## How to Win the US Powerball 5/69 According to Math

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.

Table of Contents

### 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.

0-odd-5-even |
3-odd-2-even |

278,256 ways to win | 3,671,745 ways to win |

10,960,257 ways to fail | 7,566,768 ways to fail |

Only 1 opportunity to match the winning combination out of 40 attempts. | 33 opportunities to match the winning combination out of 100 attempts. |

VERY HIGH RATIO OF FAILURE | VERY HIGH RATIO OF SUCCESS |

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

Your 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.

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:

Patterns | Combinations | Probability |
---|---|---|

3-odd-2-even | 3671745 | 0.326710926970499 |

2-odd-3-even | 3560480 | 0.31681059585018 |

4-odd-1-even | 1780240 | 0.15840529792509 |

1-odd-4-even | 1623160 | 0.144428359872876 |

5-odd-0-even | 324632 | 0.0288856719745753 |

0-odd-5-even | 278256 | 0.0247591474067788 |

11,238,513 | 1 |

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

Best Patterns | Fair Patterns | Bad Patterns |
---|---|---|

3-odd-2-even | 4-odd-1-even | All-even-numbers |

2-odd-3-even | 1-odd-4-even | All-odd-numbers |

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.

Best Patterns | Fair Patterns | Bad Patterns |
---|---|---|

3-low-2-high | 4-low-1-high | All-high-numbers |

2-low-3-high | 1-low-4-high | All-low-numbers |

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).

Choosing a 3-low-2-high combination instead of a 5-low combination (e.g., 1-2-3-4-5) WILL NOT increase your chances of winning because all combinations are equally likely. You should avoid 1-2-3-4-5 because a 5-low-0-high pattern has fewer ways to win and more ways to fail. I recommend choosing 3-low-2-high because it offers the best ratio of success to failure.

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:

Patterns | Expected frequency in 449 draws | Actual frequency in 449 draws |
---|---|---|

3-odd-2-even | 147 | 148 |

2-odd-3-even | 142 | 138 |

4-odd-1-even | 71 | 75 |

1-odd-4-even | 65 | 61 |

5-odd-0-even | 13 | 14 |

0-odd-5-even | 11 | 13 |

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.

Choosing a 3-odd-2-even combination instead of 5-even (e.g., 2-4-6-8-10) 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 is that the 0-odd-5-even pattern has fewer ways to win and have more ways to fail. You should choose 3-odd-2-even because it gives you the best ratio of success to failure.

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.

Patterns | Probability | Expected Frequency |
---|---|---|

3-odd-2-even | 0.326710926970499 | 327 |

2-odd-3-even | 0.31681059585018 | 317 |

4-odd-1-even | 0.15840529792509 | 158 |

1-odd-4-even | 0.144428359872876 | 144 |

5-odd-0-even | 0.0288856719745753 | 29 |

0-odd-5-even | 0.0247591474067788 | 25 |

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

Patterns | Probability | Expected Frequency |
---|---|---|

3-low-2-high | 0.326710926970499 | 327 |

2-low-3-high | 0.31681059585018 | 317 |

4-low-1-high | 0.15840529792509 | 158 |

1-low-4-high | 0.144428359872876 | 144 |

5-low-0-high | 0.0288856719745753 | 29 |

0-low-5-high | 0.0247591474067788 | 25 |

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.

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.

Combination | According to low-high analysis | According to odd-even analysis |

1-2-3-4-5 | WORST | BEST |

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.

Best | Middle | Worst |
---|---|---|

Patterns #1 to #4 | Patterns #5 to #28 | Patterns #29 to #56 |

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:

Pattern | Probability | Expected occurrence |
---|---|---|

Pattern #1 | 0.0668850941 | 7x in 100 draws |

Pattern #56 | 0.0005506067 | 5x in 10,000 draws |

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.

### 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:

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. 🙂

How to Win the US Powerball 5/69 According to Math 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

## Statistics for Algorithm predictions for Australia Powerball.

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### Algorithm predictions statistics for Australia Powerball Lottery

Thu 28 Jan 2021

Next Powerball Jackpot

Get Algorithm predictions to win lottery

Summary | |
---|---|

Total predictions made | 652 predictions |

Successfull predictions | 72 predictions |

Possible winnings | $3,907 |

Lottery | Draw Date | Winning |
---|---|---|

Powerball |
Thu 07 Jan 2021 | (5 of 7) $25.0 |

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