You'd be dead lucky to win OZ Lotto

Dr David Warton
Friday, 26 June, 2009
David Warton

Many Australians are getting excited about the record \$90 million dollar jackpot in the next OZ Lotto draw on Tuesday 30 June, but you should understand that your chances of winning it are almost incomprehensibly small.

In fact, if you buy a ticket the day before the draw, you have a greater chance of dying before the lottery is drawn than you do of winning the big one!

The chance of winning from a game of OZ Lotto is about one in 45 million.

To get a sense of how small that it, consider what would happen if I dumped two reams (1,000 pages) of A4 paper onto every seat at the Sydney Cricket Ground and asked you to take a guess at which is the one "winning" page out of the four truckloads of paper that I have scattered all around the SCG.

What you have there is about a one in 45 million chance of winning - and an awful mess.  If I forgot where the winning page was and had to check each page individually to find it, it would probably take me over three years (closer to two years if I worked weekends).

Many people are taking the punt that they won't die before the next draw and are buying more tickets in the hope of swinging the odds more in their favour.

Yes, this does increase your chance of winning the jackpot, but it also increases the amount of money you can expect to lose.  Last year a class of second-year UNSW students worked out the expected rate of return when you play different NSW Lotteries games. That is, they worked out the average amount of money you would expect to win or lose if you played OZ Lotto many times.

They calculated that for every dollar you spend, you can expect to recover somewhere between 15 and 60 cents, depending on the game and the draw.  The rate of return is essentially the same irrespective of how many times you enter and irrespective of whether you buy a Standard or System ticket, but one thing you can be sure of is that the more you spend, the more you can expect to lose.

One interesting sure-fire strategy, if you have a bit of spare change, would be to spend \$50 million buying tickets to cover all possible combinations of numbers.

This would take the fun out of it, but it would guarantee that you'd win the jackpot.  The problem is that you wouldn't be guaranteed of winning \$90 million because you would have to share the spoils with anyone else who won.  If you shared the jackpot with two or more others you would come out millions of dollars behind.

So, in short, playing lotto doesn't make mathematical sense because you can expect to lose in the long run, and that's probably true even now with a \$90 million dollar jackpot.  That's never stopped my mother though.

Dr David Warton is a Senior Lecturer in the UNSW School of Mathematics and Statistics and the UNSW Evolution & Ecology Research Centre.
http://web.maths.unsw.edu.au/~dwarton/