The Best Lotto Combination Using Odd and Even Numbers
Do you pay attention to the odd and even numbers when making a lotto combination? If not, you’re missing a great opportunity.
Our preschool or grade school teacher taught us that numbers could be odd or even. Although some people might not know it, these odd and even numbers matter in playing lotteries.
Regardless of which lotto game you play, combinatorial and probability analysis can guide you in making the right choices.
Let’s start.
Basic Odd/Even Patterns
A combinatorial and probability analysis will not tell you the next winning combination. Instead, it will let you know the most favorable combinations to give you more favorable shots.
For example, in the Massachusetts Lottery 6/49 game called the Megabucks Doubler, we can divide numbers into the following odd/even sets as follows:
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}
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}
A 6/49 game is one where you pick six numbers from 49. In this game, there are seven combinatorial patterns by which you can make a combination.
Every pattern describes the composition of odd and even numbers. As the table above shows, each group has its number of possible combinations.
The Best Odd-Even Composition
In a 6/49 lotto game, each combination has a probability of 1 in 13,983,816 based on the probability formula:
Thus, you probably think whatever combination you play doesn’t matter. But that’s not true because picking 2–4–6–8–10–12 is not a sensible decision you can make.
But how can we explain this?
Well, the key is in the ratio of success to failure.
Since combinations have different compositions, combinatorial groups with varying ratios of success to failure exist. We get this ratio when we calculate the odds. And we express odds using the following formula:
Suppose you follow your culture’s tradition that odd numbers are unlucky. This could lead you to pick all six even numbers. There are 134,596 ways to combine numbers where there is no odd number. Therefore, your ratio of success is one to 103. That means in 104 attempts, you only get one favorable shot.
That’s too bad, considering your job as a lotto player is to get the best shot possible. You might consider a combination with a balanced mix of odd and even numbers.
There are 4,655,200 ways you can combine numbers following the 3-odd-3-even composition. Therefore, you get 33 favorable shots out of 100 attempts.
Realize that the 6-even pattern has the worst ratio of 1 to 103. This means that it would take 104 attempts before you have the chance to match the winning combination.
Based on this value, a 6-even combination might not appear even once in 100 draws. It is again the 3-odd-3-even combination that may appear most in 100 draws (about 33 times).
This does not apply only to a 6/49 game. You may also apply this knowledge if you want to play other lottery draw games. Remembering a balanced mix of odd and even numbers is the main point. Read How to Win the Lotto 6/49 According To Math.
Odd-Even Combinations In Mega Millions
In Mega Millions, you need five numbers from 70 and an extra number from 25.
The odd/even sets here are:
Odd = {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69}
Even = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70}
The winning odds computation becomes more complicated with the extra ball. The chance to win the jackpot is 1 in 302,575,350 for matching all six numbers.
Let’s make it simple. You could win the second-division prize of $1,000,000 by matching the main five numbers. You could have better odds by applying a balanced mix of odd-even combinations.
Every lottery draw game has its own set of combinatorial patterns. The table above shows that the calculations for the 6/49 game differ from that of the Mega Millions.
In 6/49, there is only one best pattern. In Mega Millions, you may choose between a 3-odd-2-even and a 2-odd-3-even. In 100 draws, either pattern gives you the best shot to match the winning combination 33 times. So you get a ratio of 1 to 2. In short, in 3 attempts, you get one favorable shot.
The 3-odd-2-even or a 2-odd-3-even pattern may occur most frequently in the Mega Millions draws. Let us see if this holds in the actual draw results.
Here, we have 13 draw results for Mega Millions. The 3-odd-2-even and 2-odd-3-even patterns occurred nine times. Thus, these patterns could give you the best shot possible. Their actual occurrences also conform to their ratio of success to failure.
Odd-Even Patterns In UK Lotto 6/59
This game requires you to pick six numbers from 59. In this game, there are 45,057,474 possible combinations. The odd/even sets are:
Odd = {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59}
Even = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58}
The odd-even patterns here are
For this game, the worst pattern to use is also 6-even. Its ratio is 1 to 94. So, 95 attempts are necessary to get one favorable shot of winning.
The best you can use is the 3-odd-3-even pattern with a ratio of 1 to 3. That means you get one favorable shot out of four attempts.
We have 12 draws of the UK Lotto 6/59 from the official website as of June 4, 2021. Here are the patterns from this small sample.
3-odd-3-even occurred five times
2-odd-4-even occurred three times
1-odd-5-even occurred once
4-odd-2-even occurred two times
Thus, it was the 3-odd-3-even pattern with the highest number of occurrences. If you want to play and be closer to the jackpot, combine balanced three-odd and three-even number compositions.
Smaller Game, Better Odds
The first step towards a better chance of winning is choosing a lotto game with fewer balls, lesser pick size, and no extra ball.
Winning a 6/49 jackpot is 1 in 13,983,816, while 1 in 302 million in Mega Millions. Although the pick size in Mega Millions is smaller than in 6/49, the former has a larger number field than the latter and an extra ball.
If you want to play a game whose probability is better than 6/49, UK Lotto, and Mega Millions, one alternative is the Northstar Cash offer by Minnesota Lottery.
It is a game where you must pick five numbers from 31. There are 169,911 possible combinations here, so your best bet is a combination with three odd and two even numbers.
As shown in the table below, the 3-odd-2-even pattern dominates the draws.
According to the law of large numbers, the same pattern will dominate the game and continue to dominate as more draws occur.
Here is another example of a smaller game with better odds. The Gimme 5 is a 5/39 game similar to California Fantasy 5. There are a total of 575,757 combinations in this game.
Odd = {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39}
Even = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38}
The table above shows that the best pattern for a 5/39 lotto game is the 3-odd-2-even.
From these 13 draw results of Gimme 5, there were five draws whose winning combinations have the 3-odd-2 even pattern.
Make the Right Balance
Are you inclined to use even numbers because they give you a positive vibe? Do you favor odd numbers instead because your traditions regard even numbers as unlucky?
You might need more than partialities to achieve your goal of winning the lottery. That’s because most winning combinations must have a balanced mix of odd and even numbers.
It’s also important to choose odd, even numbers not only from one side of the number set.
For example, 1–2–3–4–5–6 might have the ideal odd-even composition for a pick-6 draw game. But it is still not a sensible choice.
According to probability theory, a truly random lottery draw picks numbers distributively across the number field. So you need to balance your low and high numbers. Read The Winning Lottery Formula Based on Combinatorics and Probability Theory.
Digging deeper into the combinatorial analysis, you will discover that odd-even composition is just half of the equation. You also have to look at the low-high composition of combinations. Thus, the process can be extra challenging.
If you hate math, you can use a calculator. See Lottery Calculator: Knowing the Best Lotto Combinations Without a Math Degree.
