore, U.S. Mega Millions 5/70 has different probability calculations than Powerball 5/69.
The following table shows the calculation for different lotteries.
Tip No. # 4 – Skip some draws to save money so you can play more lines to increase your chances of winning.
The more lottery tickets you buy, the better your chances of winning the lottery. This method only applies when harnessing the power of combinatorics. Read the Free Guide to learn more about Combinatorics.
Understand your lottery and its expected value
So you say to all the members of your lottery team, “Well folks, let’s buy more tickets because this strategy increases our chances of winning.”
Not so fast.
You haven’t heard what the expected value or EV looks like yet.
So what is EV?
The EV or expected value is the indicator that tells you when the lottery is profitable and when it is not.
By way of illustration, let me use the US Powerball as an example.
As of this writing, the US Powerball has an estimated jackpot of $ 384 million.
So, at $ 2 per ticket, my EV calculation is negative at $ 0.37.
The expected value of the US Powerball at a jackpot of $ 384 million
The table shows that the EV is negative so it tells me that it will not be profitable when you play the US Powerball with a jackpot of $ 384 million.
Compare that EV to the time when the US Powerball hit the $ 1.5 billion mark in January 2016. We can see a big improvement in EV.
The expected value of the US Powerball at a $ 1.5 billion jackpot
The table above says that playing Powerball in January 2016 is “probably” a good idea.
EV provides a general idea of how profitable a game will be in the long run.
So in theory:
Positive EV means a profitable game.
Negative EV means wasted effort.
But wait a minute.
You probably think the only time you get into the ticket buying frenzy is when the lottery is in its positive EV. Right?
Incorrect …
Positive EV doesn’t always end up positive
While in theory a positive EV is a good sign to buy lottery tickets, in practice a positive EV doesn’t always give you positive returns.
Add in other factors like taxes, annuity, cash option, ability to split the jackpot, and you end up with a negative expected value.
An analysis by the Business Insiders team of the $ 1.5 billion Powerball jackpot shows a negative expected value of – $ 0.25 after the tax is withdrawn.14
Simply put, positive EV in the lottery rarely happens. Realistically, the lottery always returns a negative expected value.
Therefore, playing the lottery can never be a substitute for a real job to earn a full time income. The lottery is truly a gambling activity and should be considered for fun and excitement only.
Positive expected value only works when a lottery has a reduction clause. This loophole in the lottery made MIT students benefit from the Massachusetts Cash WinFall for 7 years. Check out the lottery guide on how this drop-down clause works in your favor.
EV calculation differs from lottery to lottery and is dependent on payout.
So next time you play, try asking yourself, “Do I have a positive EV?” Get a pencil and paper and do your math.
Tip # 5: Use only money that you can afford to lose.
Positive expected value in the lottery does not occur in reality. Don’t expect long-term profit, even if the jackpot increases. This EV lesson should teach you to treat the lottery simply for entertainment and not as a substitute for a full-time income. You play just for fun. In our day to day, we save some money for something. In your case, you should save money for lottery entertainment in the same way that you set aside money to watch movies every week.
Make even and odd numbers balanced in your combination
Did you know that the odd and even numbers in your combination are important?
They do.
When you don’t count the odd and even numbers in your combination, you hurt your chances of winning.
To understand the probability of a combination based on odd and even numbers, we must take it from the context of number patterns.
In this case, we need to find the many different forms of odd and even numbers that combine to form a combination.
In a 649 lottery system, there are 7 ways to combine numbers with odd and even numbers.
| Pattern | Sample combination |
| 6 odd and 0 even | 3 – 7 – 19 – 21 – 33 – 41 |
| 5 odd and 1 even | 5 – 9 – 13 – 23 – 31 – 42 |
| 4 odd and 2 even | 1 – 4 – 11 – 28 – 39 – 45 |
| 3 odd and 3 even | 6 – 9 – 18 – 23 – 31 – 42 |
| 2 odd and 4 even | 9 – 10 – 22 – 24 – 33 – 40 |
| 1 odd and 5 even | 3 – 6 – 22 – 28 – 36 – 46 |
| 0 odd and 6 even | 2 – 4 – 12 – 20 – 30 – 42 |
The next question now is which of these odd and even patterns is the best to play in the lottery.
And the way to find the answer is by using the theory of probability and combinatorial mathematics.
To find the probability, we need to find the number of favorable combinations that we can produce from each pattern.
Again, we use the binomial coefficient formula to determine the number of favorable combinations for each pattern. Here is the full table below:
The sum of all those favorable results will represent the total number of possible combinations in a 6/49 lottery system which is 13,983,816.
Probability calculation
To obtain the probability of each pattern, we use the same probability formula described above. Therefore, the probability of these odd and even patterns is as follows:
The probability table means that the combinatorial 6-odd-0-even group only has a 1.3% chance of drawing. And this is the worst odd and even pattern in that the 6/49 game is a concern.
You should focus on the 3-odd-3-even pattern.
Now, I can hear a crowd yelling, “But Edvin, all combinations in the lottery are equally likely, aren’t they?”
Of course, we already know, all combinations have the same probability. That’s because there is only one way to win the jackpot.
So a combination like 2-4-6-8-10-12 has the same probability as any balanced 3-odd-3-even line.
But don’t forget the concept of probabilities.
We have explained that probability is the measure of the probability of an event occurring. Mathematically, this measure can be obtained by dividing the number of favorable events by all possible combinations.
On the other hand, the probabilities are expressed mathematically as:
In other words, odds are the ratio of success to failure:
In the case of the 0-odd-6-even versus 3-odd-3-even pattern, we can clearly see a big difference in the odds.
A purely 6 pair combination will give you a probability of 1 in 134,595, but keep in mind that this advantage will only occur once in 100 draws. In other words, your chance to win the jackpot only happens every 100 tries. And you don’t want to waste your money so many times. You do?
In comparison, a combination of 3 even, 3 odd, will get you closer to winning the jackpot every 3 draws.
Based on our calculations from game 6/49, we can group the patterns into best, good, bad, and worst:
There is no point spending your money on patterns that only give you less of a chance to get closer to the winning numbers.
You’d better choose a combination of 3 even, 3 odd, because this pattern is drawn 33% of the time. That is, for every 100 draws, you have a chance to match all the winning numbers approximately 33 times instead of just once.
To win the lottery, you must keep your combination as close as possible to the type of combination that is drawn most frequently.
This is how probability theory helps. Provides a reliable guide on how to pick lottery numbers with the best possible shot.
Of course, you don’t get any prizes for matching the pattern. You only win when you match all the numbers.
What you want to do is use these patterns to guide you closer to the winning combination.
Please note that probability theory is only a guide.
Probability does not tell you exactly what will happen. But it does give you a clue as to what the most likely outcome will be in the future.
Let me show you a probability study that I have done on a real lottery system.
TattsLotto 6/45 analysis: theoretical prediction vs. actual lottery results as of February 1, 2020
The comparison chart below shows the probability prediction compared to the 734 actual draws from the Australian game TattsLotto.
Data was collected from January 7, 2006 to February 1, 2020.
This comparison chart shows that a probability estimate is an excellent tool to guide lottery players.
As you can see, the probability estimate matches exceptionally close to the actual 734 TattsLotto draws.
As I said, the probability calculation is different for each lottery system. For a 6/45 system, the probability of the 3-odd-3-even pattern is 0.33484590659860100.
Based on that probability value, it indicates that approximately 246 3-pair 3-pair pattern is expected to occur in 734 TattsLotto draws.
We make the estimate by multiplying the probability by the number of draws.
Estimated frequency (3 even 3 odd)
= 0.33484590659860100 x 734
= 245.776895443
= 246 times
The actual Tattslotto results from Jan 7, 2006 to Feb 1, 2020 show that 3-odd-3-even occurred 229 times, and we estimate around 246 times. It is not exact, but the prediction is very close.
Looking at the comparison chart above, with a quick glance, the agreement between the prediction and the actual observed frequency is clear.
What does this comparison table tell you?
It tells you that you can literally predict the lottery (up to a point).
But don’t get me wrong. What I mean by lottery prediction is that you can determine which types of composition are most likely to occur most often and how many times are most likely to occur in a given number of draws.
More tests of real lottery draws
Probability is a mathematical tool and it is the best tool we can use to predict how the lottery will behave in the future.
You do not need the previous lottery results to know what works in the lottery.
We only need two variables to calculate the best type of combinations.
For example, in a UK Lotto 6/59 format, the variables are:
n = 59
r = 6
Those two variables are sufficient to calculate probabilities.
The good thing about mathematical calculation is that you can try it.
And the best way to test the calculation is to compare it to the actual lottery results.
For example, we use the probability value to estimate the likely outcome of certain lottery number patterns in a given number of draws.
Expected frequency = (probability) X (number of draws)
We then compare our estimate of the actual lottery results to find out how far or how close we are to reality.
To prove that our calculation is correct, you must follow this simple rule:
The expected frequency should closely match the observed frequency given a sufficiently large sample of withdrawals.
You have already seen my probability analysis for the Tattslotto 6/45. The study shows a close correspondence between the expected frequency and the actual frequency.
But the study is not just a coincidence. The truth is that probability theory applies to all kinds of lottery systems. Below are more tests of other lottery systems:
Euro Jackpot 5/50 Odd-Even Analysis: Prediction vs. Actual Draws as of Jan 31, 2020
Euro Millions Odd-Even 5/50 Analysis: Prediction vs. Actual Draws as of February 4, 2020
Irish Lotto 6/47 Odd-Even Analysis: Prediction vs. Actual Draws as of Feb 5, 2020
Odd-even analysis of U.S. Powerball 5/69: prediction vs. actual draws as of February 5, 2020
Did you notice how close the probability predictions are to the actual lottery results?
If you did, great. That is the power of mathematics.
Tip No. # 6: choose the best odd-even combination
To give you the best chance of winning, make a balanced mix of odd and even patterns. When you don’t count the odd and even numbers in your combination, you hurt your chances of winning.
Make a balanced combination of high and low numbers in your combination
As with odd and even numbers, you need to make sure you have balanced the high and low numbers in your combinations.
Again, in order to calculate probability, we have to take everything from the context of number patterns.
This time, let’s play a 5/69 lottery game. A famous example of a 5/69 game is the US Powerball.
To start, let’s divide the 69 numbers into two sets:
Low numbers = {1,2,3,4,5,6,…, 35}
High numbers = {36,37,38,39,40,…, 69}
We have to know the number of ways we combine high and low numbers.
So here are the possible patterns:
- 5 low and 0 high
- 4 low and 1 high
- 3 low and 2 high
- 2 low and 3 high
- 1 low and 4 high
- 0 low and 5 high
We determine the number of favorable combinations for each pattern as follows:
Next, we need to calculate the probability.
Some lottery systems do not require an extra ball, but some games like the US Powerball require an extra ball to win the jackpot.
In both cases, we will only use the primary balls, which are the 69 balls from the first drum. Therefore, the total number of possible combinations in a game of 5/69 is 11,238,513.
Here is the probability table for low and high number combinations for a 5/69 game.
Based on the probability table, we can predict the probable outcome of the US Powerball 5/69 in 100 draws.
Based on our probability estimate, we now know that two patterns on the US Powerball come out better than the rest of the patterns.
Below is a comparison chart showing the probability prediction against the actual lottery draws for the Powerball game as of February 5, 2020.
US Powerball 5/69 Analysis: Likelihood Prediction for Low-High Patterns vs. Actual Results as of Feb 5, 2020
Like I said, it is not a coincidence. The theory of probability applies to all lottery systems.
Take a look at the graph for the game U.S. Mega Millions below:
Analysis by U.S. Mega Millions 5/70: Probability Prediction for Low-High Patterns versus Actual Results as of Feb 4, 2020
Again, it doesn’t make sense to pick your numbers based on the worst patterns.
Pick your numbers to match the pattern that appears most often.
In this case, the best low-high number patterns in any pick-5 lottery game are the 3-low-2-high and 2-low-3-high number patterns.
It is worth knowing the probability of their combinations.
However, most lottery players do not pay attention to number patterns. And the problem is that they are not aware that they are playing the worst combinations.
Tip No. 7: Make a balanced mix of high and low numbers in your combination
When you play the lottery, in addition to getting the correct odd-even pattern, you also need to get the correct low-high pattern in your combination. Use a lottery number generator to make it easier for you.
Do your homework, check the previous winning numbers of any 5/69 lottery system in the last 100 draws. The combination of 3-low-2-high and 3-odd-2-even numbers will always occur more frequently than any other type of combination. It is a mathematical certainty.
Take advantage of advanced number combinations (don’t miss this section)
Now, I have explained the odd and low-high even patterns. But these basic types of combinations hardly scratch the surface.
Let me explain.
Probability analysis can be troublesome and quite confusing.
For example, a combination like 1-2-3-4-5-6 falls under the 3-odd-3-even pattern. Therefore, based on our odd / even analysis, this combination is considered one of the best.
But we know that is not true because, conversely, from our low / high analysis, such a combination has one of the worst odds.
So obviously when it comes to two separate analyzes, you will be presented with two contradictory points of view.
Therefore, we must find a way to determine the point of reconciliation between the two analyzes.
Fortunately, Lotterycodex has a solution. The solution is to put all the factors together in a combinatorial equation. And I reveal the formula in the free guide. The results of the calculations are what I now call Lotterycodex patterns.
Using these advanced combinatorial patterns, we can determine the best, bad, and worst type of combinations in any lottery game.
The number of advanced patterns depends on the format of the lottery.
But you don’t have to worry about math calculations. Lotterycodex provides the calculator.
Let’s talk about some examples of these advanced number patterns below.
Get the best possible shot through advanced combinatorial patterns
It is important to understand that “choosing the correct pattern will not win you any big prizes.”
But these number patterns are a great guide to help you pick numbers with the best possible chance.
It does not help you choose the next winning numbers. But it helps you get closer to the winning combination. Remember, we are only using math to get the “best shot” possible.
Remember, no one can claim the best strategy to win the lottery; all we can do is do our best. And math is still the best tool for the job. So in our case, we use combinatorics and probability theory to guide us.
Now in the US Mega Millions, pattern # 52 is calculated to occur 3 times in every 1,000 draws. But lottery players keep spending their money on this number pattern.
At Tattslotto 6/45, pattern # 68 is calculated to occur 2 times in 1,000 draws. But lottery players blindly fall into this bad pattern when they pick numbers at random.
In a 5/35 lottery system, it is better to play a number pattern that occurs seven times in every 100 draws rather than using pattern # 49, which only occurs three times in 1,000 draws.
The idea of a number pattern in the lottery is simple.
There is no point spending your money on number patterns that occur once on a blue moon. Why waste your money on a number pattern that only appears once in 10,000 draws when there is a better pattern that occurs 7 times in 100 draws?
I can almost guarantee that most players are wasting their money on many of these lousy number combinations. You’re probably one of them, but you don’t even know it.
You can’t fix something you don’t know exists.
It is about time that you know and be aware of all the types of combinations that will lead to lottery success.
Tip # 8: Choose to play number combination with a high probability
Why waste money on number patterns that will only occur once in 100,000 draws? To win the lottery, you have to pick your numbers based on a number pattern that has a high probability of occurring. Of course, matching the right pattern doesn’t help you win the grand prize. But it does guide you closer to the winning combination. Math does help.
Know when to skip the lottery
Do you know that probability theory also provides information on when to skip the lottery?
It does.
This is why probability theory is so essential for all lottery players.
Now keep in mind that probability cannot provide information about the perfect moment. It’s not possible.
However, probability helps you know whether a specific giveaway will waste your money or not.
That information is too important to take for granted.
For example, once a pattern occurs in yesterday’s draw, you know that it is not likely to happen again in the next draw.
It can happen, but most likely not. At least that’s how it works most of the time.
But to understand how the lottery works, we have to see the big picture.
Let me explain that to you little by little.
Each lottery draw is independent
The lottery is a random game. It is true.
And each lottery draw always provides random results that are independent of previous draws.
And that means that yesterday’s number combination is likely to happen again in the next draw.
And no matter how unlikely it is, it’s possible for the same number pattern to happen again in 5 draws in a row.
In a truly random game, we don’t know what will happen.
This is because previous draws will have no effect on the current drawing.
That is the exact opinion of many people who say that the lottery has no memory. This belief paralyzed many lottery players for centuries. But we will clarify this later.
First, each lottery draw is just a small part of a bigger picture.
Many people don’t see how the lottery works as a whole. They only see what happens in a tie.
There are physical laws that govern the universe.
In the same way, the laws of mathematics govern the lottery.
So don’t just look at the lottery for a small number of draws. Try to understand how the lottery works as a whole to see the big picture.
So what is this mathematical law that governs the lottery? We are talking about the law of large numbers.
The law of large numbers
The law of large numbers states that given enough trials, the actual results always converge on the expected theoretical results.15
In the lottery, as the draws continue to occur, the lottery follows a particular path as dictated by theoretical probability.
Again, I would like to emphasize that the lottery prediction comes from the context of “number patterns”.
As we have already shown, we have shown that we can predict the best type of combination in the lottery.
This prediction is possible because each type of combination has a probability value that, when tested in enough draws (usually large tests or draws), the actual lottery results always match or (converge) with the theoretical calculation.
That is the mathematical law. Actual results will take place as predicted by probability.
More evidence that actual draws agree with probability prediction
Let’s take a look at another comparison chart to illustrate my point.
The graph below is a probability study I have conducted for UK Lotto. Data was collected from October 10, 2015 to February 5, 2020.
We have tried it over and over again. The graph shows an agreement between the estimated frequency and the actual frequency.
From the table above, the 3-odd-3-even pattern has a probability value of 0.3292514800097320.
It means that in 449 draws, this pattern can occur about 148 times.
However, in actual draws, this pattern occurs 137 times.
It is not exact, but it is very close. And that is the very nature of probability estimation.
If you look at the other patterns, you will see that all the probability predictions closely match the actual results.
What are all these probability calculations trying to show?
It shows that given a large number of draws, the lottery must follow the dictation of probability. A predictable trend that even lottery officials cannot change or control.
So here is the main point:
The lottery as a whole, no matter how random and independent its draw may seem, follows a definite path as dictated by the probability principle.
Following the principle of the law of large numbers, as the lottery draw goes on to infinity, the convergence of the expected frequency and the actual frequency becomes more and more apparent.
So when we have to study how the lottery works as a whole, we enter the realm of the law of large numbers. And therefore, the issue of each drawing in the lottery being independent becomes irrelevant.
This great concept in the lottery is essential because when you see the big picture, you know how to play and be smart most of the time.
And one of the smart moves you can make is the “timing” strategy.
So let’s talk about the weather now
Ok, the LLN does not help you win the lottery per se.
It just helps you understand why probability theory and the law of large numbers are so relevant in our search for a hack on how to win the lottery.
So, in addition to determining the best type of combinations, probability theory can provide useful information on when not to play with the chosen combination.
For example, in a 5/35 lottery system, a pattern has a probability of 0.0748539885. What this means is that this pattern occurs seven times in 100 draws.
So this pattern happens around 14 ties in the middle. That is, if this pattern appeared yesterday, then it tells you not to waste your money on the next 8 draws using the same number pattern.
Of course, the same pattern can happen again in subsequent draws. It can happen again in 3, 4 or 5 draws in a row. But the probability of it happening is tiny because the law of large numbers has to go into effect.
Since we understand how the lottery works as a whole, we have probability theory to guide us on how to deal with this randomness and still make better decisions for most draws.
And because probability cannot tell the right time to play, your intuition should tell you that maybe you can start playing on the eighth or ninth draw. Again, we don’t know. But fortunately, we have a probability principle that gives us a clue.
Therefore, the number of draws that you are not playing because you know the chosen pattern is not due is a huge money saver.
What you can do is take this opportunity to save money so that you can play more lines when your chosen pattern is ready.
Tip No. # 9: know when to skip a lottery draw
When you know the probability value of your chosen pattern, you can guess how often a number pattern occurs. Use this information to determine when gambling is not profitable. Take this opportunity to reserve money to buy more tickets.
Use the lottery system
The lottery wheel is a popular and effective tool, and it technically works.
A lottery wheel is based on a mathematical principle of hedging.
There are many types of lottery systems. The most popular are the complete wheel, the abbreviated wheel, and the filtered wheel.
Various lottery operators provide an option for players to play on the full wheel system. In Australia, they call it a system game.
The full wheel system allows you to choose more numbers. If you choose to play system 7, then you choose seven numbers.
For example, in a pick-5 lottery game, if you choose seven numbers: 8, 16, 17, 21, 24, 25, 36, the system will produce a total of 21 possible combinations for you based on these seven numbers.
Suppose the numbers 8, 17, 24, and 36 are drawn, then the system gave you two matches of 4 and nine matches of 3.
With the full wheel shown above, you lose 10 tickets but at least win 11 of them.
The downside to the full wheel system is that it tends to get expensive when you have to select more numbers. The more numbers you choose, the more combinations you will need to buy to get maximum payout coverage.
For example, selecting ten numbers will produce 252 possible combinations. If you pick 12 numbers, the possible combinations will quickly increase to 792.
Again, it all comes down to how many combinations you can afford to buy.
The abbreviated and filtered wheel allows you to reduce the combinations for budget reasons.
But not all number wheel systems are the same.
There is a great deal of lottery software online. But I recommend the one that is able to separate the best combinations from the worst through probability analysis. At the time of writing, Lotterycodex is the only lottery wheel that does just that.
Tip # 10: when playing, use the best number wheel system
When there are 3 or 4 winning numbers among the numbers with wheels, you have a chance to win multiple instances of lower level prizes. Keep doing this to win smaller prizes until you hit the jackpot. So use a number wheel whenever possible. In the free guide section, I talk about a superior type of lottery wheel that allows you to win not only small prizes but also big prizes.
Eliminate the impossible
One of the famous Sherlock Holmes quotes says:
“Eliminate the impossible, what remains, however improbable, must be the truth.”
In the lottery, you can do the same strategy.
Many people will not agree with this because they believe that each combination in the lottery has the same probability of occurrence as any other.
But let me clarify one thing here.
In the lottery, the number and the combination are two different terms.
When you speak of a number, it is the specific number in the number field.
On the other hand, a combination is a selection of numbers. So in a pick-5 game, your choice of 5 numbers represents a combination.
From a mathematical point of view, each number has the same probability of being drawn as any other. And no matter what the previous frequency was, all the numbers in the number field always have the same possibilities.
When numbers are combined, the probability of the combination varies. The probability depends on the pattern.
Perhaps the most popular pattern is the existence of consecutive numbers. Just look at the infamous 1-2-3-4-5-6.
According to a report by TheGuardian, around 10,000 people play this type of number combination in each draw. A host of players to take home around £ 400 each in the event this combo comes in a draw.
But apart from consecutive numbers, you have to think of other types. I have studied the low-high pattern above, and we can immediately say that many patterns belong to a group with a very low probability of occurring.
The big problem is that people are not aware that there are bad patterns in the lottery.
The following patterns should be considered in your number selection process:
- Decades
- Last digits
- Sequences
- Group of numbers
- Prime numbers
- Sum of all numbers
And there is more. The ones I mentioned above are just the tip of the iceberg.
In short, there are millions of lousy number combinations in the lottery.
If you’ve been playing the lottery for many years, you are probably one of the ones who wasted money on those useless combinations.
There are so many complexities in math that you have to deal with. Fortunately, you don’t have to calculate yourself. We have a list of calculators for all types of lottery systems.
Tip No. 11: avoid wrong number combination pattern
There are millions of bad combinations in the lottery. Combinations that follow the same composition are put together as combinatorial groups. And the combinatorial groups have different probabilities.
Do not use statistics to predict the outcome of lottery draws
For decades, many lottery players think that the way to understand the lottery is through statistics. They collect the last 100 results and get predictions from what they have observed.
However, the application of the statistics method in the lottery often fails because it misleads you into believing that something works until there is enough data to prove it wrong.
First of all, probability and statistics are two closely related disciplines, but they are two distinct concepts that approach a problem in different ways.
And the main difference has to do with our knowledge of the existing facts. That is, we first determine what the known facts are when we try to solve the problem. And depending on our knowledge, our problem could be statistical or probabilistic in nature.
For example, we have a box of 49 marbles. Suppose we know that there are yellow, cyan, gray, and green marbles inside the box, but we do not know how many marbles there are for each color group.
When we do not know the composition of the table, we immediately see that we need statistics to infer the composition of the table based on a random sample.
But this is not the case with the lottery. The lottery has a finite set of numbers and therefore we have adequate knowledge of the composition of the entire game.
So any question related to that is a probability problem rather than a statistical one.
For example, we can ask the question:
What is the probability that they will win 1-2-3-4-5-6 in tomorrow’s lottery drawing?
This problem can be rephrased as:
What is the probability that we will get a combination consisting of 3 low even numbers and 3 low even numbers?
And voila! You get compelling proof why you shouldn’t play the 1-2-3-4-5-6 combination in a 6/49 lottery game. (See How To Win The 6/49 Lottery Game Based On Math.)
This is how probability works in the lottery. It gives you the power to calculate the best possible shot.
However, the theory of probability in the lottery can be better understood with the application of combinatorial mathematics.
That is why Lotterycodex is based on the science of these two mathematical principles. And the results are a high-precision, high-precision prediction that statistics don’t provide.
And given enough opportunities based on the law of large numbers, the probability calculus is always precise and accurate. And it always is.
Tip No. # 12: use probability theory to get the best possible shot
I invite you to consult the free guides section. In this guide, you will learn how combinatorial math and the probability formula work together to see the future lottery result.
Don’t waste your money on silly lottery strategies
You need to understand what works in the lottery and you need to back it up with solid evidence. Any conclusions you have drawn from the observation must be falsifiable.
Superstition doesn’t fit that criteria. And there is a lot of nonsense since the lottery was invented.
By simply avoiding silly lottery strategies, you are way ahead of 90% of lottery players, even without employing a bit of math strategy.
So what are these strategies that don’t work? Here are some examples:
- Hot numbers
- Law of attraction
- Numbers from your dream
- Cold numbers
- Prime numbers
- Lucky numbers
- Fortune spell
- Horoscope numbers
- Quick picks
- Statistical analysis (just a waste of time)
The quick pick machine is not a dumb lottery strategy. It’s just that a quick pick machine doesn’t give you better control.
If you know math, use math and forget about quick selection. Why trust the quick harvest machine when you can do better? So that’s the silly thing about using a quick select.
But of course, if you hate math, use Resourcefuldev calculator and it will calculate everything for you.
Tip No. # 13: understand that some lottery strategies don’t work
You have to change the way you play the lottery if you want to see good results. Superstition has no place in a random game like the lottery. Math is still the only tool you can use to give yourself the best possible chance. By just avoiding all these misconceptions, you are way ahead of the rest.
Implement a solid lottery game plan
It is true. It can increase your chances of winning the lottery. But the probability of you winning the grand prize is still tiny.
You have to play more lines and choose numbers with some mathematical sense.
Put all the winning factors together and playing the lottery will be expensive entertainment. Therefore, a lottery game plan should be implemented to ensure that you are doing it correctly.
Just because math can help you pick good numbers doesn’t mean you can play the lottery all you want at random.
A better approach to playing the lottery requires a proper mindset.
You have to save money and wait for the right moment to play. More lines play an important role in your chances of winning.
Winning only comes after a long losing streak, so anyone who gambles without the proper attitude can run the risk of becoming addicted to the lottery.
Therefore, a lottery game plan is necessary to avoid any adverse consequences that the lottery game may bring to your life.
Additionally, a lottery game plan teaches you how to save money, helps you understand the value of waiting, and helps you improve your patience.
Tip # 14: Make a proper plan and implement it consistently
The lottery is like a war. To win the war, you must plan before the actual battle. Your toughest enemy in the lottery is the odds. So you don’t want to play the lottery without proper planning.
How to win in each draw
No one can predict the next winning lottery numbers. Not even the most talented math prodigy in the world can tell the next winning numbers.
But let me tell you right now, there are two groups in the lottery. You are a group that always loses in the lottery. And another group that “always” wins the lottery.
I’m sure you want to be part of the latter group. Imagine that. In every lottery draw, you win every time.
Tip # 15: Know how not to lose
Most lottery players keep losing money all the time. But in your case, there is a sure way to win the lottery. It’s not about winning the grand prize, but it’s a winning proposition that you’ve been waiting for your whole life. And it works even if you are a solo player. Visit the calculators section to learn more about the reverse lottery strategy.
Don’t forget about your future
Ok, follow the game plan that I proposed. Take my advice to save money. And now you get big savings. That’s great!
Are you ready to play the lottery? Right?
How about putting some of those savings into a mutual fund or stock market investment? What you think?
Ok, maybe the stock market is not your thing.
But think about this.
If you play the lottery, you can win that huge amount of money.
But it is also possible that it will not happen either.
But here is something you should know. When you put in some investment money (be it a mutual fund or a stock market), that money will grow exponentially over time.
I understand that people are different.
Like I said, if you have to play the lottery, have fun and at least you have some mathematical sense for choosing numbers.
But if you are open to more productive entertainment, I invite you to consider the bag as an alternative playpen for yourself. I do it myself and say it is fun and profitable.
Hey, you can do both. Consider playing the lottery as a hobby while investing for your retirement at the same time.
Tip No. # 16: put more money in investments than in the lottery
Playing the lottery is fun and good. But remember that the lottery is not an investment. Play the lottery as a hobby, but consider investing in yourself, the stock market, the business, a mutual fund, a retirement fund, or any activity that allows your money to grow, so you don’t worry about money in your old age. You may win the grand prize, but it may also not happen either. Therefore, it is better to have an alternative.
How to win the lottery – in a nutshell
It is difficult to win the lottery because the lottery is really a random game. And the odds are truly astronomical. But you can do something to turn the lottery odds in your favor.
I invite you to visit the free guide section where I reveal the role of combinatorial mathematics and probability theory in predicting the outcome of the lottery.
Here is the summary of what we have discussed so far:
- Choose a lottery system that is easy to win
- Remember that probabilities and probability are two different terms (choose to be less wrong)
- Follow probability
- Play fewer giveaways so you can save money and buy more tickets
- Understand your lottery and its expected value
- Combine odd and even numbers evenly
- Balance high and low numbers
- Use the power of advanced number combinations
- Know when not to skip a giveaway
- Use a lottery wheel system (a top wheel is discussed here)
- Eliminate the impossible
- Use probability and avoid statistics
- Avoid silly lottery strategies
- Implement a solid lottery game plan
- Choose to win in every lottery draw.
- Put more of your money in investments than in the lottery
- Lastly, play the lottery just for fun.
With proper planning and perseverance, you can make it happen one day. Add a little math sense and winning is only a matter of time. And remember, there is no trick to winning the lottery. Simply a sensible approach that this article tries to share with you.
I have explained the mathematical way of winning the lottery. But we are only talking about the tip of the iceberg. Here are some more honest lottery tips for you.
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