Gambling is both really dumb and also… kinda smart

Let me start this with a really remarkable statistic, because I’m a fan of a killer stat:

Think about powerball. You need to pick seven numbers in order, plus the eighth ‘powerball’, and they’re all selected at random. It’s entirely a game of chance and the chances of you winning are almost zero.

But how close to zero are they?

Horses for courses

Let’s say you had to choose the winner of next year’s Melbourne Cup. And you’re blindfolded.

And you don’t know the names of any of the horses that are running.

And you don’t have a shortlist.

You don’t have a longlist.

Let’s say you a list of all of the horses in the known universe, and that’s all you have to go from.

You are more likely to choose the winning horse, in that scenario, than you are to win powerball.

And that’s if you have bought two tickets to powerball, too. You are still more likely to win with your one guess of one horse from all living horses today — not just racehorses, but every single horse — than with two guesses of the numbers that win you the powerball jackpot.

So it’s pretty dumb.

But it’s also kinda smart, and to explain that, I’m going to have to use some numbers.

I heard you like numbers

In Australia, powerball players choose 7 main numbers from 1-35 and 1 Powerball number from 1-20.

The odds of winning the jackpot in Australian Powerball are approximately 1 in 134,490,400.

Let’s say you buy a ticket every week for your entire life, starting at 18 and you live to 80 (you lucky thing!). So that’s 62 years, of 52 weeks: 3,224 plays.

Let’s say you buy the cheapest multi-game ticket, which last time I checked is $8.10, and buys you six games (which is six attempts):

1. Cost per week: $8.10 for 6 games
2. Weeks played in a lifetime: 52 weeks * 62 years = 3,224 weeks
3. Lifetime cost: $8.10 * 3,224 = $26,114.40 AUD

Odds calculation:

1. Games played in a lifetime = 62 years * 52 weeks * 6 games = 19,344 plays
2. Probability of not winning on a single play = 1 – (1/134,490,400) ≈ 0.99999999256
3. Probability of not winning in 19,344 plays = (0.99999999256)^19344 ≈ 0.99985619
4. Probability of winning at least once = 1 – 0.99985619 ≈ 0.00014381
5. This equals about 0.014381%, or about 1 in 6,954

So, with this playing strategy:

1. You would spend $26,114.40 AUD over 62 years (not accounting for inflation).
2. Your odds of winning the jackpot at least once in your lifetime would be about 1 in 6,954.

Losing, in context

A 1 in 6,954 chance of winning the jackpot might not seem very good. But think about spending $26,000 on starting a business, with a one in 7,000 chance of selling that business for $20 million.

The average jackpot value for powerball this year, so far, is about $22 million. (Which you can check yourself, if you don’t believe me).

Nicely, this means you’ve got a roughly 1 in 7,000 chance of making a 1,000 to 1 return on investment. That’s not great, for sure. But over your life, you’re likely to earn a lot more than $22,000. The average person on the median income in 2023 dollars will earn about $3.4 million over their life, according to the boffins at the Centre for Future Work. (This assumes 60% of worked hours are performed by males, who earn more — patriarchy, ugh — and while I think it gels broadly with the reality as observed, it’s not something I’ve actually researched in a while).

And when you compare the cost of entry to the money you’ll make, and what else you might spend that money on, this is not going to be the dumbest thing you’re likely to spend $22,000 on.

And it’s a pathway to riches that anybody has a shot at. You don’t have to inherit money from your wealthy parents or be a mega-successful athlete (or the Prime Minister).

So yeah, gambling is dumb, but it’s also understandable. And honestly, not that dumb.