February 15, 2017

Another way not to improve your Lotto chances

I was on Radio LIVE Drive earlier this evening, talking about lotto (way to be stereotyped). The underlying story is on Stuff

A Nelson Lotto player who won more than $100,000 playing the same numbers 12 times on the same ticket says he often picks the same numbers multiple times.

“So that when my numbers do come up, I can win a greater share of the prize.”

The player won 12 second division prizes on a single ticket bought from from Nelson’s Whitcoulls on Saturday, winning $9481 on each line, totalling $113,772.  

There’s nothing wrong with this as an inexpensive entertainment strategy. As a strategy for getting better returns from Lotto it can’t possibly work, so the question is whether it doesn’t have any effect or whether it makes the expected return worse.

In this case, it’s fairly easy to see the expected return is worse. If you play 12 lines of Lotto every week, with 12 different sets of numbers, you’ll average one week with a Division 2 win every thousand years.  If you use the same set of numbers 12 times each week, you’ll average one week with 12 Division 2 wins every twelve thousand years. You might think this factor of 12 in the odds is cancelled out by the higher winnings, but that’s only partly  true.

This week there were 25 winning Division 2 tickets, which each got an equal share of the $237,000 Division 2 prize pool. The gentleman in question held 12 of those 25 winning tickets, and so got about half the pool.  If he’d bought that set of numbers and 11 others he would have held 1 of 14 winning tickets and won, not 1/12 as much, but about 1/7th as much.   By increasing the number of winning tickets, he reduced the prize for each of his tickets, and so his strategy has slightly lower expected return than picking 12 different sets of numbers.

On the other hand, these calculations are a bit beside the point. If you play Lotto for the expected return you’re doing it wrong.


Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »