Lotto: no, you’re still not going to win

There’s a story about Lotto on Stuff that starts off promisingly

Forty Kiwis took out Lotto First Division on Wednesday night – the most first division winners in a single draw in the game’s 30-year-history.

With that many winners sharing the $1 million prize, they’re only getting $25,000 each.

This is one of the big reasons that you can’t just divide the prize by number of possible combinations and get the expected value of a ticket.

Further down, though we get this

Despite these overwhelming odds there are times when it makes mathematical sense to buy a Lotto ticket.

That’s when Powerball jackpots get so large the value of the prize pool is greater than the amount spent on tickets.

Technically, this is true. The problem is you don’t know the amount spent on the tickets, because NZ Lotto doesn’t tell anyone. So as a strategy, it’s useless.  The link goes to another story headlined Why professors of statistics play Lotto too, when the prize is big enough.  That surprised me, so I read on to see who these professors of statistics were.

There are two professors mentioned in the story, Martin Hazelton of Massey and Peter Donelan of the university currently known as Vic.  You should definitely pay attention to their opinions: Martin, in particular, is probably the country’s top statistical theorist.

They don’t, however, say they “play Lotto too, when the prize is big enough”.  Professor Hazelton doesn’t say anything on that issue. Professor Donelan is quoted right at the end of the story

“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.”

And that’s probably true. Nothing wrong with Lotto as an entertainment — the monetary return on investment is low, but the same is true for beer, movies, rugby, or twilight walks on the beach — but it will very rarely “make mathematical sense.”