The Lottery Fallacy

Time for a post on scepticism, I think. Specifically I want to take a swipe at the Lottery Fallacy because it is one that pretty much everyone falls foul of at some point. Humans, as a species, are not good at statistics. We do not have an intuitive grasp of what a set of numbers with which we are presented really means. For example, we don’t always grasp the difference between relative and absolute numbers; we’re awful at judging risk; we frequently mistake correlation for causation and we generally fail to grasp that genuinely random data contains clumps of apparently ordered data.

The Lottery Fallacy is a further example where we misconstrue the numbers and take home a false impression of what’s really happening. The classic and eponymous example is the person who buys a winning lottery ticket. The odds are, of course, overwhelmingly minuscule that any one specific individual will win. In the UK national lotto, for example, there are 49 balls and you have to pick 6 winning ones for the jackpot. The odds of winning, then, are (49÷6) x (48÷5) x (47÷4) x (46÷3) x (45÷2) x (44÷1) = 13,983,816 to 1. So if you buy yourself one lottery ticket you have a little less than a 14m to one shot of winning, which is why most people don’t win. Ever.

Every couple of weeks or so, though, someone does win, it’s really quite likely. That person, knowing that the chance of them winning was very small, could easily ascribe some kind of cosmic meaning to their victory, though. It was meant to be, they might say, or they were chosen. Well, they weren’t chosen. What needs to happen is a change of perspective. We need to think: what is the chance that someone will win the lottery on a given drawer? I don’t know the answer but I would imagine it’s something like one in three, so in no way an unlikely event.

Let’s look at it another way. Take a standard deck of cards and shuffle them. Imagine all of the different possible orders to the cards. It’s a staggering number: 52 x 51 x 50 x 49…. and so on down to one. The answer is an obscenely large number. It is


That’s 3.95 sextillion different possible combinations. To put that into context, if you were to look at 9,000 combinations per second for the entire 13.8 billion years that the universe has existed you still wouldn’t have covered them all yet. However, if you were to look at your shuffled deck you wouldn’t be overwhelmed by the enormously unlikely combination that happened to be in front of you. If it crossed your mind at all then maybe you’d remark that you could see some small clumps of order but that, overall, nothing extraordinary had taken place. And so it is when you win the lottery. Yes, it’s unlikely that that ticket you bought would be the winner, but it wasn’t unlikely that someone would win.

Another example where the fallacy applies is to the creationist argument that our existence is so unlikely that it must have been guided by a god. It is, indeed, mind bogglingly unlikely that our particular consciousness evolved in this particular organism on this particular planet. The odds are so tiny as to make it basically impossible. But what are the odds that some consciousness evolved in some organism on some planet anywhere in the universe? Much, much less unlikely I would suggest.

So there you have it. If you happen to find yourself on the beneficial end of some great stroke of luck, and I hope you do, bear in mind that it doesn’t make you special, the universe is still indifferent as to your existence. Someone probably had to win and it may as well have been you.

Image courtesy of Enochlau


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