How to Win Australian Powerball According to Math?

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Last updated on May 19, 2024

Are you wondering how to win the Australian Powerball game? Despite the game’s randomness, let’s examine different mathematical strategies to improve your chances.

Ready to learn? Let’s begin.

Voices from the Lottery Community

Hi Edvin,

I have just recently purchased the 7/35 calculator for Australian powerball and I am working through your strategies. I wanted to say thank you so much to you and your team for your efforts.

Found your strategy fascinating and I wasn't phased about parting with the price of entry for the calculator whether it leads to success or not. Afterall, it is entertainment as you say.

I have a question for you, if you don't mind. The Australian Powerball offers a ticket that is called "Pick 6" or "Pick 5" where you are guaranteed either 1 or 2 numbers. I was curious to see what you would advise with "Pick" games vs as many numbers as you can buy.

Again, thank you so much for your time

Enjoy your day,
LG

Australian Powerball Odds Explained

The Australian Powerball is an exciting lottery featuring a unique format that attracts players with the promise of big jackpots. You select seven numbers out of 35 and one Powerball from 1 to 20. You must match all seven main numbers and the Powerball to hit the jackpot. However, even without the jackpot, many other prizes are available based on the number of matching numbers, including the Powerball.

Here are the different ways to win the game. At the time of writing, there are nine prize divisions.1

DivisionHow to WinProbability
Division 17 numbers + the Powerball1 in 134,490,400
Division 27 numbers1 in 7,078,443
Division 36 numbers + the Powerball1 in 686,176
Division 46 numbers1 in 36,115
Division 55 numbers + the Powerball1 in 16,943
Division 64 numbers + the Powerball1 in 1,173
Division 75 numbers1 in 892
Division 83 numbers + the Powerball1 in 188
Division 92 numbers + the Powerball1 in 66
According to the provided table, you must match seven numbers plus the Powerball to win the jackpot. The probability of winning the jackpot is 1 in 134,490,400. Buying a second ticket improves your odds to 1 in 67,245,200. If you purchase 100 tickets weekly, winning the first division could take more than 25,864 years.

Experts note that you’re more likely to be attacked by a shark than win the top prize. However, remember: no swimming in the ocean, no risk of shark attacks. Similarly, you can’t win if you don’t play.

Mathematically speaking, purchasing additional tickets can increase your odds of winning. The Australian Powerball provides flexible gameplay options, including System Entry, PowerHit, and Pick Entry, allowing you to buy more tickets and play strategically.

Let’s talk about each of these gameplay options in detail below.

The PowerHit Entry

Playing the game with the PowerHit option guarantees you match the extra Powerball, technically providing 20 lines to cover all the numbers in the second barrel.

For example, if your primary numbers are 1-2-3-4-5-6-7, you would play this same combination but with different Powerball numbers.

  • 1-2-3-4-5-6-7 + Powerball 1,
  • 1-2-3-4-5-6-7 + Powerball 2,
  • 1-2-3-4-5-6-7 + Powerball 3,
  • …., continue up to 1-2-3-4-5-6-7 + Powerball 20.

The System Entry

This entry allows you to cover more possible combinations from your set of numbers. This is a classic example of a combinatorial application commonly known as the lottery wheel.

A lottery wheel strategy effectively traps the winning numbers.

In Australian Powerball, you can choose between 8 to 20 main numbers for a system entry, and you can also select one Powerball number.

When you play System 11, you’re entering 330 possible combinations. For instance, if your selected set includes the numbers {1,2,3,4,5,6,7,8,9,10,11}, your plays would include combinations starting from 1-2-3-4-5-6-7, moving through variations like 1-2-3-4-5-6-8, and continuing up to 6-7-8-9-10-11.

Combining a System entry with PowerHit maximizes your chances of hitting more matches. However, this strategy can become costly, as each line covers all 20 Powerball numbers, resulting in 6,600 lines for System 11 and 128,700 for System 15.

The Pick Entry

This entry type enables you to play with a guarantee of one or two correct numbers based on the pick game you choose. If you opt for Pick 6, you’re assured of one correct number and play 29 lines to cover the numbers not selected. For instance, choosing 1,2,3,4,5,6 means you would play combinations like:

  • 1-2-3-4-5-6-7-Powerball,
  • 1-2-3-4-5-6-8-Powerball,
  • 1-2-3-4-5-6-9-Powerball,
  • …, up to
  • 1-2-3-4-5-6-35-Powerball.

Similarly, with Pick 5, you’re guaranteed two correct numbers. This option requires you to play 435 lines, combining your five chosen numbers with every possible pair from the remaining numbers to complete a set of seven.

Additionally, you can combine pick games with PowerHit. However, this strategy is quite expensive. For instance, combining Pick 5 with PowerHit involves purchasing 8,700 lines.

Which Play Option is the Best?

Remember, buying more tickets is the only strategy that improves your chances of winning the lottery. More tickets increase the number of opportunities for favorable outcomes.

Thus, analyzing your success-to-failure ratio can help you make informed decisions when playing Australian Powerball.

Calculating odds reveals the distinction between success-to-failure ratio and probability. It’s important to note that ‘odds’ and ‘probability’ are distinct concepts with different calculation methods.

When calculating odds, we compare the number of ways to achieve favorable outcomes with the number of ways to achieve unfavorable outcomes.

Take the PowerHit option as an example: it gives you 20 ways to win the jackpot. Given that the Australian Powerball has 134,490,400 possible combinations, subtracting the 20 winning lines results in 134,490,380 ways not to win the jackpot.

134,490,400 − 20 = 134,490,380 unfavorable outcomes.

Thus, the success-to-failure ratio is 1:6,724,519.

S/F Ratio(Power Hits) = 20/134,490,380 = 1/6,724,519

This ratio implies that for every 6,724,520 attempts, one favorable outcome is compared to 6,724,519 unfavorable outcomes.

Gameplay Options and Their Corresponding S/F Ratio

The table below provides a complete rundown of the S/F ratio for each gameplay option.

Entry OptionNumber of Favorable Shot(s)S/F Ratio
Standard Play1 line1:134,490,399
Power Hits20 lines1:6,724,519
System 88 lines1:16,811,299
System 936 lines1:3,735,843
System 10120 lines1:1,120,752
System 11330 lines1:407,546
System 12792 lines1:169,810
System 131,716 lines1:78,373
System 143,432 lines1:39,186
System 156,435 lines1:20,899
System 1611,440 lines1:11,755
System 1719,448 lines1:6,914
System 1831,824 lines1:4,225
System 1950,388 lines1:2,668
System 2077,520 lines1:1,734
System 8 with Power Hits160 lines1:840,564
System 9 with Power Hits720 lines1:186,791
System 10 with Power Hits2,400 lines1:56,037
System 11 with Power Hits6,600 lines1:20,376
System 12 with Power Hits15,840 lines1:8,490
System 13 with Power Hits34,320 lines1:3,918
System 14 with Power Hits68,640 lines1:1,958
System 15 with Power Hits128,700 lines1:1,044
Pick 629 lines1:4,637,599
Pick 5435 lines1:309,172
Pick 6 with Power Hits580 lines1:231,879
Pick 5 with Power Hits8700 lines1:15,458
Notice how the S/F ratio improves as you play more lines.

The Role of a Syndicate

The probability of winning the jackpot is 1 in 134,490,400; however, utilizing various play options can offer better odds and the best chance of winning. This strategy, though, typically demands a substantial entertainment budget.

Keep in mind that the lottery has a negative expected value. While winning smaller prizes may be possible, you will incur losses on average. Please be skeptical of claims that you can frequently win small prizes while waiting for the big jackpot.

If you’re playing alone, I recommend sticking to standard play. To take advantage of strategic gameplay options, consider playing as part of a syndicate to offset the costs of more complex strategies.

Playing the Australian Powerball Randomly

While various play options guarantee certain outcomes, they are primarily accessible to syndicates, and few solo players can utilize them.

How, then, do we calculate the probability for solo players who randomly play the game and purchase one or more tickets using standard play?

Despite the long odds, playing the Australian Powerball gives you a relatively better chance of winning prizes other than the jackpot. With a 1 in 44.63 chance of winning something, the probability of a single ticket not winning any prize is 0.9776. The probability of losing n times in a row is this number raised to the power of n. For instance, purchasing two tickets results in a 95.57% chance of not winning anything.

P(losing) = 0.97762 tickets = 0.9556891430217

Purchasing approximately 31 tickets can balance the odds of winning any prize to a 50/50 chance, while buying 406 tickets increases the certainty of winning to 99.99%. Since the probability of winning P(winning) is the complement of the probability of losing P(losing), we calculate the probability of winning any prize using the following formula:

P(winning any prize) = 1 – 0.9776406 tickets = 0.9998987385

The table below illustrates how purchasing 31 tickets results in a 50/50 chance of winning any prize.

This image shows a table where purchasing 31 tickets will give you 50/50 chance of winning any prize in the Australian Powerball game.
This is a graphic chart for Australian Powerball showing two lines. The blue line represents the percentage for winning any prize. The red line represents the percentage for winning none. The two line intersect at 31 tickets, the point at which you get a 50/50 chance of winning any prize.

The graph demonstrates that purchasing more tickets increases the likelihood of winning any prize.

However, considering the probability, having a 99.99% certainty is more favorable for the lowest-tier prize. Nevertheless, winning smaller prizes remains challenging, and winning the jackpot is even more difficult.

Analyzing the Australian Powerball Game Using Lotterycodex

So, how do you win the Australian Powerball? Players must make informed choices, and combinatorics2 and probability theory3 can help.

While all combinations have an equal probability, they vary in composition, resulting in different success-to-failure ratios.

Understanding this success-to-failure ratio and the composition of your selection can help you make informed decisions when choosing numbers. Learn more from this guide: The Winning Lottery Formula Using Math.

To illustrate, Lotterycodex distributes the number field for the Australian Powerball game into four different sets as follows:

The sets of numbers used by Lotterycodex to analyze success-to-failure ratios of different combinatorial groups in Australian Powerball. The sets are LOW-ODD, LOW-EVEN, HIGH-ODD, AND HIGH-EVEN.

These selection sets ensure the probability of the game is distributed fairly across the number field.

Calculating the S/F Ratio

Australian Powerball has 6,724,520 possible combinations of 7 numbers from 35. We don’t include the extra 20 balls in the probability study because it is not mathematically practical.

These 6.7 million combinations are divided into 120 groups based on their composition.

Let’s consider a composition of seven numbers: three yellow, two cyan, one gray, and one green. There are 217,728 ways to combine numbers using this composition, so this group is estimated to occur approximately three times in 100 draws.

{3yellow, 2cyan, 1gray, 1green} = 217,728 possible combinations

S/F ratio = 217,728/(6,724,520 – 217,728)

= 217,728/6,506,792

= 1/29.88

= 1/30

In short, this composition occurs approximately once every 31 draws. Put another way, one is a favorable shot, and 30 are unfavorable shots for 31 attempts.

Let’s consider another composition of seven numbers: one yellow, five gray, and one green number. This composition allows for 9,072 ways to combine numbers; therefore, this group is estimated to occur approximately three times in 2,000 draws.

{1yellow, 5gray, 1green} = 9,072 possible combinations

S/F ratio = 9,072/(6,724,520 – 9,072)

= 9072/6,715,448

= 1/740.24

= 1/740

The ratio indicates that this composition occurs approximately once every 741 draws. One is a favorable shot, and 740 are unfavorable for 741 attempts.

Combinatorial Groups are not Created Equally.

The two compositions we used as examples above are described in Lotterycodex as Template #5 and Template #81, respectively. Notice how you get more favorable shots with the former.

As a lotto player, you wouldn’t want just one favorable shot after playing 741 attempts. Therefore, it’s advisable to avoid template #81 and opt for template #5.

Yet, in Australian Powerball, Template #5 is not one of the dominant templates. Only one template dominates—it’s Template #1.

Australian Powerball Follows the Dictate of Probability Theory.

To win a lottery game, you must predict the general outcome based on the law of large numbers.

The image below illustrates how a 7/35 lottery game will behave over time:

This images shows how a 7/35 lottery game such as the Australian Powerball game behave over time based on the law of Large Numbers. Template #1 dominates the lottery draws having an expected frequency of 111 times in 2000 draws. Template #120 being the least are estimated not to occur in 5000 draws.

Calculated by Lotterycodex Calculator

As shown in the table above, Template #1 consistently dominates the game over time. What’s particularly intriguing is that, according to the law of large numbers, Template #1 will continue to assert its dominance in the lottery game as more draws occur.4

As a lotto player, you should aim for the best shot possible. You may not be able to predict the exact combination that will win. However, knowing how the lottery behaves over time will give you the power to make informed decisions when selecting your numbers.

These Lotterycodex templates will help you make informed choices.

Which Strategy is the Best?

Mathematically speaking, purchasing more tickets increases your chances of winning. However, the mathematical information presented should ultimately influence your choice based on what works for you.

Apart from mathematics, other factors can influence your decisions.

  • Budget
  • Odds vs. Return
  • Risk Tolerance

Remember, the expected value of the lottery is always negative. You cannot profit from it. The lottery is just entertainment. Always spend the money you can afford to lose.

I highly recommend joining a lottery syndicate when playing. Play responsibly.

Additional Resources

  1. Everything You Need To Know About Powerball Prizes    []
  2. Combinatorics    []
  3. Probability Theory    []
  4. The Law of Large Numbers    []

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