The Best Lotto Combinations Using Low and High Numbers
In a lottery game, numbers are not just odd or even numbers. Numbers may also be low or high. Not noticing the importance of low-high and odd-even numbers is not a good number selection strategy.
The lottery is a game of chance because results come from random draws. All the balls inside the barrel have the same size, shape, weight, and texture, so there is no bias.
Now, take note that numbers are just a representation of individual balls. So we use combinatorial mathematics and probability theory to understand how the balls behave in a truly random draw. Read The Winning Lottery Formula Based on Combinatorics and Probability Theory.
So when we analyze a ticket with 1–2–3–4–5–6 on it, we don’t use the numbers printed on the ball for calculation. This is improbable because a truly random draw tends to pick numbers distributively across the number field.
There is no way to foresee which numbers will win next. Yet, the law of large numbers shows that even though a lottery game is truly random, it is mathematically deterministic to an extent.
In a truly random lotto game, losses are inevitable, but there is something you can do to enjoy the game. You can’t beat the lottery odds, but at least you can play with the best shot possible.
Let’s look more deeply into the combinatorial aspect of the game.
The Best Lotto Combinations Based on Composition
Let us use a 6/45 game as an example.
This is the basic game format followed by Australia’s Tattslotto. You must pick six numbers from 45 to make a playable combination. This game has 8,145,060 possible combinations.
All 8,145,060 combinations have the same winning probability, as the formula below determines.
Based on this probability formula, we know that it doesn’t matter what combinations you choose. But your gut feeling is so strong that buying a ticket with 1–2–3–4–5–6 cannot be right.
How can we explain such a feeling?
We should also consider the formula for odds. Only a few know that odds and probability are two different terms and are not mathematically equivalent. We express the odds using the formula below:
Odds refer to the ratio of success to failure. It lets you look at your lotto game more granularly based on combinatorial groups. Because even though all combinations have the same probability, not all are created equally.
For example, 2–4–6–8–10–12 differs from 3–5–7–9–11–13 because the former is composed of all even numbers, and the latter is composed of all odd numbers.
Since combinations differ in composition, combinatorial groups exist. And combinatorial groups don’t have the same ratio of success to failure.
Analysis of composition is very important when making choices. For example, 1–2–3–4–5–6 has three odd and three even numbers. But since all numbers are low, this combination may not be your best choice. Such a combination rarely occurs in a random lottery draw. If you notice, most of the winning combinations are composed of low and high numbers.
But of course, such a straight combination is not impossible, but it is improbable. Read How Math Explains Unusual Events, Strange Combinations, and Coincidences in the Lottery.
Let’s analyze the 6/45 game using low and high numbers. Let’s divide the number field into the following sets:
Low = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23}
High = {24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45}
These sets will produce the following combinatorial groups:
From the table, you can confirm that 1–2–3–4–5–6 is not a combination worthy of your money and effort. But as you can see, there’s a line that’s worse than that. Line 40–41–42–43–44–45 can be the worst.
We can see a big difference if we compare the worst with the best group, as shown below:
1–2–3–4–5–6 has a ratio of 1 to 108, which could mean a favorable shot might come only after 109 attempts. This favorable opportunity might not even occur in 100 draws.
If one play costs $1, using this combinatorial group, you will not make the most out of a $100 budget. Hence, you may choose the 3-low-3-high and 3-odd-3-even patterns to get the best value for your money.
Remember that all combinations have the same probability, however…
The reason you should choose the 3-low-3-high group is because you want to get more favorable shots in 100 attempts. You don’t want to get just one favorable shot after wasting your money on 109 attempts using the 6-high group.
Remember to spread your number selection across the number field. Yet, you also have to ensure a balanced mix of odd and even numbers. That’s why combinatorial and probability analysis is very important. Read The Winning Lottery Formula Based on Combinatorics and Probability Theory
Let a calculator do the math for you; so you can simply concentrate on playing using the best combinations. (See Lottery Calculator: Knowing the Best Lotto Combinations Without a Math Degree)
Best Lotto Combinations for Big Games
Big games may refer to the size of the jackpot prize or the number field.
One example of a big game is Powerball. Its jackpot prize starts at $20 million and increases until somebody wins. You must pick five numbers from 69 and a Powerball from 26 to play.
Considering these six numbers, this game has 292,201,338 possible combinations. Thus, the probability of winning is 1 in 292,201,338.
A similar combinatorial analysis we tackled above might not be of big help because of the extra ball. Still, you would only use the opportunity to win $1 million if you could match the five numbers without the extra ball. Read How to Handle the Tricky Extra Lottery Ball.
In Powerball, you may fall to one of the worst combinations in the game. The table below shows you some of the worst combinations.
There are millions of useless combinations in the Powerball game. You need a more advanced combinatorial and probability analysis to analyze your game better. In this article, I use the Lotterycodex method.
In Lotterycodex, numbers are grouped into four sets:
With advanced combinatorial analysis, you leave the hard work to a calculator that will compute and analyze all possible combinations. The calculator then separates the best from the worst group. Your job as a lotto player is to choose the group that will give you the most favorable shots.
In a 5/69 game, only one pattern is the best of 56. The table below will show you how a 5/69 game performs over time:
As you see from the table, pattern #1 dominates the game. It continues to dominate the game in 2000 draws and continues to dominate in 5000 draws. This is a mathematical certainty to fulfill the law of large numbers.
What is the composition of pattern #1? I discuss how patterns work in a separate article. Please read this Free Guide: The Winning Lottery Formula Based on Combinatorics and Probability Theory.
Best Lottery Odds Exists in Smaller Games
Small games can further enhance your odds of winning. Look at the table below.
The best game to play is one with the least possible combinations. That’s because this game has a smaller pick size, fewer balls, and no extra ball.
From the list of lotto games above, the Mass Cash is the best among the draw games from the Massachusetts Lottery. The jackpot in Mass Cash is 900 times easier to win than Powerball.
With this knowledge, you could create a winning game plan for Mass Cash using the Lotterycodex method.
When playing the lottery, spend only what you can afford to lose. And try to be sensible with your choice of combinations.
