## Illinois Lottery Tips According to Math

Last updated on January 2, 2021
Here is a guide for learning how to play the Illinois Lottery better. You will understand applied probability and combinatorial methods governing a truly random game. And you don’t need a math degree to understand the method.
A good thing to know, there’s a calculator that you can use to help understand your game better and be a smart lotto player.
Let’s begin, shall we?
Don’t use a statistical method
Statistics have for years been the way for many lotto players to understand the game of lottery. People look at the past results to determine hot numbers (frequently drawn) and cold numbers (seldom drawn).
While there is truth in this observation from a small number of draws, you could see that all the numbers in the field will converge in the same expected frequency as the number of draws gets larger and larger.
Most times, people alternatively use statistics and probability with the notion they are the same. Yet, statistics and probability are two different mathematical concepts we can use for dealing with problems.
A question could be either a statistical problem or a probability problem. To know what kind of problem it is and see how to solve it, we must assess our knowledge of the given facts. If the available data is inadequate to solve the problem, we resort to the statistical sampling method.
For example, if there are 100 socks in a drawer and we don’t know how many are black and how many white socks are there, we ask a statistical question:
What is the proportion of black and white socks in the drawer?
This type of question is not the case in the Illinois lottery.
Since the lottery has a finite structure, our knowledge of its composition is adequate. We know exactly that the Illinois Lotto 6/52 game comprises 26 low numbers (1 to 26) and 26 high numbers (27 to 52). And we know that there are 23 odd numbers and 22 even numbers in the Lucky Day Lotto 5/45 game.
Remember, statistical analysis is not necessary when a finite game is involved.
Now, if a statistical analysis doesn’t help, what does? Be ready to know in the next section.
How to play the Illinois lottery using combinatorics and probability
Many people believe that since the lottery is random, no strategy could help any player win. The truth, the very random nature of the lottery can help you play better through the use of probability and combinatorial analysis.
See my post The Winning Lottery Formula Based on Combinatorics and Probability Theory.
The image above appears pixelated because of the streaks and clusters as depicted by gray and white spaces. It shows the lottery’s behavior in a truly random draw, suggesting ways not to be mathematically wrong when you play the Illinois lottery.
See The Visual Analysis of a True Random Lottery with Deterministic Outcome.
Using mathematics, we can compute the combinatorial patterns according to the finite structure of the game. And we can use a probability formula for separating the good from the bad and the best from the worst combinations.
For example, we can ask a probability question such as:
What is the probability that the next winning combination will be composed of 3-low-odd-numbers and 3-low-even numbers?
And the answer will make you realize that a 1-2-3-4-5-6 combination must be avoided when playing a lottery game.
This method cannot be done accurately and precisely through statistical analysis.
Of course, it is impossible to predict the next winning combinations. Still, we can foretell the lottery’s overall outcome because a truly random game must follow the law of large numbers or LLN. See my post on how to win the Lottery.
What Is The Law Of Large Numbers Or LLN?
This probability theorem states that the average results from many trials should be close to the expected value.
There are combinatorial groups in the lottery that follows the frequency dictated by its probability with the increasing number of draws. I will give you lots of examples below.
But before we go to the details, we must define some words to prevent some confusion along the way as we delve into the mathematical method of winning in the Illinois lottery.
Numbers and combinations are not the same
Keep in mind that numbers and combinations are two different terms.
While you need to pick numbers to play the lotto, you have to complete the six numbers to win the Illinois lotto 6/52 game’s jackpot.
And you need to pick five numbers to win the Lucky Day Lotto 5/45 game.
In other words, you need a combination to win.
So, 3,15,27,39,49, and 51 are all different numbers. But when they are put together, they form the combination 3-15-27-39-49-51, which perfectly describes a 6-odd composition.
While each number may have the same attribute (for example, all balls from the urn have the same weight, the same size, and the same texture), combinations cannot be the same in characteristics. For example, some combinations may have consecutive numbers, and some don’t have.
Combinations can be grouped according to their composition. For example, we can separate those combinations with no even numbers (all numbers are odd numbers). We can separate those combinations with high numbers from those that are composed of all low numbers.
In short, combinations are not created equally.
The difference indicates that a lotto strategy exists. We will focus on this mathematical strategy by establishing the existence of inequality among combinations.
So as an Illinois lottery player, you are lucky because things are looking up.
All numbers and combinations have the same probability
As I have mentioned earlier, hot and cold numbers don’t exist in a random lotto game. According to the law of large numbers, those less frequently occurring numbers will catch up soon.
In short, each number will give you the same chance of winning. All numbers will converge in the same expected frequency given a large number of draws. That’s why statistical analysis of the previous results of the lottery is such a futile exercise.
And this means that we have no power to know what numbers will occur in the coming draw.
Now, like numbers, all combinations have the same probability. Even the notorious 1-2-3-4-5-6 combination has an equal chance as any other combination. The reason is that there’s only one way to win the jackpot.
So mathematically speaking, a probability value of 1/ 13,983,816 would make the chance of (1-2-3-4-5-6) occurring “almost impossible.”
But the same probability value stands for all other playable combinations in Illinois lotto 6/52.
The same holds for all combinations in the Lucky Day Lotto 5/45 game.
All combinations are subordinate to the same probability formula.
The most important thing to remember is that we have no power to manipulate probability calculation results.
But that doesn’t mean we’re hopeless.
If numbers and combinations are equally likely, what kind of strategy is available for Illinois lotto players?
The key is in your choice.
Surely as a lotto player, you have the power to make the right choice and be “wrong less” for the majority of the time.
You have to learn how not to be mathematically wrong.
Even though you can’t change the underlying probability and cannot beat the lottery’s odds, you can calculate all the possible scenarios and make the right decision based on the calculation.
How can we calculate and make the right decision? That’s the topic we will be discussing next.
Focus on the ratio and be wrong less
Many players are familiar with the concept of “equally possible” idealization that applies to all combinations. That’s true because, from a mathematical point of view, the probability 1/13,983,816 stands for all the playable combinations.
But this “equally possible” idealization leads lotto players to believe that a strategy doesn’t exist.
Most lotto players think that there’s no right or wrong way to play the lottery because the probability is the same across the number field.
That’s not true.
It seems to me that people forget the concept of odds.
Probability and odds are two different mathematical concepts. See my post Odds, Probability, and the Lottery. Probability refers to the likelihood that the combination you chose will match all the winning numbers of a lottery game. Here’s how we express probability:
On the other hand, odds refer to the ratio of you winning the game over losing in the game. And here’s how we express odds:
It is heartening to know that the entire lottery game consists of combinatorial groups. And each group has a different ratio of success to failure. Thus, your chosen odds will make a difference in your game strategy.
So being able to pick the best odds must be your goal if you want to get the best shot possible.
And by saying the best shot possible, that means choosing the best ratio of success to failure.
The calculation of odds is crucial for decision making. You can see exactly the many ways you will win and the many ways you will lose. You can calculate all the possible odds and choose the most favorable one.
While you cannot manipulate probability and cannot beat the odds, you have the power to choose better odds. Do not waste effort on things you cannot control. Math will help you focus on things you have control over.
Remember, your goal is to win the Illinois lottery, and the right thing to do is to get the best ratio of success to failure.
Now don’t forget that the only way to increase your chance of winning is to buy more tickets. But buying hundreds of tickets is useless if you’re making the wrong choices. Therefore, when you buy more tickets, make sure that you also get the best ratio of success to failure.
How do we know the best ratio?
We start with knowing the composition of the combination.
Composition matters. And composition is best explained using combinatorial patterns.
The importance of composition and combinatorial patterns
To win in a lottery game, the combination you have chosen must match some or all of the numbers drawn for that lottery game.
You win the jackpot prize if all the numbers in your combination match the drawn winning combination.
The combination is very important, and to have an effective combinatorial design, you must understand the lottery’s finite structure. Realize the relationship among these numbers when you put them together in a combination.
Let’s use the combination 2-4-6-8-10-12 as an example.
Notice that the combination consists of all even numbers and all the numbers are all low numbers.
This combination has a non-random characteristic.
You see, combinations can have different characteristics depending on the composition.
See the table below for other examples of characteristics for different combinations.
CombinationComposition1-2-25-26-37-38contains three sets of consecutive numbers1-2-3-41-42-43contains two sets of consecutive numbers20-23-25-26-27-29numbers are the 20s17-18-19-20-21-22contains straight consecutive numbers
These variations in the compositions divide an entire lottery game into combinatorial groups. And this composition study is best to describe combinatorial patterns.
Let me give you examples of how to apply the ratio of success to failure in the Illinois lottery concerning combinatorial patterns.
Applying the ratio of success to the Lotto 6/52 game
There are 230,230 ways to combine 6-low-0-high. And there are 20,128,290 ways to combine numbers using other combinatorial patterns. Therefore, a combination of this type is expected to occur approximately once out of 88 attempts you play the game. On the other hand, there are 6,760,000 ways to combine 3-low-3-high, and there are 13,598,520 ways to combine numbers the other way. Therefore, that gives you approximately 33 opportunities to match the winning combination out of 100 attempts that you play the lotto 6/52.
Notice the number of ways you will fail if you choose the 6-low patterns and compare it with the 3-low-3-high pattern. Obviously, the 3-low-3-high pattern gives you more ways to win and fewer ways to fail.
You see that the best choice of group is 3-high-3-low while the worst is 6-high-0-low.
Knowing which is best and worst makes the most out of your time and resources spent on playing Illinois lotto games.
Precise calculation is always better than mere “gut feeling.”
We can compute the possibilities and then analyze the various choices that can affect your success.
As shown in the above comparison of the ratio between two choices, it will not be ideal to play 6-low-0-high combinations like (1-2-3-4-5-6) or (2-4-6-8-10-12).
Applying the ratio of success to the Lucky Day Lotto 5/45 game
This time, let’s base our analysis using odd and even numbers.
There are 26,334 ways to combine 0-odd-5-even. And there are 1,195,425 ways to combine numbers using other combinatorial patterns. So, a combination from this group is expected to occur approximately once out of 46 attempts. On the other hand, there are 409,101 ways to combine 3-odd-2-even, and there are 812,658 ways to combine numbers that are not 3-odd-2-even. Therefore, that provides you with approximately 33 opportunities to match the winning combination out of 100 attempts that you play Lucky Day Lotto 5/45.
The table above shows that when the number of ways to win increases, the number of ways to fail decreases.
It means that when inequalities are involved, you will choose a more balanced combination because it offers more ways to win and less chance to fail. Right?
And that’s the power of using mathematics to know all the possibilities and thus make the right choice to lose less.
The strategy here is in the act of choice.
RememberYou cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you have the power to make the right choice. Even choosing not to play is a strategy by itself.
To win in the Illinois Lottery, you need to compute all the possible odds and pick the one that will give you the best winning ratio.
To further understand how composition matters and why it is so important for decision-making, let me discuss what you can do to improve your combination’s composition.
Choose a balanced odd and even numbers
Let’s group all numbers into odd and even groups for Lotto 6/52 game.
Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51
Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52
The table above shows that an all-even and all-odd composition are the worst type of combinations to play in a lottery game.
As you see, there are more ways to combine 3-odd-3-even combinations. And therefore, you can make a reasonable expectation that the lottery draws will be dominated by 3-odd-3-even combinations. Because there are more ways to win, the number of ways you fail decreases. Therefore, a 3-odd-3-even combination gives you the best ratio of success to failure.
Next, let’s group the Lucky Day Lotto 5/45 game’s odd and even numbers:
Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45
Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44
If you want to make the most out of your time and money spent playing the Lucky Day Lotto 5/45 game, you will most definitely want to play for the odds that will give the best outcome.
Meaning, instead of picking a combination that will occur just once in 100 draws, you might as well play for a combination that has the highest number of occurrences in 100 draws.
In the Lucky Day Lotto 5/45, the (3-odd-2-even) and (2-odd-3-even) groups will always dominate the game as the number of draws gets larger and larger. And following the law of large numbers, this behavior is bound to continue at infinity.
RememberChoosing a 3-odd-2-even combination instead of 5-even (e.g., 2-4-6-8-10) WILL NOT increase your chances of winning because all combinations have the same probability. The reason you shouldn’t choose 2-4-6-8-10 is that the 0-odd-5-even pattern has fewer ways to win and have more ways to fail. You should choose 3-odd-2-even because it offers you the best ratio of success to failure.
This probability analysis reinforces the method of choosing the best groups that will give you more opportunities to win and less chance to fail. That’s how important the ratio of success to failure to players of the Illinois lottery.
Have a balanced low and high numbers
To understand what high and low numbers are, let us group 52 numbers into two sets. The numbers in the first half are low, while the second-half numbers are the high numbers.
Low = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26
High = 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52
A 6-low-0-high number combination contains all numbers picked from the first set.
And a 3-low-3-high combination contains three numbers from the first set and three numbers from the second set.
The 6-low-and-0-high patterns are examples of 1-2-3-4-5-6 combinations. And this is why straight combinations are such a worthless combination that every player of the Illinois lottery must avoid at all costs.
Since there are more 3-low-3-high numbers from the universe of 13 million combinations, it shows that the lotto 6/52 game tends to distribute the drawing of winning numbers across the entire number field.
Again, this inequality among combinatorial groups helps lotto players make the right choice most of the time. The same inequality answers why it’s possible to predict the Lotto game’s general outcome (to an extent). Of course, the same explanation stands for the Lucky Day Lotto 5/45 game.
The 1-2-3-4-5 combination may be notorious and popular but based on the table above; it’s not the worst one. The table shows that line 41-42-43-44-45 is the worst type of combination you can play in the Lucky Day Lotto 5/45 game since it follows the format of the 0-low-5-high group.
RememberChoosing a 3-low-2-high combination instead of a 5-low combination (e.g., 1-2-3-4-5) WILL NOT increase your chances of winning because all combinations are equally likely. You should avoid 1-2-3-4-5 because a 5-low-0-high pattern has fewer ways to win and more ways to fail. I recommend choosing 3-odd-2-even because it offers the best ratio of success to failure.
The table above reinforces the benefits of calculating possibilities because you can see exactly how the whole lottery game performs as the draws continue to take place.
And when you know how the lottery behaves, you can plan your game ahead of time.
Now that you understand how odd-even and low-high patterns affect your decision, it’s time to delve into a more advanced strategy to apply to the Illinois lottery.
Enter Lotterycodex.
Use Lotterycodex to improve your game
Sometimes, two separate analyses contradict each other. And it is the case between low-high and odd-even probability analysis.
For example, under the odd-even analysis, the 1-2-3-4-5-6 combination is considered one of the best since it has a balanced mixture of odd/even numbers (3-even-3-odd mixture). But then we know that 1-2-3-4-5-6 is one of the worst according to low-high analysis.
We have to find a solution to this contradiction.
The solution is Lotterycodex patterns.
Lotterycodex can make an exact probability measurement and then tell you which choices are ideal and problematic. Lotterycodex is all about accuracy and precision.
It simplifies picking combinations incorporating both low-high and odd-even analysis in one combinatorial and probability analysis.
The combinatorial design applied to Illinois Lotto is composed of 4 sets from the 52 numbers. By dividing them into 4, we get:
Low-Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25
Low-Even = 2,4,6,8,10,12,14,16,18,20,22,24,26
High-Odd = 27,29,31,33,35,37,39,41,43,45,47,49,51
High-Even = 28,30,32,34,36,38,40,42,44,46,48,50,52
Based on these sets, we can measure why 1-2-3-4-5-6 is such a bad combination with no contradiction at all.
For the Lotto 6/52 game, there are 84 patterns in all. Again, not all patterns share the same odds, so you must choose the one that will yield the best success-to-failure ratio. Check out the image below.
For the Lucky Day Lotto 5/45 players, we will discuss Lotterycodex patterns later below in a separate section. For now, let me show the corresponding patterns for the Illinois Lotto 6/52 game:
Out of the 84 patterns, you will want to spend money only on the six best patterns and avoid the middle and the worst patterns. Otherwise, you will only waste your money away.
If you have been an Illinois Lottery player for some time now, you probably have played for the worst or middle patterns without being aware of it. With Lotterycodex, you are fully aware of what combinatorial patterns will work best in your game.
Lotterycodex can separate the good, the bad, the worst, and the best combinations in any lottery game. There is no room for assumptions. There is only a precise probability calculation for your guide in taking the best course of action when playing lottery games.
Forget the old lottery wheel systems
There are many kinds of lottery wheeling systems, such as:
The Full-wheeling system allows you to select more numbers. However, this is an expensive strategy because the more you choose, the more combinations you must purchase to maximize your win coverage.
The abbreviated and the filtered wheeling system still offers you a winning shot (despite the small prizes you could win) and are not as expensive to play as the full wheel system.
All the above lottery wheels work according to the traditional concepts of covering. These lottery wheeling systems could either make you spend more or win less.
Lotterycodex is here to solve that old system.
It works according to the principle of covering with probability theory to separate the good, bad, best, and worst combinations.
At the time of writing, the Lotterycodex calculator is the only lottery wheel that performs combinatorial and probability analysis in one system.
It will give you the ability to spend money wisely, as you will buy lotto tickets with a high ratio of success of winning the jackpot prize (not just small consolation prizes).
Lucky Day Lotto has the best odds
Considering all factors, it is the Lucky Day Lotto 5/45 that I recommend the most among the Illinois lottery games. It has the least odds. And it doesn’t require an extra ball to win the top prize, which makes it even more attractive.
Its prize payout is not as high as those from Powerball, Lotto 6/52, and Mega Millions. However, it is an attractive game to play, especially when lady luck blesses you to have a life-changing experience.
Now, if you play the Lucky Day Lotto 5/45 as a syndicate, winning is much easier.
It will be too difficult to predict which single pattern will make you win. Through the table above, you could be closer to finding the solution to the puzzle.
With one best pattern out of 56 patterns, it yields the ideal success-to-failure ratio.
The odds in a 6/52 lotto game are 1:20 million. The odds in the Lucky Day 5/45 lotto is 1:1.2 million. Therefore, the Lucky Day Lotto is about 17 times easier than Lotto 6/52 game.
But choosing the best game in Illinois is always a subjective matter.
We mention the power of knowing and making the right choice; here is where you exercise that power.
You should weigh in all criteria. Consider the prize payout, the extra ball (if any), and your budget for entertainment. After considering all the criteria, decide the optimal trade-off that you are willing to take.
Know the parameters of the game and decide based on those parameters. Know the pieces of mathematical information about each Illinois lottery game and make up your mind.
Predicting the results of the Illinois Lottery
The underlying probability is unchangeable. There is no way to beat the lottery odds. Yet, you can choose how to play to make the game worthwhile.
Matching a pattern will not make you win any prize. You need to understand and accept this.
But if you could visualize a lottery game much better, you will discern its future behavior, as dictated by the Law of Large Numbers. This probability method is far better than gathering the past drawn numbers and assuming which numbers are hot and cold.
Take, for example, patterns #1 and #84 in the 6/52 lotto game.
Pattern # 84 has a 0.0000842890 probability value. From this probability value, we can predict the results of the Lotto 6/52 game ahead of time. Plus, you can also see how …