Choosing the most common winning lottery numbers is ineffective and contradicts the exact behavior of a truly random game according to the law of large numbers.
Let’s start the discussion with a letter from a curious player.
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Do Common Winning Lottery Numbers Improve My Chances?
Dear Edvin,
Let me start by saying that I’ve been playing Powerball and Mega Millions on and off for over 20 years. I only play when the jackpot prize is over $100 million. The most that I have won is $20, and it gets so frustrating that I keep losing.
I really want to win so I can have money put aside for my children’s education and end all my money worries once and for all.
Please help me improve my chances in the lotto. Will picking numbers that appear more frequently help me hit the jackpot?
I hope you could help me and thank you for your time.
The Most Common Winning Lottery Numbers Don’t Exist
Many lotto players mistakenly believe that when a number appears more frequently than others, it will perform well in the next draws.
Well, it’s about time that you realize it’s not. Just because some numbers appear more frequently in lottery draws doesn’t mean they are the best numbers to play.
Truth be told, hot numbers don’t exist.
If you have been following my lottery study, you should know it follows certain mathematical laws. One of these laws is called the law of large numbers, or LLN. The LLN explains why choosing to play the most common winning lottery numbers is such a bad idea.
What is the Law of Large Numbers?
There are many ways to explain the Law of Large Numbers. One straightforward explanation comes from Wikipedia, which says:
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.1
Wikipedia.com
The Law of Large Numbers in Simple Terms
LLN means that when you toss a fair coin ten times, you probably will see a significant discrepancy in the probability of the head against the tail. However, if you repeat the process independently one thousand times, you will see that the head and the tail exhibit the same probability.
In the lottery, given enough large draws, each ball in the number field exhibits the same probability.
For example, you may notice that some numbers appear more frequently, and some don’t perform equally well. However, the LLN states that as the number of lottery draws takes place, the frequencies of all balls in the number field will tend to even out. Those less frequently appearing numbers eventually catch up as lottery draws get larger.
This theorem consistently occurs in any random game, most notably the lottery. Until now, I have not seen any proof that picking the most common winning lottery numbers will increase your chances of hitting the jackpot prize.
Focus on Composition, Not on Individual Numbers
Combinations and numbers are two different terms. You don’t win the lottery with just a number. You have to combine numbers to play a lottery game and be in it to win it.
For example, you must pick five numbers in Euromillions and six numbers to play the Tattslotto game.
It doesn’t matter what numbers you pick. What matters is that you make informed choices based on the frequency ratio that works for you.
But how do we know we’re getting the best frequency ratio?
One of the secrets is looking at the composition of your combination.
For example, this line 4-12-20-32-38-42 is a combination where all numbers are even. In a lotto 6/49 game, there are 134,596 ways to combine numbers using the 0-odd-6-even composition.
This group is expected to occur once every 100 draws. As a lotto player, you don’t want to spend your money on 100 draws to get one favorable shot.
There are 4,655,200 ways to combine numbers using a 3-odd-3-even composition. You get 33 favorable shots in every 100 draws.
According to probability theory,2 most winning combinations must come from the 3-odd-3-even group because they are the most prevalent composition.
So, to get the best shot possible, consider picking numbers that belong to the group that occurs more frequently in most draws.
Now, it doesn’t matter whether or not your numbers are hot or cold. It’s the composition that matters in a truly random game.
But Some of You May Be Confused
“But Edvin, all combinations exhibit the same probability. Don’t they?”
I agree. No matter what you do, the underlying probability never changes. So, even a straight 1-2-3-4-5 combination is equally likely.
But you have to look at the lottery game in a different light.
Don’t forget that odds and probability are related terms but they are not the same.3 In fact, they use different equations.
We use probability to measure the likelihood of an event occurring. In contrast, odds measure the number of ways you get favorable and unfavorable shots. In Lotterycodex, we use the frequency ratio to highlight the number of ways you get favorable shots.
The last thing you want to do for yourself is to spend your money on a group of combinations that will give you only one favorable shot after playing 100 draws. Read The Winning Equation for Lottery Success.
Those most common winning lottery numbers don’t matter since all numbers even out after many draws.
How to Generate the Best Lotto Numbers
Some say they might also use cold numbers since they will catch up soon after many draws. Right?
Wrong.
Probability is a mysterious force in a truly random game. In all lottery games, regardless of the size of the number field, the drawing of numbers tends to be distributed evenly across the number field.
So, when you divide the number field into hot and cold groups, both groups eventually converge on the same probability value over a large number of draws.
At Lotterycodex, we created a unique system that handles low-high and odd-even numbers in one combinatorial and probability analysis.
Let’s take a look at the UK Lotto game.
Lotterycodex Sets:
LOW-ODD = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29
LOW-EVEN = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30
HIGH-ODD = 31,33,35,37,39,41,43,45,47,49,51,53,55,57,59
HIGH-EVEN = 32,34,36,38,40,42,44,46,48,50,52,54,56,58
When we subject these sets to the Lotterycodex calculator, we get 84 combinatorial templates, each with a distinct composition.
Interestingly, six of the 84 templates are prevalent and provide the most favorable frequency ratio.
The table below shows a summary of Lotterycodex analysis for a 6/59 game:
Below is a sample of probability calculations on how some of the above templates will perform over a large number of draws:
As you may notice above, template #1 dominates the lottery draws. Another thing you may notice is that the same template always dominates the game as more draws take place. This is a mathematical certainty due to the law of large numbers.
The law of large numbers states that the same Lotterycodex template will dominate as draws increase.
Combinatorial and probability calculations can be very complex.4 If you are good at combinatorics, you can do the calculation manually; however, if you hate math, you can use a Lotterycodex calculator for your game.
A Lottery Game is Truly Random
Math remains the only tool to understand how all these random lottery balls work. Due to its finite structure, we use combinatorics and probability theory in the lottery.
I mentioned a “finite” structure, so forget about whatever “statistical tools” you use to strategize your game. For decades, people have mistakenly believed that historical results will provide a clue for the next lottery draw. Nothing can be further from the truth.
Fortunately, you don’t need a degree in math to make it work. Let a calculator to do the heavy lifting for you. A Lotterycodex calculator can generate lotto combinations for you so that everything will be delivered to you on a silver platter.
Questions and Answers
The Law of Large Numbers (LLN) describes that each number has an equal chance of being drawn over many draws, irrespective of how often it has been drawn. LLN suggests that over time, all numbers will even out; therefore, the most common winning lottery numbers don’t exist.
No, the notion that specific numbers are more likely to be drawn because they have appeared frequently in the past is a misconception. All balls are equally likely in a fair and random lottery draw.
Combinations are not created equally because they have varying compositions and they exhibit varying frequency ratios. Lotterycodex separates them into combinatorial groups, allowing you to see which dominates the game over time. This study provides a more probabilistic insight than relying on individual numbers.
No. Past events cannot influence the outcome of future draws due to the complete randomness of the lottery.
Lotterycodex cannot guarantee you winning a jackpot. However, a Lotterycodex calculator can provide mathematical information that helps you make informed choices, get the best shots possible, and be closer to the winning combinations for most draws.
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