How to Win the Lottery According to Math

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Last Updated on May 9, 2025

Winning a lottery jackpot is life-changing. But how to win the lottery? Well, mathematics can provide useful information.

This article will guide you in making better decisions using combinatorial mathematics and probability theory. My study shows that some combinatorial groups are predetermined to occur more often than others, even though all combinations are equally probable. It’s a mathematical certainty.

Let’s break it down in simple terms. Along the way, we’ll dispel the myths, examine the odds closely, and cover the pitfalls. If you know what’s stopping you from winning, you can create a smarter strategy within the mechanics of the game. It doesn’t matter what lottery format you follow whether 5/50, 6/49, or 7/35, the strategies I will present here works for you because combinatorial and probability analysis applies to all game of chance.

Let’s get started!

This is how to win the lottery: Cast your line where the fish are biting. This metaphorical image depicts how odds in favor and the law of large numbers work in the lottery. Five friends are fishing in the ocean. One is catching more while the other four are missing the fish.
“Cast your line where the fish are biting.” In the context of the lottery, this line suggests choosing the strategy where winning is most likely achievable. Lotterycodex suggests making informed choices to get more favorable shots.

Understanding The Odds: No Guaranteed Way To Win the Lottery

On average, winning the U.S. Powerball will take 292 million attempts. If you play 100 tickets every week, then you need to play 2,920,000 weeks to hit the jackpot. That corresponds to 56,154 years (if you ever lived that long). You see, the risk of losing money is very high. Winning any prize in Powerball is 1 in 24.87 (0.0402). So, the probability of not winning a prize is 95.98%. We square this number to get your probability of losing twice in a row.

P(losing twice) = 0.95982

To have a 50/50 chance of winning a prize, you must purchase at least 17 tickets. To have a 99.99% guarantee of winning any prize, you will need 224 tickets.

P(winning any prize) = 1 – 0.9598224 tickets = 0.9999

This Powerball chart shows two lines: the blue line representing the winning probability and the red line representing the losing probability. The two lines intersect at 17 tickets, indicating the point where Powerball players have a 50/50 chance of winning any prize by purchasing 17 tickets. However, the potential win could be the lowest-tier prize.
The two lines intersect at 17 tickets, indicating the point where Powerball players have a 50/50 chance of winning any prize.

But you have to accept that you are more likely to win a $4 prize, as the probability leans towards the lowest-level prize.

How to Calculate the Odds of Winning

To compute your odds, we must calculate the total number of combinations in the game. We use the combination formula C(n,r) to calculate the number of possible combinations, where n is the size of the number field, and r is the number of balls drawn.1

Binomial coefficient is an essential formula in probability theory where it calculates the possible combinations from a set

Where:

n = The size of the number field
r = the pick-size

Using the above formula, we determined that there are 13,983,816 possible combinations in a lotto 6/49 system. From that given value, determining the odds is as simple as separating the number of ways you win and lose.

The formula to calculate odds of the lottery. It is basically the separation between the possible ways to win and the possible ways to lose

There can only be a single way of winning the jackpot, so, the chance of winning the grand prize can be written in the following format:

Odds in favor (win the grand prize) = 1 / (13,983,816 – 1) = 1:13,983,815

The odds 1:13,983,815 indicates that you have one favorable shot against 13,983,815 ways you lose. That means winning takes 14 million attempts to win a 6/49 jackpot.

Don’t think you can claim small prizes more often while you wait for the big hit. Participating in the lottery cannot be a substitute for a full-time income because there’s no guaranteed method of winning. You have to know how the game works randomly over time.

Win the Lottery Using Combinatorics and Probability Theory

The lottery is a game with a finite set of outcomes. Every possible result is already predetermined by probability theory.

Statistics may look at past results to find patterns, but that’s not how a random game works. In the lottery, past draws don’t affect future ones. For example, “hot or cold” numbers don’t matter because every draw is completely random and independent of previous events.

Instead of searching for trends in historical results, focus on understanding how the game is structured using combinatorics and use probability to forecast outcome and make informed decisions. The answers are in the math, not in past data. So, stop chasing patterns—the lottery is about probabilities, not patterns. Read The Lottery Formula: Combinatorics and Probability at Work for more information.

Use Math to Validate Your Gut Feeling

The only way to improve your chances is to buy more tickets. But buying lots of tickets won’t help if you don’t choose wisely. For example, some players use the line 1-2-3-4-5-6. Many avoid it, saying if it wins, the jackpot will likely be split with many others. While that’s true, it’s not the right reason to avoid it. We cannot use the same reasoning to explain why we should avoid 1-10-11-20-21-22.

Look at these combinations below:

I asked 100 players if they’d spend money on these combinations. They all said NO. This is surprising because they believe every combination has the same chance. People trust their instincts instead of reasoning with math. But gut feeling alone isn’t a solid explanation.2

There’s a mathematical explanation why you fret to play certain combinations.

Does my statement make sense so far? If you agree, let’s dive into the possible strategies you can use to win the lottery. We’ll start with the basics and gradually move into the most advanced mathematical approach.

Pick the Easiest Lottery Game to Win the Lottery

When choosing a lottery game, the first factor to consider is the number field. The smaller the set of numbers, the better your odds. For example, a drum with 42 balls offers better chances than one with 49 balls. Similarly, 32 is better than 35, and 35 is better than 39.

The second factor is the pick size. A Pick-5 game is more favorable than a Pick-6 game. Therefore, always opt for a game with a smaller pick size and a smaller number field. The table below shows the odds for different lottery matrices.

This table of odds from different lottery systems.  The 5/20 has odds of 1 to 15,503.  A 6/90 game has odds of 1 to 622,614,629. The better choice is 5/20
Based on the table above, the 5/20 system is the easiest game to win.

As shown from the table above, the ratio 1:15,503 is a good choice because it offers a better probability of winning than a game with 1:622,614,629 odds. With fewer possible combinations, your chances of hitting the jackpot are much more favorable, making each ticket purchase more effective.

The Hidden Catch of the Extra Ball

Extra balls can impact your chances of winning. They go by different names. In Powerball, it’s called the Powerball. In EuroMillions, it’s the lucky star.

Some games, extra balls are drawn from the same drum and it doesn’t affect your probability. For instance, Tattslotto draws two supplementary numbers from the same set, enabling players to win additional prizes and yet allows lotto player to win the jackpot without the extra number. The Irish lotto operates in similar manner.

However, when one or more extra balls are drawn from a separate drum, the already minuscule probability of winning becomes even worse. This additional ball is meant to provide additional chances to win smaller prizes. It’s a sneaky move to provide the impression of better overall odds. In reality, the additional ball makes it more difficult to win the jackpot.

Many lottery games in the United States have no extra ball. You might want to consider the Illinois Lucky Day Lotto with a starting jackpot of $100,000 that grows. At the time of writing, the jackpot of the Lucky Day Lotto is $350,000.

The table below shows you the odds of the most popular lotteries in the world.

Odds of the most popular lottery systems in the world.  Trinidad/Tobago Cash Pot 5/20 is the lottery with the easiest odds.
Based on the table, Trinidad/Tobago Cash Pot 5/20 proves to be the easiest while Italian Superenalotto is the most difficult one to win.

To increase your chance of winning a lottery jackpot, choose a game that is not too hard yet offers a jackpot prize which is big enough to change your life.

Making Informed Choices: The Math Behind Favorable Shots

I always encounter people saying, “All combinations are equally likely.” I agree. There’s no question that the 1-2-3-4-5-6 combination is equally likely as any six numbers you can pick from the top of your head. That’s because there’s only one way to win a jackpot.

The probability of 1-2-3-4-5-6 combination is equal to 1 over the total number of combinations

But you have to look at the game in a different light.

Realize that odds and probability are related terms but not mathematically equivalent. Probability is the likelihood of an event occurring. Mathematically, we express probability as:

Probability is equal to the number of favorable combinations over the total number of combinations

On the other hand, odds are the ratio of favorable to unfavorable outcomes. In standard mathematical terms, this is commonly known as the “odds in favor” or simply odds. And odds use a different equation as shown below:

Odds is equal to the number of favorable combinations over the difference between the total number of combinations and the favorable combinations

We can define the difference of the two equations in the following simple terms:

Probability = Chance

Odds = Advantage

You cannot change the probability of a game or beat the odds, but you can make informed choices to get more favorable shots or advantage. And that brings us to our next topic, composition.

Composition: The Key to Lottery Success

Making an intelligent choice is about choosing the best odds or advantage. That’s why we suggest that you choose a lottery game with easier odds. However, you can make your strategy even more granular. That’s where composition makes sense. In fact, this is your key strategy on how to win the lottery.

Combinations can be organized into groups based on their combinatorial composition. And we use the odds equation to calculate the number of ways you get favorable and unfavorable shots.

However, odds in favor are often associated with winning and losing, which may create confusion when applied to group of compositions.

To avoid ambiguity and maintain consistency, we use the term “frequency ratio” to highlight the relative frequency of occurrence of each combinatorial group, offering a clearer representation of favorable shots rather than framing it in terms of winning or losing.

Let’s examine the combination 2-4-6-8-10-12. Notice that all these numbers are even numbers.

In a 6/49 game, there are 134,596 ways to combine six even numbers. So, on average, you have 134,596 favorable shots against the 13,849,220 ways you will not. This event gives you a meager frequency ratio of 1 to 103. That means, out of approximately 104 attempts, one is a favorable shot, and 103 are sure losses. Read: How Odd and Even Numbers Influence Lottery Outcomes.

The odds of 6-even combinations is equal to 1 every 103 draws

In short, the ratio of 1:103 is an expensive strategy. You don’t want to spend your money on 104 attempts and get only one favorable shot.

Positioning Yourself for a Lottery Win

You heard me say that all combinations have the same chance. It’s a mathematical fact, giving the game a unique property that makes it fair for everyone participating. But just because all combinations are equally likely doesn’t mean all hope is lost.

The truth is that combinations are not created equally because of varying compositions.

Let’s prove that. This time, let’s switch to low and high numbers.

There are 4,655,200 ways to combine three low and three high numbers. This gives you about 33 favorable shots out of every 100 attempts, or a frequency ratio of 1:2. Read The Impact of Low and High Numbers on Your Lottery Chances.

Frequency Ratio = 4,655,200/9,328,616 = 1:2

Relatively, the ratio means you only need three attempts to get one favorable shot on average.

According to probability theory, a truly random draw spreads the probability fairly across the entire number field. So, a winning combination composed of purely low or high-number are rare events. Randomness doesn’t favor one set over the other, and past results show that most winning combinations have mix of low and high numbers.

Let’s compare two compositions: one consisting entirely of high numbers and another with a balanced mix of low and high numbers.

6/49 Game's frequency ratio comparison involving low and high numbers. The table shows that 0-low-6-high composition on average gets one favorable shot in every 103 unfavorable shots. The 3-low-3-high composition on average gets one favorable shot in every two unfavorable shots.

As you can see from the table above, 3-low and 3-high is a better choice since you get 33 favorable shots in 100 attempts. The math shows you should not pick all low numbers because doing so will only give you just one shot after spending on 100 tickets. Clearly, getting a favorable shot depends on the composition of your combination. This ratio analysis proves that composition matters to win the lottery.

Let the Frequency Ratio Help You Make Informed Choices

A ratio indicates relative frequency. In other words, the ratio 1:103 doesn’t mean that a 0-odd-6-even composition should appear exactly once in 104 draws. Based on the law of large numbers, we should expect a series of draws to approach this theoretical expectation. A ratio is a relative measure, not an absolute value. Confusing the two can lead to flawed reasoning, similar to the gambler’s fallacy.

Focus on understanding the behavior of your game over time. To illustrate, let’s compare two players who decide to play under different frequency ratios.

Who gets the best shots in the lottery? Ethan chooses a combinatorial group with a frequency ratio of 1 to 2. So in 3 attempts, Ethan gets 1 favorable shot and 2 unfavorable shots. On the other hand Ben has a frequency ratio of 1 to 103 giving him only one favorable shot in every 103 unfavorable attempts. Ethan gets 693 best shots and Ben gets only 20 in 20 years.

Your goal is to win the lottery, and the first thing you should know when selecting numbers is your frequency ratio. Ben in our example above, suffered losses 2,060 times but the worse part is that he had only 20 shots in 20 years. You cannot change the underlying probability, and you cannot beat the odds, but you can calculate and make informed choices. Ethan on his part did a great job at playing with 1,387 losses but at least he had 693 opportunities to win a jackpot.

You should choose the composition where the most favorable shot is most likely achievable, putting you closer to the jackpot. Let the frequency ratio guides you when making choices.

Use Combinatorial Templates To Guide Your Number Selection

It’s time to go deeper into the combinatorial strategy.

Truth be told, a combination of 3-low-3-high or a combination of 3-odd-3-even numbers doesn’t represent a clear combinatorial advantage.

Here’s why.

Probability analysis can be confusing if you are not careful. For example, a combination such as 1-2-3-4-5-6 falls under the 3-odd-3-even composition. However, notice that it also belongs to the 6-low-0-high group, suggesting a poor composition. As you can see, two separate analyses present contradicting conclusions.

A lottery problem that involves huge set of numbers requires complex combinatorial and probability solutions. We must look at the lottery’s number field in a new light.

Here in Lotterycodex, we designed a unique partition scheme that ensures fair distribution of probability across the entire number field. We call it the Lotterycodex sets. For example, we group numbers into LOW-ODD, LOW-EVEN, HIGH-ODD, and HIGH-EVEN sets:

Lotterycodex sets for a 5/60 game. The sets are LOW-ODD (odd numbers from 1 to 29), LOW-EVEN (even numbers from 2 to 30), HIGH-ODD (odd numbers from 31 to 59), HIGH-EVEN (even numbers from 32 to 60)
5/41 Lotterycodex Sets: LOW-ODD (All odd numbers from 1 to 25), LOW-EVEN (All even numbers from 2 to 24), HIGH-ODD (All odd numbers from 27 to 49), HIGH-EVEN (All even numbers from 26 to 48)
Lotterycodex sets for a 7/35 game. The sets are LOW-ODD (odd numbers from 1 to 17), LOW-EVEN (even numbers from 2 to 18), HIGH-ODD (odd numbers from 19 to 35), HIGH-EVEN (even numbers from 20 to 34)

Using the number sets above, we analyze compositions and present our analysis in the form of templates. The calculations vary based on the lottery format. Therefore, a 7/35 game will yield different sets of templates from a 5/35 game.

Basically, a template describes the composition of a combinatorial group. For example, in Lotto Max 7/50, 1-2-3-4-5-6-7 belongs to Template #77. This composition is predicted to occur approximately 3 times in 2000 draws based on it’s ratio of 1:634. This ratio explains why you should not play 1-2-3-4-5-6-7 and other combinations that belong to Template #77.

Optimizing Your Advantage Using Combinatorial Templates

It’s important to understand that “choosing the right template will not win any grand prize.” You must match all the right numbers. But templates are an excellent guide to help you pick combination with the best shot possible. We separate the most prevalent, the occasional, and the rare groups to give you a straightforward approach to making informed choices.

The tables below are examples of combinatorial templates that may vary based on the lottery matrix.

Prevalent (#1 to #4), Occasional (#5 to #28), Rare (#29 to #52), Extremely Rare (#53 to #56)
This Lotterycodex analysis for a 5/32 game applies to Idaho Weekly Grand, Colorado Cash 5, Super Kansas Cash, and all 5/32 games anywhere in the world.
Prevalent (#1 to #6), Occasional (#7 to #38), Rare (#39 to #68), Extremely Rare (#69 to #84)
6/45 groups applicable to Australia’s Tattslotto and any 6/45 game format regardless of the name.
Prevalent (#1 to #4), Occasional (#5 to #16), Rare (#17 to #68), Extremely Rare (#69 to #120)
Groups that applies to any 7/50 lottery such as Canada’s Lotto Max.
Prevalent (#1), Occasional (#2 to #13), Rare (#14 to #31), Extremely Rare (#32 to #35)
These groups apply to all 4/30 lotto if such game exists.
Imagine two types of players participating in a 5/69 lottery game in a span of 35 years. Which lottery player are you? Are you the one using template #1 or the one using template #56. Template #1 user gets 243 best shots in 35 years. While template #56 user gets only 2 best shots in 35 years.

Many players blindly choose combinations with a very poor frequency ratio. You might be doing the same without realizing it. But how do you know? You can’t fix something you don’t know exists. So, be familiar with combinatorial groups in your lotto game and make an informed choice. Use a Lotterycodex calculator to help you out.

Certain templates are primed to prevail over time. This is not known to many but if you know how to take advantage of this mathematical certainty, you gain an advantage that most players are missing. Check out the Lotterycodex calculator and see the templates that applies to your game.

Embracing Randomness to Win the Lottery

All random events obey the dictate of probability theory.

What does it mean? It means that the lottery is mathematically predictable to an extent. Therefore, we are 100% sure that our probability calculation is precise and accurate based on the law of large numbers.

There are two kinds of processes: deterministic and random. The process that results from a combination of these two is called a probabilistic process. This is why our lottery forecast based on probability theory always match the actual lottery outcomes.

Let me remind you that this article does not hope to bring you an illusion of control.3 We cannot predict the next winning combination. Using probability theory and combinatorial mathematics, you can make informed choices based on how the game behaves over time.4

The image of lottery game's randomness shows streaks and clusters.
This picture of a lottery’s random behavior offers a sensible clue on how to avoid mistakes when playing the game. Read on: A Truly Random Lottery with a Deterministic Outcome

We can mathematically determines which templates dominate and will continue to do so as the number of draws approaches infinity. When you play lotto, you aim to follow this prevalent group and be closer to the winning combination for most draws. Then, luck is a matter of time if you play long enough and allow this strategy to work.

Predicting these prevalent groups is mathematically certain. It’s not magic. That’s how combinatorics5, probability theory6, and the law of large numbers work together.

Predicting the World’s Most Popular Lottery Games

Based on the law of large numbers, the most prevalent templates will continue to dominate as the number of draws gets larger and larger. If you want to give yourself the best possible advantage, you might consider strategically aligning your choices with the most dominant groups.

These templates don’t alter each combination’s equal shot at winning; rather, they shed light on which compositions appear more frequently over the long run, helping you see your game from a more data-driven angle.

Below, you will see how mathematics predicts the behavior of some of the world’s most popular games using combinatorics and probability calculations.

Euromillions & EuroJackpot 5/50

Since Euromillions and Eurojackpot have similar format, they share the same combinatorial and probability analysis. Here are some examples of their templates and how probability predicts their frequency over time.

This image is the 5/50 game's probability estimations: 
Template #1 occurs 7 times in 100 draws, 138 times in 2000 draws and 345 times in 5000 draws. Pattern #3 occurs 6 times in 100 draws, 126 times in 2000 draws and 316 times in 5000 draws. Pattern #5 occurs 3 times in 100 draws, 69 times in 2000 draws, and 172 times in 5000 draws.
Generated using Lotterycodex Calculator

There are 56 combinatorial templates in a 5/50 lotto game. Four of these templates exhibit dominance. Familiarizing yourself with these combinatorial templates can be very helpful, as they guide you in making more favorable decisions.

United States Powerball 5/69

In a 5/69 game, notice that only few templates are prevalent. Since the lottery obeys the law of large numbers, the same groups of templates will continue to prevail over time as the number of draws increases. This is a mathematical certainty. In Lotterycodex, we identify four prevalent templates in a 5/69 game.

Take a look at how Lotterycodex accurately predict the general trend of the U.S. Powerball based on our latest analysis.

TemplatePredicted vs Actual Frequency
#1
50
51
#2
47
56
#3
47
48
#4
47
48
#5
24
23
#6
24
21
#7
24
36
#8
24
24
#9
24
27
#10
24
19
#11
22
18
#12
22
19
#13
22
19
#14
21
23
#15
21
20
#16
21
20
#17
16
11
#18
16
18
#19
16
15
#20
14
8
#21
14
6
#22
14
16
#23
14
20
#24
14
19
#25
14
14
#26
13
11
#27
13
11
#28
13
14
#29
7
8
#30
7
5
#31
7
7
#32
7
7
#33
7
6
#34
7
3
#35
6
4
#36
6
2
#37
6
13
#38
6
10
#39
6
7
#40
6
5
#41
3
1
#42
3
4
#43
3
4
#44
3
3
#45
3
3
#46
3
3
#47
3
2
#48
3
2
#49
3
1
#50
3
4
#51
3
3
#52
3
6
#53
1
0
#54
0
0
#55
0
1
#56
0
0

Lotto 6/49

6/49 is probably one of the most favorite format played by players around the world. There are 84 templates in a Lotto 6/49 game and only six of them are dominant. Mathematically, these 6 prevalent groups will always dominate the lottery draws as long as the randomness of the lottery draw remains undisturbed. As a lotto 6/49 player, you should consider playing these dominant groups to get more favorable shots.

This image is the 6/49 game's probability estimations: Template #1 occurs 5 times in 100 draws, 106 times in 2000 draws and 265 times in 5000 draws. Pattern #4 occurs 5 times in 100 draws, 97 times in 2000 draws and 243 times in 5000 draws. Pattern #7 occurs 4 times in 100 draws, 71 times in 2000 draws, and 177 times in 5000 draws.
Generated using Lotterycodex Calculator

United States Mega Millions 5/70 Game

Let’s check another popular game in the United States. There are 56 templates in Mega Millions and only four are prevalent. Take a look at our latest analysis below and see how the actual lottery results tend to agree with our probability forecast based on the law of large numbers.

TemplatePredicted vs Actual Frequency
#1
50
57
#2
50
56
#3
47
54
#4
47
45
#5
25
36
#6
25
20
#7
23
21
#8
23
25
#9
23
25
#10
23
17
#11
22
24
#12
22
11
#13
22
22
#14
22
22
#15
21
20
#16
21
18
#17
16
20
#18
16
19
#19
16
13
#20
16
6
#21
15
13
#22
15
20
#23
14
15
#24
14
16
#25
13
15
#26
13
7
#27
13
11
#28
13
15
#29
8
5
#30
8
6
#31
7
10
#32
7
4
#33
7
9
#34
7
5
#35
7
3
#36
7
8
#37
7
11
#38
7
4
#39
6
4
#40
6
2
#41
3
7
#42
3
5
#43
3
7
#44
3
4
#45
3
2
#46
3
2
#47
3
6
#48
3
1
#49
3
3
#50
3
2
#51
3
1
#52
3
1
#53
1
1
#54
1
1
#55
0
0
#56
0
0

Multi-State Cash4Life

The truth is that combinatorial and probability analysis will tell the same conclusions regardless of the format of the game. For example in Cash4Life, only few groups dominate the draws. If you happen to play group that rarely occurs in a draw, then it’s not impossible for you to win a jackpot, however, realize that the waiting time might be very long. This means your dream lottery win may not happen in your entire lifetime. This is especially true if your combination belongs to templates #29 to #56. Take a look at how the Cash4Life draws behave over time below.

TemplatePredicted vs Actual Frequency
#1
151
147
#2
151
163
#3
151
132
#4
151
143
#5
70
87
#6
70
80
#7
70
62
#8
70
71
#9
70
69
#10
70
66
#11
70
68
#12
70
65
#13
70
89
#14
70
71
#15
70
86
#16
70
60
#17
44
48
#18
44
45
#19
44
54
#20
44
38
#21
44
37
#22
44
36
#23
44
39
#24
44
36
#25
44
37
#26
44
33
#27
44
52
#28
44
39
#29
20
22
#30
20
20
#31
20
18
#32
20
17
#33
20
26
#34
20
16
#35
20
23
#36
20
25
#37
20
17
#38
20
28
#39
20
24
#40
20
21
#41
9
5
#42
9
10
#43
9
9
#44
9
11
#45
9
8
#46
9
9
#47
9
9
#48
9
6
#49
9
5
#50
9
10
#51
9
10
#52
9
12
#53
1
1
#54
1
3
#55
1
3
#56
1
2

You should be thankful for the lottery’s randomness. If something is disturbing the random nature of a draw, any probability predictions we make cannot be trusted.

Win the Lottery by Playing Less Often

FOMO (fear of missing out), as far as probability theory is concerned, is pure “irrational fear.” Rather than worrying, play less often to save money for your lottery entertainment, then use the savings to buy more tickets and increase your chances of winning.

In probability theory, we measure the probability between 0 and 1. Zero indicates impossibility, and one means certainty.

In probability, 0 means impossibility and 1 indicates certainty

When you buy two tickets, the probability of winning a 6/49 jackpot becomes 2/13,983,816 or 1 in 7 million. And you can improve it to 10/13,983,816 or 1 in 1.4 million if you buy ten tickets. In short, more tickets put you closer to the value of one, which means guaranteed win.

The probability of buying more than 1 ticket.  There's a zero probability if you don't buy a ticket.  The probability is certain if you buy all the possible combinations.

Of course, buying all the tickets is not achievable. Somewhere in the middle, you’ve got to define how many tickets you can afford to buy (and lose). The table below shows the calculations for different games.

The probability of buying 1, 20, and 300 tickets in different lottery systems
The table indicates that the Trinidad/Tobago Cash Pot 5/20 presents the most advantageous odds among the lotteries featured.

Play less often to save money for your lottery entertainment, then use the savings to buy more tickets, giving yourself a better shot at the jackpot.

Use a Lottery Wheel to Play Strategically

OK, buying more tickets increases your chances of winning. That is especially true when you employ a lottery wheel.

I hear someone asking, “Hey, Edvin. Isn’t the probability of playing one ticket in ten separate draws the same as playing ten tickets in a single draw?” Of course, they are the same because

10/13,983,816 = 10 x (1/13,983,816).

However, playing one ticket at a time won’t allow you to cover more events. We call this a covering strategy. It’s a powerful method to help you cover more winning numbers with more tickets.

You can do this covering strategy in two ways:

The big difference is that random picking relies purely on luck, while a lottery wheel strategically maximizes coverage. This approach effectively traps the winning numbers when certain conditions are met.

The most common wheeling systems include full-wheel, abbreviated, and filtered. Some game operators allow players to use the full-wheeling system. For instance, in Australia, Tattslotto and Australian Powerball players have the option to use the system play which serve as a full-wheel.

How Lottery Wheel Works?

In a pick-5 game, if you pick seven numbers: 8, 16, 17, 21, 24, 25, 36, the wheel will produce 21 possible combinations based on this set. Suppose the numbers 8, 17, 24, and 36 are drawn. The system has provided you with two 4-number matches and nine 3-number matches.

With the full wheeling shown above, you lose on ten tickets, but at least you win on 11. The disadvantage of the full-wheeling system is that it tends to become expensive.

The more numbers you choose, the more combinations you need to buy for maximum coverage. For instance, if you select ten numbers, then it will produce 252 possible combinations. If you pick 12 numbers, the possible combinations will increase quickly to 792. So, it comes down to how many combinations you can afford. Thus, the full wheel is more commonly useful for lottery syndicates. The abbreviated and filtered wheel will be an economical alternative when the budget is limited, especially for solo players.

Title: Lotterycodex Wheel
Overlay text: Download combinations customized to your risk tolerance and personal preferences. 
Image background: A list of templates from #1 to #5. Templates #1 is prevalent and the rest are labeled as occasional groups. On the rightmost side are columns for download buttons where you can click to download your chosen template. A red arrow is pointing to the download button of template #1 indicating that it is the best choice.
Number wheeling is better implemented using a Lotterycodex calculator. Lotterycodex is the only number wheel online that uses combinatorial math and probability theory in one system to separate combinatorial groups based on their varying frequency ratios, helping you choose numbers intelligently.

Use Lotterycodex calculator as a lottery wheel to trap the winning numbers strategically.

Playing/Skipping Lottery Draws Strategically

Probability theory also provides a decent estimation of when you may skip certain draws. However, you cannot tell when the perfect timing is because of randomess. Past draws cannot influence the outcome of an independent draw. However, the law of large numbers suggests that when you see the game’s behavior over many draws, you have information on how to make smart choices. One smart move you can make is skipping and playing only when the probability is more favorable.

Let’s use Lotterycodex template #1 in a 5/35 lotto game as an example. This template has a frequency ratio of 1:13 and appears approximately seven times in 100 draws.

This is a Lotterycodex analysis of a 5/35 lottery game. The image shows that template #1 has the most favorable frequency ratio of 1:13 indicating that this template occurs approximately 7 times in 100 draws, 359 times in 5000 draws.
Calculated using Lotterycodex Calculator

The ratio of 1:13 doesn’t mean the template should appear exactly seven times in 100 draws. Realize that the template will approach this average as the number of draws increases. Again, your objective should be to understand the behavior of your game from many draws and not based on short-term outcomes.

Gambler’s Fallacy

Don’t fall for the gambler’s fallacy just because you believe you have mathematical information.7. When someone believes that a certain event will occur because it is due to happen, they engage in a gambler’s fallacy.

We cannot predict the outcome of any random draw. However, we know that a random draw obeys the dictate of probability. For example, Template #1 has a 13.86% probability of occurring twice in a row.

This means that it’s not impossible but very unlikely. According to probability theory and the law of large numbers, template #1 will occur approximately seven times in 100 draws over time. You have a piece of mathematical information to skip some draws. Use this opportunity to set aside money and play more lines when you are ready.

Use Forecasting Tool to Guide You When to Play and When to Skip

We’re monitoring winning numbers closely, so you don’t have to. Our predictions guide you on when to play and which templates to skip, placing you at a strategic advantage.

If you’re in the US, see our latest forecasts for the following multi-state games:

PowerballMega MillionsCash4Life
Gimme 5Lotto AmericaLucky for Life
Tri-State MegabucksArizona Fantasy 5And more lottery forecast…

When playing the lottery, it’s important that you know when to play and when to skip when it makes sense.

Avoid Improbable Combinations

One of the famous quotes of Sherlock Holmes says:

Eliminate the impossible; whatever remains, however improbable, must be the truth. – Sherlock Holmes

Sherlock Holmes reinforces the fact that improbable things occur. True, improbable events indeed occur. Therefore, one might say it’s okay to pick an unusual combination. Right?

Wrong. Let me explain.

Consecutive Numbers

Perhaps the most popular combination that epitomizes the consecutive pattern group is the infamous 1-2-3-4-5-6. According to a report by TheGuardian, about 10,000 people play this type of number combo in every draw. A massive number of players will bring home a measly prize each should this combo happen in a draw.8 A combination of this type can come in different flavors, such as the following:

Two sets of consecutive numbers1-2-3, 40-41-42
Three sets of consecutive numbers1-2, 30-31, 50-51
Three sets of consecutive numbers in one group11-12, 15-16, 18-19
Two sets of consecutive numbers in one group30-31-32, 37-38-39
Four consecutive numbers1, 66-67-68-69

These unusual combinations are not impossible to occur. When learning to win the lottery, you must know how to handle consecutive numbers. History shows strange combinations winning in a draw.

strange and unusual winning numbers in the lottery.  Examples are five numbers from twenty group.  or 4 straight consecutive numbers.

Unusual Combinations May Occur

Truth be told, these unusual combinations are not impossible to occur because the law of truly large numbers suggests that unusual things, outrageous events, and coincidences can happen if given abundant opportunities.9 But just because unusual combinations can occur doesn’t mean you must pick your numbers the same way.

As an intelligent lotto player, your main objective is to follow the trend based on the law of large numbers. Please don’t be confused between the law of truly large numbers and the law of large numbers. They are two different laws. The law of truly large numbers (LTLN) explains why unusual events occur. On the other hand, the law of large numbers (LLN) concludes general outcome from many draws.

Let me show you the actual results of real lotteries and see if you can spot a trend. You don’t need to understand how LLN or LTLN work for now, but by looking at the tables below, you will understand why you should avoid improbable combinations at all costs.

Frequently analysis of the Tattslotto game as of March 21, 2024 shows that combinations with no consecutive numbers and at least two consecutive numbers occur more frequently. Combinations having no consecutive numbers getting the lions share of the graph.
Frequency Analysis of the US Powerball game as of March 21, 2024 shows that combinations with a lot of consecutive pairs occur less frequently. Combinations with no consecutive numbers getting the lion's share of the graph.
Frequency analysis of the Euro Millions game as of March 21, 2024 shows that combinations with no consecutive numbers and at least two consecutive numbers occur more frequently than other categories.
Frequency analysis of the Euro Jackpot game as of March 21, 2024 shows that combinations with no consecutive numbers and at least two consecutive numbers occur more frequently in 729 draws. Combinations without consecutive numbers exhibiting 488 occurrences.
Frequency analysis of the Irish Lotto game as of March 21, 2024 shows that combinations with no consecutive numbers and at least two consecutive numbers occur more frequently. Combinations without consecutive numbers having 447 occurrences of 891 draws. Combinations with one set of consecutive numbers exhbiting 344 occurences.
Frequency analysis of the Mega Millions game as of March 21, 2024 shows that combinations with a lot of consecutive pairs occur less frequently in 630 draws. Combinations without consecutive numbers occurred 461 times. Combinations with at least one set of consecutive numbers occurred 154 times.
Frequency analysis of the UK Lotto game as of March 21, 2024 shows that combinations with a lot of consecutive pairs occur less frequently in 876 draws.

If your favorite lottery format doesn’t match any featured games above, use our free lottery calculator to determine how your game behaves when drawing consecutive numbers.

Watch Out for Regularity.

Another type you should avoid at all costs is the combination that exhibits regularity. For example, combinations with equal intervals are unlikely to be drawn. We are not saying it is impossible, but you need a very large quantity of draws to see these combinations occur.

The combination 5-12-19-26-33-40 shows seven interval between numbers.  This is improbable to occur in a lottery draw.

Sometimes, the number’s interval increases at the same rate.

The combination 5-12-20-29-39-50 shows the interval between numbers are increasing by one. A demonstration of what is improbable in a draw.

Out-of-balance Combination

Most winning combinations have a balanced composition. Therefore, probability says you should pick combinations to represent number groups in a balanced way. Here are some examples of out-of-balance combinations:

CombinationWhy improbable
7-23-24-26-28-29Groups 10-19, 30-39, 40-49 are not represented
5-7-11-14-16-19Groups 20-29, 30-39, 40-49 are not represented
10-12-15-16-18-19Numbers belong to only one group
40-41-42-43-44-45All numbers belong to only one group and all consecutive
1-2-3-30-31-32Two sets of consecutive numbers from two groups

We don’t say those out-of-balance combinations have no chance. We say such combinations are highly improbable but not impossible. If you have played for many years, you have probably spent money on one of these improbable groups.

Avoid non-random combinations. Always pick your combination from a group with a favorable frequency ratio.

Don’t Waste Your Money on Silly Lotto Strategies

There has been a lot of silliness ever since the lottery was invented. You must understand what works and support it with solid evidence. In science, a hypothesis must be testable and falsifiable. Certainly, superstitions don’t fit that criterion and many strategies simply don’t work. Here are some examples:

Don’t rely on the quick pick machine when you can make informed choices through calculations? Calculate the possibilities and make informed choices when playing. There’s more to lottery games than meets the eye. Study how randomness works in the lottery. Read: The Lottery Formula: Combinatorics and Probability at Work. If you hate math, then use a Lotterycodex calculator.

Superstitions will not provide the solution to the lottery puzzle. Mathematics remains the only tool that can provide useful information to help you make informed decisions.

Enjoy the Lottery for What It Is

Even someone with paranormal power cannot predict the lottery. Even a psychic asks how to win the lottery.

The toughest odds I’ve seen are the ones in South Africa and Italy’s Superenalotto, where you pick from 90 numbers. Winning in such games is like hoping for a miracle.

Some say you’re more likely to be killed by a shark than win the lottery. That’s not always true. There are lotto games with better odds like Washington’s Match 4, Minnesota’s North 5, Louisiana’s Easy 5, California’s Fantasy 5, and Virginia’s Bank a Million offer much better odds.

The truth is, you can’t meet a shark if you never swim in the ocean.10 The same goes for the lottery—you have to be “in it to win it.”

Face the Odds

People play despite the slim chances. One reason is availability bias. Hearing about recent lottery winners makes people think winning is more likely than it really is.11 Adults, like kids, enjoy games. So, playing once in a while for fun at the tease of ‘What if I win?’ isn’t a bad idea.. So if you play the lottery. Play for fun. Keep it exciting.

Don’t try to outsmart the system. No lottery hack can predict the exact winning numbers. Others have tried to cheat, but it never works.12

It takes a lot of proper attitude, patience, and perseverance to play and win.

Avoid Losing Money in the Lottery

The lottery is a billion-dollar business, but players are almost always on the losing side. So, who wins? The government, the operators, and ticket sellers. Here’s the secret: you can win every draw by taking a share of the lottery profits.

For example, you can run your lotto shop! While it requires a significant upfront investment, it comes with perks—like earning revenue and a small commission from your customer’s payout.

Don’t have the capital for a big startup? Here are a couple of alternative options:

Ebook: Inverse Strategy - How to Play the Lottery Without Losing Money
This ebook shares creative ways to profit from the lottery. One idea is so brilliant it costs less than a dollar to start earning—and it’s 100% legal. I call this section “The Inverse Lotto Strategy” because it flips the odds and turns them into an opportunity. This ebook is only available inside the Lotterycodex calculator.

Play the Lottery But Don’t Forget to Invest

If you buy a lotto ticket, you may hit a massive windfall. But it’s also possible that it may not happen. When you put some money into investments (e.g., stocks, mutual funds, or index funds), that money will grow over time. Your money doesn’t grow in the lottery because it is not an investment. Play if you want fun, but remember to invest for retirement.

When you play the lottery, make sure to consider putting more money into your retirement plan than in the lottery
Put more money into your retirement and play the lottery for fun.

Key Takeaways: Actionable Tips to Win the Lottery

If you want to win the lottery, here are some guidelines you may follow:

FAQs About the Lottery

How to win the lottery guaranteed?

The only option for guaranteeing a jackpot is buying all combinations. This option, however, is essentially out of reach with a variety of issues including cost, logistics, and negative expected value. A better option is to play as a group. This strategy doesn’t provide any assurance of a win but provides a chance for players to combine resources together, purchase more tickets, and realistically optimize chances for success. When paired with a lottery wheel, a group ensures that it wins smaller prizes while it may be on its way to winning the jackpot.

What is the best way to pick lotto numbers?

Always keep the frequency ratio in mind while selecting the numbers to get favorable shots. Lotterycodex provides combinatorial templates to guide you in making informed decisions while selecting numbers.

Is it possible to profit from the lottery?

Playing a game of lottery is gambling and should not be a replacement for a full-time job. You will not profit out of the lottery even if you are winning small prizes more often because the expected value is always negative. That is, your possible losses in terms of money tend to exceed the potential winnings.

Explore more:

References

18 comments

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  • Thank you for a very pragmatic and lets be real approach to demystifying the lottery as a mathematical system.

    This has been the most worthwhile article I have read in all my time as a lottery hobbyist.

  • I can’t quite remember the last time I read such a long article online. But this right here worth the read. I thoroughly enjoyed the straightforward explanation and power of maths. Thank you.

  • This article is the most detailed and comprehensive guide to playing the lotto. The advice given here is extremely intelligent and practical. I have been intuitively following most of the tips given here and have had many a successful “small” win. I apply the word “heuristic” for my way of choosing. I have even used Markov Analysis to try to zero-in on timing. However, I think the best advice on timing comes from the mathematical principle of “Cover” and the wheeling system, as described in this article. I have also studied the mathematics of the Brazilian LotoRainbow and I understand it very well. It remains possible that we can always adopt additional strategies to augment the many tips given in this article. We can therefore always arrive at a very small statistical cluster of numbers that provide an almost safe and confident set of affordable numbers that can be frequently and consistently played with a decent measure of small wins.

  • When the Lotto first started in this state, I took all my savings, available cash & bought about $4,000.00 to $6,000.00 dollars of lotto tickets in Carmel. I checked each ticket manually, thinking needing all numbers to win. Several month later I realized that I had four or five tickets with five numbers correct on each. When I went back to Ron’s liquer store in Carmel to cash them in, I was told that it is too late now. I could have won about $1,000,000.00. Consequently, lost a job, not much money left & going to school & sleeping in my car, resulted from this dilemma. Only played lottos sparingly since then.

    • The problem is the odds are always against you. Therefore, buying $4,000 worth is never a good option. Even though you won $1m. Probability dictates that all other people who try your strategy will end up with less money than they put in.

      The first scratch card I ever brought won £250. They cost £1. Haven’t brought one since because although I didn’t win £1m, the second place prize of £250 had unfathomable odds. In that respect, I won the scratchcard lottery and beat it by not playing again.

      I do play the UK national lottery and win small prizes. My lottery games were initially funded by the £250 scratchcard win. 6 years later, and I’m still hovering between break even and small losses.

      This is a good position to be in as it means you are winning some of the time vs people who have rubbish numbers and never win.

      The key is understanding the odds are against you and your bank balance will always go down over time until you win big and stop playing. If this was any different lotteries would not exist as they wouldn’t be profitable business models.

      Your goal should be, how can I reduce the speed my bank balance reduces over a period of time. You do this by increasing the probability of picking good numbers. The fun part of the game is comparing your games to your friends. Seeing who wins the most and looses the least amount of money.

  • 1-good lesson, 2-winning strategy, 3-just for fun, 4-don’t take seriously, play within your limits, and lots of thanks for your favourable advise and useful recommendation on this regard, GOD BLESS and MORE POWER.

  • I haven’t read something so empowering like your articles for a long long time. I have already designed my mathametical and probablistic approach to playing lotto. In the last 5 years I have been playing soccer bets but I decided to change course and that is how I came across your articles.🙏💪

  • In a game where they draw 20 numbers out of 70, a ticket cost is $5. You need to matched at least 12 numbers and up from those 20 numbers drawn to win big prizes but there is also a trick to win at least 500$ ,if your 20 numbers are not drawn in that game, meaning you did not get any of those winning numbers. Question how to calculate or solve a possibility that my 20 combination of numbers out of 70 are not the winning numbers? Is it possible if you can share me different groups of 20 combination of possible non winning numbers out of 70 ?

  • Thank you for your valuable information. While reading your thoughts I understood you completely in that you opened my brain box to realise that I am not going to win Powerball although I try every week. I only play for fun and as you suggested I make it a little interest every Thursday. I never play the Pokies .
    My game is two power hits. If I win (if) maybe the following week , I will have 4 games.
    I like your idea of combining groups of wining numbers. Thank you again, I enjoyed your article and I think I might keep trying. Haha. Margaret.

  • Hi,

    you are writing “Of course, buying all the tickets is not achievable.”.

    Why is that? Isn’t there a way to buy for example all 229 million power bal combinations? According to my calculations with a Jackpot like now (1.7 billion) I would still win about 750 million if 3 people (including me) would win the jackpot.

    So I need 1. a system to put all bets and 2. A strong investor 😀 to pay about 584 million in the bets (plus all the logistics behind)

    Would like have you thoughts on that. If interested I can share my excel sheet.

    BR
    Robert

    • As someone who invests in the stock market, I’d rather use the 584 million to buy stocks that I believe in, instead of risking it in a lottery. Lottery games are not investments; they’re forms of gambling. Just play the lottery for fun.

  • Hello, thank you for your generosity in sharing such detailed and comprehensive information on having the best shot at winning the lottery. As a struggling single parent I really appreciate it your knowledge and research. Thank you! 🙂

  • Wow this was an amazing and insightful post. Very well detailed and allows me to walk away confident about what the Lottery offers. Feels like I can see behind the wall of a “big win” and decide for myself how I would actually like to approach the lottery in accordance to my actual budget and lifestyle. Very useful information. Thank you!

  • Hi, I am playing since last 15 months lottery draw , but I couldn’t match my one numbers also , Now I read your article ,It’s really very tuff to get my goal , But I learn from here lots , and I will try my best agian to start from 0 .Thank you so much . Can you send me more details of 1/39 Of matching numbers details please. Thank you once again.

By Edvin Hiltner