Lotto Powerball $34m jackpot: Chance of winning like 'tossing a coin 26 times and all coming up heads' - mathematician

Mathematician David Hand puts the odds of winning Lotto Powerball in perspective.
Mathematician David Hand puts the odds of winning Lotto Powerball in perspective. Photo credit: iStock.

Given the chance of winning Lotto Powerball is one in 38.3 million, players have the odds stacked against them.

For an idea of how lucky they would be to win Wednesday's $34 million Powerball draw, Professor David J. Hand, mathematician at Imperial College in London, said players could picture each New Zealander with eight buttons.

"Imagine that all the millions of buttons are red, except just one, which is blue. If you randomly pick a button, then your chance of picking the blue one is the same as your chance of winning the jackpot," he explained.

Another way to compare the odds is by the simple act of tossing a coin.

"Winning the New Zealand lottery jackpot has the same chance as tossing a fair coin 26 times and finding they all came up heads," Hand added.

As each draw is random, there isn't a way to beat the system. At $1.50 per line and 38,383,800 different possible lines, in theory, players could spend $57,575,700 and buy all the possible outcomes of the draw, winning (or sharing) the jackpot. But this is the reason rollovers are capped.

"If the jackpot reaches $50 million, a 'must be won' draw is held. That means that your $57,575,700 would only guarantee winning up to $50 guaranteed profit after all."

Players could increase their chances by buying more tickets - although this isn't recommended.

"If a single line (ticket) has a one in 38 million chance of winning the jackpot, then your chance of winning if you buy 10 (different) tickets is one in 3.8 million. Buy 1000 different tickets and it's 1 in 38,000, [or] buy a million different tickets and it's one in 38," Hand explained.

Buying Lucky Dips rather than using favourite numbers, such as birthdays, has a better chance of paying off. That's because there's a good chance regular numbers are chosen by other players.

"In the very unlikely event of those numbers coming up, you would have to share your winnings." 

A Lotto spokesperson said that in the last financial year (to June 2020), 31 percent of Lotto's total sales were online at MyLotto, an increase from last year.

Wednesday's Powerball draw is set at $34 million. If a single person wins, it will be the second-largest Powerball prize since Lotto began. Since it began, Lotto had created 942 millionaires - 27 this year, across Lotto, Powerball and Strike. Seven of those had won with Powerball.

Ahead of the draw, Lotto urged players to avoid the queues and get in early to buy their ticket - making sure it's before the 7:30pm close-off.