Lotterycodex Mathematics Meets The Lottery

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


The majority of the Powerball players are doing it wrong. If you’re like the majority who rely on a random selection, hot numbers, cold numbers, birth dates, anniversaries, horoscope numbers, and other unscientific lotto strategies, you are wasting money on the lottery. I guarantee that.

The fact remains, many do not win the Powerball because they keep on playing the wrong number patterns.

The classic 1-2-3-4-5-6 pattern is so notorious that at least, nowadays, many try to avoid it but Mathematically speaking millions of similar number patterns will never appear in the Powerball.

The problem, many lotto players are not aware of these worst patterns.

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 number patterns, and you do not even know that.

Let’s take a look at the odds of the Powerball and see how we can use math to increase your chances of winning.

how to win the us powerball 5/69 according to mathematics

The Odds of Winning the US Powerball

The US Powerball game is a 5/69 lottery format. So the rule is to pick 5 numbers from 1 to 69. There are 11 million playable US Powerball numbers. So, in layman’s term, your chance is 1 in 11 million chances. If we add the extra Powerball from 1 to 26, the total number of ways to win in the U.S. Powerball is one in 292 million.

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

The reality is that the Powerball, like any other lottery system in the world, is a random game. And you cannot predict the next Powerball winning numbers.

Fortunately, you can improve the probability of winning if you know how to pick good numbers. That’s how Mathematics comes in handy. To illustrate, let me discuss simple odd-even patterns below.

The Odd-Even Patterns In The US Powerball

In the lottery, one of the key factors in improving your chances of winning is to count the odd and even numbers in 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. Like I always recommend, stay with the best patterns when you play the Powerball and avoid the rest at all cost. Let me show you the proof by comparing our theoretical analysis with the actual results of the Powerball.

Odd-Even Patterns According To The Actual Results Of The U.S. Powerball

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 146 draws in Powerball from October 7, 2015, to March 04, 2017. So, in the case of 3-odd-2-even pattern, we get 47.6997953377 by multiplying 0.326710926970499 by 146.

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 146 draws Actual frequency in 146 draws
3-odd-2-even 48 42
2-odd-3-even 46 43
4-odd-1-even 23 27
1-odd-4-even 21 30
5-odd-0-even 4 2
0-odd-5-even 4 2
146 146

Probability estimation compared to actual results of the U.S. Powerball

Looking at the table, the close value between expected frequency and actual frequency proves that Powerball behaves in a predictable pattern. Fortunately, we can use Mathematics to determine the trending pattern. Thanks to the Mathematical tool called Probability.

Using the Probability formula, we can predict how an event will likely occur in a given period. For example, 3-odd-2-even pattern is expected to appear 48x, then in the actual draw, it occurred 42 times.

The 4-odd-1-even pattern is projected to appear 23 times; it occurred 27 times. While the 5-odd-0-even pattern is expected to appear four times and it occurred twice in the actual draw.

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

That is the basic idea of why we want to use Probability Analysis in Lottery. If we use probability to know the outcome of the U.S. Powerball in 1000 draws, we will come up with the prediction table below:

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

But, the lottery is not about just odd-even patterns. Within the 69 balls of the Powerball lies complex patterns that can be the key to change the probability of winning a lot better in your favor.

The Six Winning Patterns In The US Powerball

In this article, I will show you the exact patterns that will improve your chances in the Powerball. Patterns here are based on The Geometry Of Chance proposed by Renato Gianella. See my post How To Use Math To Win The Lottery.

For simplicity sake, I have divided the patterns into three groups.

Group Patterns Number of patterns
Best patterns Patterns #1 to #6 6
Fair patterns Patterns #7 to #161 155
Bad patterns Patterns #162 to #462 301
462 total patterns

Click here for the complete list.

In Powerball, and in any lottery system, I always recommend players to focus on the patterns that belong to the best group. Although you can play those in the fair group, it’s best that you concentrate on the best ones.

For example, Pattern #1 has a probability of 0.0088979743 which means this pattern occurs approximately 9x in every 1000 draws or approximately once in every 111 draws. Patterns #2, #3, #4, #5, and #6 has similar probability.

On the other hand, pattern #162 has a probability of 0.0018018398 which means, this pattern is expected to occur approximately 2x in 1000 draws.

See the huge difference between the two probability values:

Pattern Probability Expected occurrence
#1, #2, #3, #4, #5, #6 0.0088979743 8x in 1000 draws
#167 0.0018018398 2x in 1000 draws

If you want to play US Powerball to win, then pick your numbers based on patterns with a high probability of occurring. In Powerball, these are the patterns #1, #2, #3, #4, #5 and #6.

The problem, many US Powerball players are not aware of the patterns they are playing. And there are patterns in US Powerball that will never make them a winner.

For example, the table below shows the worst patterns in The Powerball.

Pattern Probability Expected Occurrence
#458 0.0000224229 2x in every 100,000 draws
#459 0.0000224229 2x in every 100,000 draws
#460 0.0000224229 2x in every 100,000 draws
#461 0.0000224229 2x in every 100,000 draws
#462 0.0000112114 Once in every 100,000 draws

See the complete list

If you are playing blindly, there’s no guarantee you are not incidentally playing one of these worsts patterns. Likewise, there’s no guarantee you are not making this big mistakes when you play the quick pick machine.

How To Play The US Powerball To Win

Mathematically, I recommend using the following strategies for all U.S. Powerball players:

  1. Avoid all-even or all-odd combinations
  2. Focus on patterns #1, #2, #3, #4, #5, and #6

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Lotterycodex Mathematics Meets The Lottery

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Edvin Hiltner

I get a good grasp of mathematical theory through persistent learning. I get my inspirations from the works of Gerolamo Cardano and Renato Gianella in the fields of Combinatorics and Probability theory.

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