The continued existence of lotteries is a demonstration of how little intuition humans have for probability. On some level, we all know that the chances of actually winning a life-changing payout are basically zero, but a whole lot of people buy tickets every week—because you never know, you might just get lucky, right? Right??
Nope.
If you want a really good demonstration of why lottery ticket purchases are essentially a voluntary tax, look no further than a site called “Lottery Every Second”, which, as its name suggests, simulates playing the lottery every second. Or, more accurately, it simulates playing two lotteries every second: Powerball, one of the most popular such games in the USA, and EuroJackpot, a similar game that operates throughout Europe.
The games work in broadly similar ways. Powerball requires you to select five numbers between 1 and 69 (nice!) and a sixth between 1 and 26. To win a jackpot, all six must match those chosen randomly in a given draw. EuroJackpot uses five numbers between 1 and 50 and two further numbers between 1 and 12; again, to win a jackpot, all the numbers you choose must match those drawn.
It’s pretty easy to work out the odds yourself: in the case of Powerball, you have a one in 69 chance of selecting each of the first five numbers correctly, and a one in 26 chance with the sixth. To get the chance of getting all six correct, you just multiply the individual probabilities together, which gives you a 1 in 292,201,338 chance of hitting the jackpot. As ever, the Europeans get a better deal, with a 1 in 139,838,160 chance.
That doesn’t sound too bad, does it? Well, this is the thing: as Lottery Every Second’s accompanying text points out, “These numbers are so large they become meaningless to our brains.” The site aims to address this problem by demonstrating just what those odds mean in reality. It explains that on average, you’d have to sit and watch it play every second for just over two years to see a EuroJackpot jackpot, and four and a half years to see a Powerball jackpot. And, as the site emphasises, that’s with one draw every second; if you’re buying a weekly ticket, then “you’d need to play Powerball for roughly 5.6 million years to have a 50% chance of winning once.”
The other thing that the site demonstrates is how much money these games rake in for their operators. The simulation keeps a running total of wins and losses, and despite the fact that, on face value, the EuroJackpot looks like a much better deal than Powerball, in both cases, the amount of money paid out is about an eighth of the amount received. In other words, for every $100 either operator pays out, they pocket about $800. That’s quite literally money for nothing.
Hopefully, seeing the absurd numbers that characterize lottery odds set out like this will motivate a few people to stop buying weekly tickets. But humans aren’t purely rational beings. We’re motivated by things like hope, impulse, and despair—and, unfortunately, we’re also really bad at evaluating probabilities. So if you’re going to keep playing Powerball regardless, we’re not going to judge you—but if you do strike it lucky, just be careful on the way home from picking up your winnings. You may well get struck by lightning or hit by a falling piano.
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