$38m Powerball: Why professors of statistics play Lotto too, when the prize is big enough

Tuesday, 15 October 2019

Lucky number 7. Actually, it's only been drawn as a Powerball number 81 times. Only ten and nine have been drawn fewer times as Powerballs.

This story was first published in November 2016. It's being republished today as the jackpot is $38m this week.

Powerball has jackpotted to $38 million, which makes it a mathematically good day to play Lotto.

Great set of numbers. Nobody has a birthday on the 33rd, 36th, or 37th.

Big jackpots drive sales, which should mean this week's prize-pool is worth more than the money collected from ticket sales.

That's a phenomenon identified by accountants KPMG in the UK when, in accountancy speak, punters' tickets have a positive 'expected value'.

Lotteries are rife with 'magical thinking'. Here Lotto hopefuls flock to New Zealand's 'luckiest' area.

* Lotto: those who won, and watched it all disappear

* Lotto hopefuls flock to New Zealand's luckiest area

* Lotto and Powerball most frequent numbers drawn

* How many houses you can buy around NZ if you strike it big**

Positive 'expected value' days are likely to happen more often in New Zealand since Powerball went twice weekly, a shift designed to generate more massive jackpots.

Professors of statistics say there's little people can do to meaningfully increase their individual chances of winning Powerball, though people can be particularly poor at recognising the fact.

'We are very poor at dealing with small probability events,' professor of statistics Martin Hazelton from Massey University.

We may overestimate the likelihood of winning a low-probability event like a lottery, or fool ourselves with magical thinking, like believing in fate, lucky numbers, or lucky areas where many winning tickets have been bought.

'Can you increase your chances of winning? Yes, and no,' Hazelton says.

No, because the chances of your seven numbers coming up remains at one in 38.8 million whichever numbers you pick.

'There is no such thing as a lucky selection of numbers,' Hazelton says. 'There's nothing you can do to increase the probability that any particular set of numbers will win.'

You can buy more tickets, which increases your chances from very slim to just slightly less very slim, or form a Lotto syndicate, spending less to get more chances of winning, though if you won, you'd have to share the jackpot.

'If you want to maximise your expected outcome, then you would want to pick numbers that are less likely to be picked by other people so you are less likely to have to share the jackpot,' Peter Donelan, head of the School of Mathematics and Statistics at Victoria University said.

That could include picking some higher numbers as many people use significant dates like birthdays, or picking number others think unlucky.

Then there are the positive expected value draws.

They do not increase the chance of your numbers popping out, but it's mathematically the best time for occasional players to buy a ticket.

Even a few statistics professors may have a flutter.

'In my household, if it was up to me, I wouldn't bother to buy one,' Donelan said.

But he suspects some stats professors do: 'I expect some do regardless of what they know.'

HISTORY OF THE BIG ONES

• January 2019: A young Taranaki woman continues her New Year celebrations by winning $22.3m in Powerball.

• August 2018: A man in his 20s from Central Otago wins $22.3m and claims the largest Powerball prize to ever be won in the South Island.

• November 2016: Powerball jackpots to $38m.

• July 2016: Powerball jackpots to $40m

• April 2016: $22.2m is won by an Ashburton player with Powerball First Division.

• September 2013: $33m Powerball prize won by a player in West Auckland.

• September 2012: Big Wednesday prize of $27m won by young Tauranga man who bought ticket when getting his hair cut.

• March 2012: A $26m Powerball First Division prize won by buyer from the small town of Te Kauwhata.

• April 2011: Powerball reached its second-ever $30m 'Must Be Won' jackpot. It went on to climb to $35m.

• October 2010: $28.7m Powerball prize won by a player in Papakura in Auckland.

• October 2009: A $22.4m Powerball prize won by buyer from Manukau in Auckland.

• June 2009: Big Wednesday reached $36m. It was won by a family syndicate.

• October 2008: Lotto Powerball reached $30m. Five winners split the prize.

• September 2005: Kathy Laugesen became the first person win $1m on Lotto's Winning Wheel.