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…