If you pick numbers using the most common winning lottery numbers, then, you are wasting your time and money. Let’s prove that from a mathematical point of view.

First off, let me show you this message that I received from one lotto player:

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.

Mr. M.G

## The Most Common Winning Lottery Numbers Don’t Work According To Math

Many lotto players mistakenly believe that when a number appears more frequently than others, it is bound to perform well in the coming draws.

Well, it’s about time, you change the way you play the lotto. Just because some numbers appear more frequently in lottery draws doesn’t mean they are the best numbers to play.

Certainly, “hot numbers” doesn’t exist. It’s just one of the myths in the world of lottery.

If you are following my study in the field of Probability theory, you will understand that the lotto follows certain immutable laws. One of these mathematical 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. The most straightforward explanation comes from Probabilitycourse.com which says:

*“The law of large numbers has a very central role in probability and statistics. It states that if you repeat an experiment independently a large number of times and average the result, what you obtain should be close to the expected value.”*

Another one that is equally easier to understand comes from TechTarget which says:

*“The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.”*

But I like the way Wikipedia puts it out 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.”*

## The Law Of Large Numbers In Layman’s Term

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 one thousand times, you will see that the head and the tail exhibit the same probability.

In the lottery, this means that given enough number of draws, each ball in the number field exhibits the same probability.

For example, you may notice that some numbers appear more frequently and some numbers don’t perform equally well. However, the LLN states that as the number of draws takes place to infinity the frequencies of all balls in the number field will tend to even out. It means that those less frequently appearing numbers in the initial draws eventually catch up as the draw continues to takes place.

I have been studying the lottery since 2014, and this theorem has been consistently happening. Up to this time, I have not seen any proof that picking the most common winning lottery numbers will increase your chances of hitting the jackpot prize.

But let’s take a deeper look into how hot numbers and cold numbers really work in the lotto.

## Hot Numbers Versus Cold Numbers

Let me show you why I do not recommend people using either hot or cold number.

By the way, if you would like to jump in quickly into the Mathematical approach of playing the lottery, then go straight ahead to the lotto analysis section. In this section, you will find the analysis for all types of lotto systems around the world. From U.S. Powerball to Irish Lotto to South African lotto system, every system is covered. Chances are, I have probability study for your favorite lottery system.

Back to hot numbers and cold numbers. For discussion, I will use the Euromillions 5/50. The image below shows the frequency of each number from April 2004 to October 2017.

Earlier I explained that the Law of Large Numbers states that the frequency of each number will converge in the same theoretical probability as the lotto draws take place to infinity.

In other words, those numbers on the cold side will eventually catch up soon as the number of draws progresses. So it’s not a good idea to pick the most common winning lottery numbers because those numbers ultimately tend to occur less frequently. This event must happen in order to let those numbers on the cold side even out.

## Hot Numbers And Their Probability

But let’s say we take the first five hot numbers from the table above. What is the probability that these numbers will occur in the next lottery draw? Let’s find out.

Using Renato Gianella’s Geometry of Chance, we will come up with this number template below:

10 | 19 | 44 | 49 | 50 |

This combination does not belong to the best probability group in Euro Millions. In fact, I would not recommend Euro Millions player to use this number pattern because its probability belongs to one of the worst probability group.

The probability of this number pattern is 0.0009557477. Any combination that follows similar pattern appears only once in every 1046 draws. If you are a serious lottery player, you don’t want to put your money on this pattern. Do you? You need a better selection of numbers with better probability and that’s how to win the lottery.

Now, I have said it, those most common winning lottery numbers don’t help. So perhaps it goes to say that the lottery players are better off choosing the least appearing ones. Right? Wrong.

Let’s analyze the cold numbers then.

## The Probability of the Cold Numbers

Let’s say; we take the five coldest numbers. What is the probability that the numbers will occur in the next draw? Let’s find out:

32 | 33 | 41 | 46 | 47 |

Again, this pattern belongs to one of the worst probability group in Euromillions. With a probability of 0.0025486605, any number combination that follows this color pattern will appear once in every 392 draws. This combination is a little bit better than the above hot numbers. Yet, this pattern is not the best to play in Euromillions.

See, when you play the lottery based on the most common winning lottery numbers, there is no assurance that you are playing the best pattern. Same holds true for the least appearing numbers. In fact, you may accidentally play numbers that follow the pattern with the worst probability. It happens.

## All Lotteries Follow The Same Principle

Let’s take a look at hot and cold numbers of other lotteries. let’s start off with Irish Lottery 6/47 from September 2015 to October 2017.

Hot Numbers | Cold Numbers |

2-7-10-16-18-27 | 13-21-23-33-35-46 |

Similar combinations appear once in every 249 draws | Similar combinations appear once in every 66 draws |

Again, the probabilities for both hot and cold combinations are not among the best in Irish lottery. The most common winning lottery numbers belong to a pattern that has 0.0040232555 probability. Any combination that follows similar pattern will only appear once in every 249 draws. The cold numbers, on the other hand, belong to a pattern that only has 0.0150872083 probability which only appears once in 66 draws.

## The Most Common Winning Lottery Numbers Of The Australian TattsLotto 6/45

Hot Numbers | Cold Numbers |

1-11-18-21-40-42 | 2-8-14-23-35-44 |

Similar combinations appear once in every 134 draws | Similar combinations appear once in every 38 draws |

## The Hot and Cold Numbers Of U.S. Powerball 5/69

Hot Numbers | Cold Numbers |

16-23-32-64-69 | 34-35-46-51-58 |

Similar combinations appear once in every 250 draws | Similar combinations appear once in every 555 draws |

## The Euro Jackpot 5/50

Hot Numbers | Cold Numbers |

7-10-18-19-40 | 2-24-36-48-50 |

Similar combinations appear once in every 196 draws | Similar combinations appear once in every 235 draws |

## The UK Lotto 6/59

Hot Numbers | Cold Numbers |

14-34-38-41-52-54 | 9-15-32-33-44-48 |

Similar combinations appear once in every 223 draws | Similar combinations appear once in every 247 draws |

## How To Generate The Best Lotto Numbers

So there, the most common winning lottery numbers don’t work. Neither do least appearing ones. Even though those cold numbers will tend to even out, it’s not a good idea to use cold numbers. Winning lotto numbers are picked at random. The lottery is more likely to spread the probability over the entire number field.

Don’t forget that the rules of the lottery require that you pick all the right numbers in combination. Therefore, the hot and cold numbers don’t matter.

So if picking numbers based on the most common winning lottery numbers will not help, then, what will?

It is the number pattern that will help you.

The lottery is governed by the rules of combinatorics. Therefore to create a strategy that is truly effective, you have to learn how the lottery works based on its discrete structures.

Combinatorics can help us define lotto patterns. Then, we can measure the probability which leads us to determine the best, the good and the worst number combinations in the lottery. The complete list of all these patterns is found in the lottery analysis section.

To play the lottery with better chances of winning, you should focus on using the right mathematical tools so that you see what works from a mathematical perspective.