What is your chance of winning Powerball?

Author
Gillian Heller
Date
29 August 2018
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Professor of Statistics Gillian Heller says buying a cup of coffee is a safer return on investment than playing Powerball.

On August 16 there were two winners of the Powerball lottery, each receiving a cool $50 million. So the question on everyone's lips is what are the chances? The answer: extremely small.

Professor Gillian Heller says buying a cup of coffee is a safer return on investment than playing Powerball.

Infinitesimal: The odds of winning and sharing a huge jackpot with one other winner - assuming 50,000 tickets have been sold - are 1 in 361 billion.

In Powerball, players pick 7 numbers between 1 and 35 (with no repeats) from the main barrel, plus a Powerball number between 1 and 20. That means the number of different possible combinations is staggering.

We can work this out by calculating all possible combinations, for example 1, 2, 3, 4, 5, 6, 7 from the main barrel and 1 for the Powerball number, or  29, 30, 31, 32, 33, 34, 35 from the main barrel and 20 for the Powerball number, and all combinations in between.

This adds up to about 134 million different combinations.

From Sydney to Perth

Thinking of it another way, if each possible combination of seven numbers and the Powerball was a dollar coin, and we laid the coins out in a row, they would stretch from Sydney to Perth. The probability of picking the one lucky winning combination is so infinitesimally small it is negligible.

If we take into account the fact that there are other players in each draw (let’s assume 50,000 tickets have been sold), the odds of winning and sharing the prize with one other winner are 1 in 361 billion.

So how big would the jackpot have to be in order to make it worthwhile playing?

A safer bet

Statistical calculations tell us that the jackpot would have to be a whopping $161 million for you to break even, had you played thousands of times investing $1.20 per game each time.

So should we play? If the experience of anticipating a possible win is worth the investment to you, go right ahead and play. On the other hand, if you are looking for a less risky return on your investment, buy yourself a cup of coffee.

Counselling, information and support is available 24/7 for anyone affected by gambling here.

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