Last updated on January 2, 2021
It is not easy to disprove superstitions without first learning why coincidences or lucky numbers occur in the lottery.
Someone sent me an email and said this:
My Uncle won the lottery several times (no jackpot, though) in the ’90s, and he claimed that luck plays an important role. I don’t know, but I am trying my lucky numbers in the lottery, yet it seems that I am not as lucky as my Uncle. Surprisingly we hear the news of players winning the jackpot twice or even more. Can you explain why sometimes the lottery favors few players?
I would agree if someone claimed that he had won the lottery because of luck. That’s because in a random event where you don’t know what’s going to happen next and you win, what else can you call that but “luck” indeed.
However, striking luck twice or several times is said to be unusual in a sense. Even if the odds of winning the lottery are seemingly improbable, some people achieve a continuous winning streak. For example, a man won the Illinois lottery twice.,
Every once in awhile, we hear unusual stories of lucky lotto players such as the Colorado man who won the Powerball jackpot twice on the same day.
Such an occurrence happened not just once. A Newark man and a woman in Virginia experienced this too on different occasions.,
So why do all these happen in a truly random, fair, and unbiased lottery game?
The answer is the law of truly large numbers or LTLN.
Good luck, bad luck, and the law of truly large numbers
Being lucky can be ascribed to randomness. When many people pooled their bets together to have fun at the lottery, someone at one point had to be lucky.
And although improbable, someone who got lucky yesterday might be the same person who may get lucky again tomorrow. That may sound extremely unusual, but mathematicians don’t look at it that way. The law of truly large numbers takes effect in a random event, whether we like it or not.
The law of truly large numbers states that given abundant opportunities (hence the term truly large numbers), even unusual events and strange coincidences are expected to occur.
Mathematicians will be surprised if we don’t see unusual stories like these in the news., ,
This particular law in mathematics applies to lotteries and all extraordinary events and coincidences in every aspect of life.
In the lottery, this mathematical law can be observed very quickly.
First, many countries worldwide operate lottery games. All these draws happening worldwide quickly add up to already abundant opportunities. At any given time, an unexpected and unusual story can happen at any place around the world.
History has proven that the vast amount of lottery draws taking place every day allows for such unnatural occurrences to exist.
From the perspective of lucky people, the inverse can happen too. These unusual events are NOT always pleasant news.
For example, in 1980, Maureen Wilcox bought tickets for the Massachusetts State Lottery and the Rhode Island Lottery. Both tickets had the winning numbers. Unfortunately, her ticket for the Rhode Island Lottery matched the Massachusetts Lottery winning combination, and vice versa.
Wilcox’s story takes away: do not play two different lotteries at the same time on the same day.
Interestingly, some events can be so bizarre and fascinating that one would think such seemingly improbable things aren’t real.
For example, mathematicians use the same law to explain why we hear stories of lotto players who have won using tarot cards. Or a pet owner got his winning numbers from his pet chicken, who accidentally walked on a calculator.
Likewise, the same law answers why a Loughton man’s vivid lottery dream came true., ,,
If you hear a story about a palm reader or a paranormal psychic who helped someone win the lottery, don’t be surprised at all. However, please don’t believe that palm-reading, psychic reading, and other supernatural tools work as a strategy to win the lottery.
The unusual lottery winning stories you hear in the news does not affirm the effectiveness of their methods. These supernatural beliefs don’t apply to any random game, let alone the lottery.
The law of truly large numbers is truly fascinating and adds color to our everyday lives. These are the stories that the mainstream media likes to cover and sometimes exaggerate.
In September of 2009, the Bulgarian national lottery was shaken after the same six numbers (4, 15, 23, 24, 35, and 42) were drawn in two consecutive draws. This event created a media storm and led the Bulgarian authorities to order an immediate investigation.
Should we be surprised by this incident? True, it’s freakishly unusual and improbable, but it can happen according to the law of truly large numbers.
David J. Hand, an emeritus professor of mathematics and senior research investigator at Imperial College London, said this:
Sometimes, though, when there are really many opportunities, it can look as if there are only relatively few. This misperception leads us to grossly underestimate the probability of an event: we think something is incredibly unlikely, when it’s actually very likely, perhaps almost certain.David J. Hand
Life is full of surprises. The lottery is not exempted from that powerful force of nature.
How to be lucky using the law of large numbers
You cannot change or manipulate your chances of winning the lottery because the underlying probability never changes. You also cannot beat the odds —no one can. However, there’s a way to play the lottery and get the best shot possible.
Buy more tickets.
However, buying more tickets is useless if you’re making the wrong choices.To get the best chance possible, we need to add another strategy—making intelligent choices.
That’s how math can help. We can line up all your options and make intelligent choices to make sure you are not mathematically wrong most of the time.
How NOT to be mathematically wrong in the lottery
Earlier, we discussed that some people are “lucky” or “unlucky” because all lotteries are bound to behave according to “the law of truly large numbers.”
So, here’s another question that you might ask: can you force luck on your side?
Lucky for you, yes. It may sound absurd, but you can—mathematically.
To borrow a line from a multi-awarded Bob Dylan song: The answer my friend is blowing in the wind. I’ll explain why in a little while.
But let me give you a more concrete example. To be lucky, you have to follow another law in mathematics called the law of large numbers or LLN.
Just to be clear, LTLN is different from LLN.
While the law of truly large numbers (or LTLN) explains why unusual events occur and why some people are lucky, the law of large numbers (or LLN), on the other hand, defines the conclusion of the lottery based on a large number of draws.
Theoretically, you can force luck on your side if you follow the conclusion. That means you are intelligently playing the lottery with the best ratio of success to failure by following the general trend (I”ll give you lots of examples below).
The depth of this strategy can be difficult to grasp at first. But, if you try your best to understand how it works, you’ll discover a powerful strategy for playing the lottery that only mathematics can provide.
Here’s a related article that might interest you: Using Birth Dates in PLaying the Lottery? Here’s What Math Says.
Fortunately, you don’t need to know mathematics to implement a mathematical strategy. This lottery calculator will do ALL the heavy lifting for you.
There, now you’re getting closer to being confidently lucky!
Before we continue further, let me state a little caveat.
Being lucky and the illusion of control
Making an intelligent choice is a pretty straightforward statement. However, probability theory is one of the most misunderstood fields in mathematics. We need to thresh out this issue carefully and in the right perspective.
To say that you can force luck on your side doesn’t mean you have the power to control the outcome of any lottery draw. The concept is very far from that.
Have you heard of the term “illusion of control?”,
An illusion of control is a dangerous belief to have for yourself. Some people believe that just because they have a strategy to win, they also think they’re in control of the lottery draws.
Let me tell you right off the bat that you can’t win the lottery more frequently. Some lotto gurus may try to convince you that you can win small prizes more often. On the other hand, I would suggest that you run away from these people as fast as possible.
I have already debunked this issue in my earlier article: The Truth About Winning Small Prizes in the Lottery
Here’s the truth: forcing luck to your favor is not equivalent to making money in the lottery. The truth is that the expected value of each ticket is always negative.In other words, the lottery can neither be a source of income nor a substitute for a real job.
The lottery’s real objective is to have fun, and the fun begins at the number-selection process. When you use the power of calculation, you can never be mathematically wrong based on the law of large numbers.
I recommend that you explore the fascinating world of math so you can fully appreciate how it is applied in the lottery setting. While the Lotterycodex calculator does all the hard work, it’s still best that you know how it works.
So, let’s move on and explain how math works in the lottery. First, we will discuss the simplest strategy then proceed to a more advanced option.
The simplest one is your choice of the lottery. The lottery game you choose can hugely influence your luck.
Your choice of a lottery game can influence your luck
When it comes to making choices, you have the power to calculate your advantage. For example, if choosing between the 6/42 and 6/49 games, the smart player would opt for 6/42. That’s the point of calculating the odds. You know that you are “not mathematically wrong” when it’s time to make a crucial decision.
Choosing the right game entails comparing the odds between the two lotteries and playing the one that offers an easier opportunity to win.
This explains why our forefathers were far luckier than us.
Prior to 1992, Lotto America offered odds of 1 in 18.6 million chances (1 in 18,643,560) for its 7/40 game format.
By the time the Powerball replaced Lotto America in 1992, players had to deal with the increase in odds of 1 to 55 million. So, lottery players during the Lotto America era benefitted from three times better odds than when Powerball was introduced.
Powerball had undergone major changes in its draw format several times since it started. The game tremendously increased the odds from 1:55 million odds in 1992 to the current odds of 1:292 million.
Comparatively, lottery players in the olden days had much better chances of winning the lottery.
But don’t despair; there is still hope of winning in the modern lottery systems.
Players nowadays have hundreds of lottery games to choose from. Powerball is not the only game you can play.
You can easily try your luck with other lottery games that have better odds.
How can we explain this from a mathematical point of view?
There are two factors to consider: the number field and the pick size.
To choose which lottery to play, bear in mind that it is easier to win a game with a smaller number field. A lottery with 49 balls is easier to win than a lottery with 59 balls.
Similarly, a lottery with 42 numbers is easier to win than a lottery with a 49 number field.
Additionally, a pick size of 6 balls is easier to win than a lottery that draws 7 balls, but a pick 5 game is even better. It is that simple.
Together, these two factors determine the odds of winning a specific lottery.
The table below shows the odds for different types of lotteries:
With these odds, it is easy to see that the best way to win a lottery is to choose one with the lowest odds. Based on the table above, the 5/20 offers better odds.
Another variable that you should consider is the extra ball. The extra ball is called by different names, including “bonus ball,” “power ball,” “lucky star ball,” and others. The extra balls may be drawn from the same drum or come from a different drum.
The Irish lottery and the Australian Tattslotto draw from the same drum as the main numbers. On the other hand, the U.S. Powerball and the Euro Millions used a different drum for the extra balls.
Drawing extra balls from a different drum makes it more difficult to win the game. For instance, the U.S. Powerball 5/69 has odds of 1:11 million without the extra ball. To win the Powerball jackpot, you also need to choose the red Powerball correctly. This ball is drawn from a second drum containing 26 balls and increases the odds to 1:292 million.
The table below shows the odds for winning the most popular lotteries in the world:
With a 5/20 lottery, the Trinidad/Tobago Cash Pot has a favorable odds of 1 to 15,504. The Italian Superenalotto 6/90 has an infinitesimal 1:622,614,630.
Players consider the large jackpot lotteries as a prime motivation to keep on playing. It is also important to consider reasonable chances of winning whenever you play the lottery.
That is just a simple example to prove that calculation is important in playing the lottery.
Now let’s go to a more advanced method.
How NOT to be mathematically wrong
Besides choosing the lottery with better odds, we can be more granular on a mathematical strategy. That’s how Lotterycodex helps to go deep into a more advanced application of mathematics in lottery games. Specifically, we talk about combinatorial math and probability theory.
Now, it’s very important to understand that mathematically, there’s no way you can increase your probability. We don’t have the power to manipulate the underlying probability.
And there’s no way you can beat the odds of the lottery. No one can!
So if that’s the case, then how can we use math to improve our playing strategy?
The answer is simple: “know the best choice and be wrong less.”
A true mathematical strategy is all about calculating all the possible choices and making an intelligent choice that will provide you with the best ratio of success to failure.
So a mathematical strategy is all about making an intelligent choice and being wrong less.
There are several things that we keep repeating about probability and the lottery. One of these is that any combination has the same probability of being drawn as any other combination.
We don’t know what combination will be drawn beforehand, but we know that it can be any of the possible combinations. As such, each combination has an equal chance of winning.
If we take a combination like 5-10-15-20-25-30, it has exactly one chance of winning out of all the possible combinations.
If all combinations have the same probability, then there should be nothing wrong with choosing to play numbers like 1-2-3-4-5-6 or 5-10-15-20-25-30. However, these combinations and others like them very rarely get drawn.
It is easy to say that players have a gut feel about not playing these combinations. However, gut feel or intuition does not have a place in playing the lottery. These groups of combinations, along with others that have non-random patterns, are considered “unusual,” “coincidences,” and “rare” events.
We avoid these numbers because they appear to be not random enough. However, we still expect them to occur at some point. The law of truly large numbers states that even the most unlikely combination will happen if given enough draws.
To better understand the concept of combinations that seldom occur, as against a more likely combination, let’s look at patterns of numbers.
Lucky numbers using odd-even analysis
Again, we ask the question, does one combination have a better odd than another? For instance, if we compare a combination of 6-even-zero-odd-numbers against 3-odd-3-even, we should see something interesting.
In a 6/49 system, the following are the comparison between a 6-even (no odd numbers) combination and a 3-odd-3-even combination:
The probabilities above show that 3-odd-3-even combinations are drawn around 333 times in 1,000 draws, while a 6-even combination with no odd numbers is drawn only nine times in 1,000 draws.
If all combinations have the same chances of being drawn, how do we explain the above difference in odds?
The simplest explanation is that there is a difference in definitions between the “odds” and the “probability.”
Probability is the measurement of the likelihood that an event will occur so we express the formula in the following way:
The odds on the other hand refer to the ratio of success to failure and we use this formula instead:
In a 6/49 system, a single combination has a 1 in 13,983,816 chance. There are 4,655,200 ways to combine 3-odd-3-even combinations. So out of 3 games, you get one opportunity to match the winning combination against two ways you will not. In simple terms, if you play 100 times, you get 33 opportunities to win the jackpot against having 66 ways you will not.
Compare this with the odds of a 6-even combination with only 1 opportunity to match the winning combination against 100 ways you will not. This means that you have less opportunity to match the winning numbers and more chances of losing.
If you want to improve your odds, you should choose a combination from a group that provides you with a better ratio of success to failure. Meaning, look for more opportunities to win with less chance of losing.
6-even-combination3-odd-3-even-combination134,596 ways to win4,655,200 ways to win13,849,220 ways to fail9,328,616 ways to failJust 1 opportunity to win in every 100 attempts that you playGet 33 opportunities to win in every 100 attempts that you playLOW RATIO OF SUCCESSHIGH RATIO OF SUCCESSNot a smart choiceAn intelligent choice
RememberYour goal is to win the lottery, and the first thing you should know before you play is to know the ratio of success to failure and choose the best one. You cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you have the power to know and make the right choice. Even choosing not to play is a strategy by itself.
When choosing combinations, always look for the number of ways you win and the number of ways you will fail.
To get the bigger picture of why you should choose 3-odd 3-even combinations, let’s look at the whole odd-even scheme.
In a 6/49 lottery, there are the set of odd and the set of even numbers:
Odd numbers = 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 numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48
We can create different mixes of numbers from the above sets to come up with different combinatorial patterns. We then compute the probabilities based on their patterns.
The table above shows that the balanced mix of 3-odd-3-even numbers has the best probability of being drawn. The worst patterns are the 6-odd and the 6-even combination.
RememberChoosing a 3-odd-3-even combination instead of 6-even (e.g., 2-4-6-8-10-12) WILL NOT increase your chances of winning because all combinations have the same probability. The reason you shouldn’t choose 2-4-6-8-10-12 is that the 0-odd-6-even pattern has fewer ways to win and have more ways to fail. You should choose 3-odd-3-even because it gives you the best ratio of success to failure.
This probability study reflects the overall performance of all the lottery systems in the world regardless of the format. Whether your game is a 6/49 game, or 6/45, or 5/69, or 5/50 game. Probability theory behaves the same way across all lottery games.
Take a look at the results of the Australian Saturday Lotto from January 7, 2006 to February 1, 2020:
Other lotteries closely follow the above graph for actual lottery results.
As expected, the results closely match that of the expected values. We recommend that when you play your lucky numbers, make sure to balance your odd and even numbers to get a better ratio of success to failure.
Lucky numbers using low-high analysis
Much like what we did with the odd-even combination, we compare different high and low combinations. Although it seems obvious where this is headed, going through the exercise clears up the matter.
Using the 6/49 lottery system, we can divide the numbers between high and low, as follows:
Low numbers = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
High numbers = 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49
See the table below for the possible combinatorial patterns and their probability. I’ve added a column for the approximate occurrence of the combinations for every 100 draws.
Recommended to use for your lucky numbers
Middle patterns (OK but not recommended)
Worst patterns (Avoid)
If using any lucky numbers in your strategy, make sure to have a balanced low and high numbers to get a better ratio of success to failure.
RememberChoosing a 3-low-3-high combination instead of a 6-low combination (e.g., 1-2-3-4-5-12) WILL NOT increase your chances of winning because all combinations are equally likely. You should avoid 1-2-3-4-5-6 because a 6-low-0-high pattern has fewer ways to win and more ways to fail. I recommend choosing 3-low-3-high because it offers the best ratio of success to failure.
As usual, the results of the actual draws is very close to the high-low analysis. Below are the results of lotteries sorted according to their high-low combinations.
The actual lottery results validated the predicted results. It only shows that probability theory can actually predict the likely outcome of any lottery draw based on the law of large numbers.
The power of the Lotterycodex calculator
Finally, here’s the Lotterycodex calculator as a superior type of lottery wheel.
The Lotterycodex is the only lottery calculator that combines combinatorics and probability theory in a single calculation. Meaning, it performs as a lottery wheel and can separate the good, the bad, the worst, and the best combinations with probability analysis.
This feature provides lotto players with a complete picture of how the whole lottery game works according to the law of large numbers.
In the earlier topics, we have discussed odd-even in one analysis. And we presented the patterns of low-high numbers in a separate analysis.
The problem with these two separate analyses is the existence of “contradicting conclusions.”
For example, according to the odd-even analysis, 1-2-3-4-5-6 is among the best combinations because of its balanced composition of 3-odd-3-even numbers. On the other hand, according to the low-high analysis, 1-2-3-4-5-6 is one of the worst combinations.
There’s a need to solve this contradiction. The best solution here is to combine the two strategies into one combinatorial/probability equation to produce a single conclusive analysis.
Lotterycodex wheel is designed to combine odd-even and low-high in one combinatorial design.
For example, in a 4/20 lottery game, the high and low numbers are:
Further dividing the sets into odd and even numbers:
These sets are the basis of the Lotterycodex Combinatorial Design:
We can use these sets to analyze a group of combinations according to their composition. For instance, one pattern can be a 2-low-odd, 1-high-odd, …