• Odds vs Evens This table highlights every possible combination of odd and even numbers and how many times that combination of odd and even numbers has been drawn in the Powerball.
• Did you know your odds of winning a prize are the same in every Powerball drawing? You have a 1 in 24.9 chance of winning a prize when the advertised jackpot is $40 million. You still have a 1 in 24.9 chance of winning a prize when the advertised jackpot is $1 billion.
• Lottery Post is proud to bring you winning ticket jackpot, prize payout amounts, and game odds for Powerball. This unique drawing prizes page can only be found at Lottery Post, and includes the.
• Odds of Winning. Around 70 to 80 percent of Powerball players use Quick Pick tickets, and the same percentage of winning entries are Quick Picks. This shows that regardless of whether players choose to select their own numbers or not, the odds of winning remain the same.

While this blog has nothing to do with bankruptcy or even law in general, I thought it would be both fun and timely to explain how and why the Powerball is so difficult to win. Especially given that the Powerball payout is at an all-time high of $1.5 Billion. Said another way, $1.5 Billion is $15,000 Million. This means that if you won today’s jackpot, you could spend $1 Million per day, every day for more than 41 years. Interestingly, if today’s Powerball is won by a single individual, that person would receive approximately $930 Million, effectively making that person a Billionaire overnight and one of the top 500 richest people in the world. So, just what are your odds of winning today’s $1.5 Billion Powerball and how are those odds calculated?

First, your odds are 292,201,338 to 1 that you will pick all five numbers and the correct Powerball number. But how does 292,201,338 to 1 stack up against other seemingly remote events occurring? Well, ironically, you are 292 times more likely to become a billionaire the old-fashioned way (you know, like creating Facebook) than winning the Powerball. You are 584 times more likely to be struck by lightning. And you are 5,844,027 times more likely to live to be 100 years old. Sadly, it seems that the odds winning the Powerball are truly stacked against you. But what makes the odds so long? I mean the concept seems so simple; all you have to do is pick six numbers. Well, the answer lies in how those six numbers are picked and more specifically in the Powerball number itself.

Overall odds of winning a Powerball prize are 1 in 24.87. The only exception to this chart is California, where cash prizes in lower tiers are pari-mutuel. Their values are determined by the number of winners in each tier and the number of tickets sold.

To win the Powerball, you must pick five numbers from a pool of 69 numbers and then match the Powerball from a pool of 26 numbers. The math gets a little confusing unless you are familiar with using factorials. And, in essence, the Powerball is simply using the power of factorials to make a seemingly easy concept (just pick 6 numbers) a virtually impossible task. As I said earlier, there are two distinct parts of the Powerball; the first 5 numbers and then the Powerball. Thus, both parts must be considered when calculating the odds. Ok, so here’s what the math looks like:

I know this seems overwhelming, but it's actually more simple than it looks. Simply put, in the first part you pick 5 numbers from a pool of 69. Thus, the factorial for the first part is 69*68*67*66*65 (because you have 69 choices for 5 numbers. This equals 1,348,621,560. But because each number 1 through 69 can only be used once, you actually increase your odds of winning by a factor of 5 or 120 (5*4*3*2*1 = 120). So you then divide 120 into 1,348,621,560 to get 11,238,513. These are your odds of picking the first five numbers of the Powerball. Said another way, there are 11,238,513 possible number combinations giving 5 choices between 1 and 69. For the second part of the Powerball, you have to pick one number from 26 possible numbers. Thus, you simply multiply your odds from the first part by 26 to get 292,201,338.

Whether you play the lottery or not, I think it is fascinating to understand the reason the odds are what they are. And while your odds of winning the Powerball are only 0.00000034223%, your odds of winning if you don’t buy a ticket are exactly zero. And one last thought. If you do play the lottery, buy two tickets. Buying two tickets increases your chances of winning by the maximum amount possible. Buying two tickets means that you now have a 146,100,669 to 1 chance of winning. You will still not win, but you have doubled your chances for just $2.00.

Last updated on December 20, 2020

The fact remains, you aren’t winning the Powerball game because you keep on playing the wrong type of combination.

Many Powerball players are wasting money on hot numbers, cold numbers, birth dates, anniversaries, horoscope numbers, and many unscientific lotto strategies.

The classic 1-2-3-4-5 lotto combination is so notorious that at least, nowadays, many try to avoid it. Still, mathematically speaking, millions of similar patterns exist within the universe of Powerball’s 292 million combinations.

The problem, many lotto players aren’t aware of the many combinations that belong to the worst number patterns that will not occur in 100,000 draws.

And here’s the trap, if you have been playing the Powerball using the quick pick machine, I can almost guarantee, you fell into one of these worst combinations, and you do not even know it.

Let’s take a look at the game more deeply and see how you can use math to play lotto for the best shot possible.

The odds of winning the US Powerball

The U.S. Powerball game is a 5/69 lottery format. So the rule is to pick five numbers from 1 to 69. There are 11 million ways you can do it in Powerball. So your probability of matching five numbers is 1 in 11 million chances.

However, to win the jackpot, you also need to match the extra ball called the Powerball from 1 to 26. So the odds to win the Powerball game becomes 1 to 292 million.

In simple terms, you might need 292 million attempts to win the jackpot. So if you play one ticket every week, then you need 292 million weeks to win. That sounds like playing for 5.6 million years or possibly more.

The odds are so terrible that you probably have a better chance of becoming the next Governor of the State of California. So it’s not easy to win the Powerball.

In my opinion, the Powerball is one of the hardest lotteries to win in the world.

But Americans do play anyway. And if Powerball is one of your favorite lotto games, then you might as well do your best.

That said, mathematics remains the only way to get the best shot possible. And specifically, I am talking about combinatorics or combinatorial math and probability theory.

The Powerball, like any other lottery systems in the world, is a random game. So you cannot predict the next winning numbers.

Fortunately, you can increase your chances of winning if you buy more tickets.

And mathematically speaking, buying more tickets is “the only way.”

However, buying more tickets is useless if you’re making the wrong choices.

You need a mathematical strategy. And a mathematical strategy is all about calculating all the possibilities and making the right choice.

So what is this mathematical strategy that we are talking about?

Are we talking about statistics? Nope!

I have explained why statistical analysis doesn’t work in the lottery in my article A Visual Analysis of a True Random Lottery with Deterministic Outcome.

For now, let me tell you right off the bat, don’t use statistics. What works?

Well, a true mathematical strategy involves understanding the finite structure of a lottery game. In this case, we need the tools of combinatorial math and probability theory.

These two mathematical tools are essential in the study of combinatorial patterns that can help determine the best combinations and the worst ones to avoid at all costs.

Before we go to the actual calculation, let’s discuss first the important concept that matters in a random game.

All numbers and combinations in the Powerball game have the same probability

It’s very important to keep in mind that all numbers have the same probability. This is always true no matter what the frequency of each number has been. In short, there are no “hot” and “cold” numbers.

And there are no unlucky and lucky numbers.

The same mathematical rules apply to all combinations. A combination such as 1-2-3-4-5 is equally likely as any other in the universe of 292 million Powerball combinations.

Now, if all numbers and combinations have the same probability, how does Lotterycodex separate the best combinations from the worst ones?

Well, the simple answer is understanding the concept of odds.

While you may be familiar with the concept of probability, the majority of us are not familiar with the concept of odds.

Odds and probability are two different concepts. They are not mathematically equivalent.

The two equations below will describe the difference between odds and probability.

Let me translate this in plain English.

Probability refers to the measurement of a likelihood that an event will occur.

While odds refer to the ratio of success to failure.

So in short, you cannot change the underlying probability and no one has the power to change a mathematical calculation.

And similarly, you cannot beat the odds of any game because whatever you do, you the odds will never change.

BUT, here’s the thing.

As a player, you have the power to choose.

And we can use mathematics to calculate all the possible choices and then make an intelligent choice to get “the best ratio of success to failure.“

As a lotto player, your objective is to make sure that you are not mathematically wrong for the majority of the time.

For example, in a Powerball game, there are 278,256 ways you can combine numbers composed of even numbers (no odd numbers).

0-odd-5-even combination = 278,256 ways you can do this.

There are exactly 11,238,513 ways you can combine pick-5 combination from 69 numbers.

Therefore, the odds of a 0-odd-5-even combination is:

Odds of 0-odd-5-even = 278,256 / 10960257

This means that when you pick numbers based on this type of pattern 0-odd-5-even, your ratio of success is 1 in 39. In short, you get only 2 to 3 opportunities to get closer to the winning numbers for every 100 times you play the lottery.

Now, let’s talk about a more balanced type of combination such as a 3-odd-2-even.

There are 3,671,745 ways you can combine a 3-odd-2-even type of combinations.

3-odd-2-even = 3,671,745 ways you can do this combination.

Therefore, the odds for this type of pattern is:

Odds of 3-odd-2-even = 3,671,745 / 7,566,768

The odds mean that you get 32 to 33 more opportunities to match the winning numbers for every 100 attempts you play the Powerball game.

Truly, you can see the difference when you calculate the possibilities because by then you know how to make an intelligent decision.

Knowing the composition of your combination matters to determine the exact ratio of success to failure.

And the best way to analyze the composition of combination is through combinatorial patterns.

So now, let’s discuss the importance of combinatorial patterns.

The power of combinatorial patterns in the U.S. Powerball

In the lottery, one of the key factors to consider is to know the composition of your combination.

The table below shows the complete odd-even patterns in the Powerball with their corresponding probability:

These odd and even number patterns can be divided further into three groups.

The table above shows that the best patterns to play in Powerball are the balanced mix of odd and even numbers.

Similarly, we can do the same combinatorial analysis for low and high numbers.

Below is how we group the low-high patterns based on their probability.

Based on the table above, the majority of the winning numbers in the Powerball lotto system are composed of balanced low and high numbers.

So if you don’t want to waste money, then don’t bet on numbers like 1-2-3-4-5 (all low numbers) or 65-66-67-68-69 (all high numbers).

Let me show you the proof by comparing our theoretical analysis with the actual results of the Powerball.

Theoretical prediction versus the actual results of the U.S. Powerball (odd-even pattern analysis as of February 05, 2020)

In Mathematics, we compute the expected frequency of each pattern by multiplying the probability by the number of draws.

Expected Frequency = Probability X number of draws

There are 449 draws in Powerball from October 7, 2015, to February 05, 2020. So, in the case of a 3-odd-2-even pattern, we get 146.69320621 by multiplying 0.326710926970499 by 449.

We round off the number to arrive at 147. Now we see that the 3-odd-2-even pattern is expected to occur about 147 times in 449 draws.

Doing similar computation with the rest of the odd-even patterns, we will come up with the following complete comparison table below:

Looking at the table, the close value between expected frequency and actual frequency proves that Powerball behaves in a predictable pattern.

A different way to say it is that Powerball lotto follows the dictate of probability.

Fortunately for you as a lotto player, you can take advantage of this probability principle to make the right decision. Thanks to mathematics.

Using the probability formula, we can predict how specific number composition will likely occur in a lottery draw.

For example, probability calculation shows that a 3-odd-2-even pattern is expected to appear 147 times. In the actual draw, the same pattern occurred 148 times. Very close prediction.

If you look at the whole graph, it doesn’t take a second to realize that prediction and actual results closely agree together.

As a Powerball player, you may want to put your money on the best two patterns. And as a smart player, you don’t want to waste your money on all-even-number or all-odd-number.

Theoretical prediction versus the actual results (low-high pattern analysis as of February 05, 2020)

And here’s a similar conclusion for the low-high patterns conducted in the same period.

Again, we can see how reliable the probability is. Math does not lie.

You can see the close match between prediction and actual observed frequency. It’s another proof that the Powerball game follows the dictate of probability.

Predicting the future of Powerball game

Now that you know that Powerball is subordinate to the principle of probability, you can then predict the outcome of the game in the future.

Here’s the possible outcome of Powerball in 1000 draws using the odd-even patterns.

And here’s the possible outcome of Powerball in 1000 draws using the low-high patterns.

The key takeaway here is simple. You don’t want to waste your money on patterns like 5-low-numbers, 5-high-numbers, 5-odd-numbers, or the 5-even-numbers.

So to get the best shot possible, you follow the 3-odd-2-even, 2-odd-3-even, 3-low-2-high, and 2-low-3-high patterns.

However, with odd-even and low-high patterns having two separate analyses have an unacceptable disadvantage.

Let me explain.

We already know that the combination 1-2-3-4-5 is one of the worst combinations under low-high patterns. However, our odd-even analysis doesn’t agree with this analysis.

As you can see when we deal with two separate analyses, we get contradicting results.

To solve this contradiction mathematically, we have to combine the two analyses into one probability analysis to arrive at a very conclusive result.

And here’s how Lotterycodex patterns are invented.

You see, the Powerball lotto is not about just odd-even patterns or low-high patterns. Within the 69 balls of the Powerball game lies complex patterns, which are the key to your lottery success.

Let’s discuss how these advanced patterns may help you get the best shot possible in the game of Powerball with 292 million combinations.

The four best combinatorial patterns in the US Powerball

Let me show you the exact patterns that dominate the Powerball game.

I have divided the patterns into three groups.

The details of these patterns are discussed in the free lottery guide section.

In Powerball and any lottery system, I always recommend players to focus on the patterns that belong to the best group. Although you can play the middle patterns, you should concentrate on the best ones. In Powerball, they are patterns #1, #2, #3, and #4.

See the huge difference between the two probability values below:

Powerball Odds Calculator

If you want to play U.S. Powerball to win, then pick your numbers based on a pattern with a high ratio of success. In Powerball, you should probably choose pattern #1 over pattern #56.

Let me remind you that you don’t win anything by matching the pattern. You only win the lottery when you match the exact numbers.

The concept of using combinatorial patterns should be helpful as a guide to get you closer to the winning combination.

But many Powerball players are not aware of the patterns they are playing.

The table below shows examples of combinations that belong to the worst group.

There are millions of these worst types of combinations. If you are playing blindly, chances are, you are playing one of the worst combinations in Powerball.

Powerball Odds Chart

How To Win The Powerball 5/69 Game

I always recommend Powerball players to play with a lotto strategy. Focus on the best patterns and avoid the worst ones.

To make your game much simpler, use a lottery calculator.

One of the best features of this calculator is the number generator, so you don’t have to go into the trouble of complex calculations.

But the concept of combinatorial pattern is just one of the many lottery tips you will learn here. Of course, the advanced strategy is discussed in the free guide section where I reveal the winning formula of combinatorics and probability theory.

Take time to enrich your knowledge of a mathematical lotto strategy. Please check out more articles in the blog section that will be helpful for you:

See my post about how a lottery wheel and number patterns work together.

Get to know the many unscientific lotto strategies that don’t work.

And learn how to use math to play lotto with the best shot possible.

Let me know your thoughts. Please join the conversation by adding your comments below. Thank you for reading. 🙂