Have you ever wondered if the spread of numbers you choose impacts your lottery chances? Though every combination is mathematically equal, some deterministic behaviors emerge involving low and high numbers over time. This article will give you probabilistic insight that might help you make more informed decisions when choosing your numbers.
Let’s dive right into it.
Table of Contents
The Composition Involving Low and High Numbers
To calculate the probability, we have to take everything from the context of combinatorial compositions. This time, let’s make use of a 5/69 lotto game. A famous example of a 5/69 game is the U.S. 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 don’t include the extra ball in a probability study because there’s no way you can define composition out of a single extra ball. So, it is not mathematically practical. Our ability to strategize is pretty much limited to the main drum where the main balls are drawn, and adding the extra ball to the equation is just not realistic.
Without the extra ball, the total number of combinations in a 5/69 game is 11,238,513. Based on our probability analysis, the draws will be dominated by the 3-low-2-high and 2-low-3-high compositions.
A lottery game picks numbers across the entire number field. Therefore, if we have two sets of numbers, low and high, then both sets are equally likely. This fair and unbiased probability compels the Powerball game to draw numbers from both sets for the majority of the time. That explains why we seldom see winning combinations composed of purely low numbers such as 1-2-3-4-5 or purely high numbers such as 65-66-67-68-69. Over time, 32% of the winning combinations are composed of a balanced composition. See How to Win Powerball According to Math.
Want Some Proof?
Here is the graph of the Powerball comparing prediction and actual frequency side by side. The dataset covers the 1,008 draws from October 7, 2015, to March 16, 2024.
Similarly, Mega Millions exhibits the same behavior. The comparative graph below shows that probability prediction and actual frequency agree. See How to Win Mega Millions According To Math.
If you play the Mega Millions or the Powerball game, pick numbers to match the more frequent composition. Use the calculator below to discover how low and high numbers behave in your favorite lotto game:
Here’s my lottery tip: Mix low and high numbers in your lottery tickets. If you want to learn more about how composition can help you achieve success, please read How to Win the Lottery According to Math.
More Validation that Selection of Low and High Numbers Matter
The Problem with Low and High Numbers
Having seen the above analysis, you may think that having a balanced mix of numbers can give you the best shot possible. Well, kind of, but not quite. The truth is that having low and high numbers in your combination doesn’t guarantee an efficient combinatorial composition.
For example, a combination such as 2-12-24-58-66 falls under the 3-low and 2-high composition. Therefore, according to our combinatorial analysis, it is a dominant composition. But it’s not true because, if you notice, the combination is composed of purely even numbers; therefore, it doesn’t offer you favorable shots.
You will encounter two contradictory conclusions when dealing with low and high numbers separate from odd and even numbers. We need a more complex calculation process to deal with this challenge.
We must combine low/high and odd/even numbers into a single combinatorial and probability analysis to prevent contradicting conclusions. This integration ensures a fair distribution of probability across the entire number field. The results are a list of Lotterycodex templates that serve as a simple guide to help you make informed choices. To know more about Lotterycodex templates, please read The Proven Lottery Formula Using Combinatorics and Probability Theory.