So a co-worker was talking about someone’s stupid plan to always play the previous winning lotto numbers. I chimed in that I was pretty sure that didn’t actually hurt their odds. They thought I was crazy, pointing out that probably no lottery ever rolled the same five-six winning numbers twice in a row.
I seem to remember that I am correct, any sequence of numbers has the same odds. But I was totally unable to articulate how that could be. Can someone help me out? It does really seem like the person using this method would be at a serious disadvantage.
Edit: I get it, and I’m not gonna think about balls anymore today.
In: Mathematics
It’s called [“The Gambler’s Fallacy”](https://en.wikipedia.org/wiki/Gambler%27s_fallacy).
The balls don’t have memories. If the draw is fair, all combinations are equally likely, every draw. One of those combinations just happens to be last draw’s numbers. And it’s exactly as likely (or unlikely) to win as any other combination.
BUT. Some combinations are likely to have bigger payouts than others, if you actually win. You want to try to avoid combinations that other people are likely to pick (meaning you’d have to share the prize). So last draw’s numbers aren’t a good idea (because, human psychology). As has been hinted at – there are almost certainly going to be multiple people who, following whatever logic, play precisely those numbers because of what they are. People follow patterns, and following the same pattern as lots of other people in a lottery is usually a quick route to a lousy payout in the massviely unlikely event that you win big*. Your actual payout from last draw’s numbers (and obvious patterns) is likely to be significantly poorer, if you actually win, than with other, more random combinations.
**RL example from memory. The second ever UK national lottery draw happened to come up with 6 low numbers – the sort of ones that could easily be part of a date. And it turns out that lots of people use significant personal dates to choose their numbers. As I recall it, there were over 100 people sharing the top prize. Which meant that, instead of winning millions of pounds (call it dollars if you’re not British, the exchange rates were close enough), they each won a few tens of thousands. Still not to be sneezed at – but a far, far cry from the hugely life-altering event I’m sure they anticipated when they saw their numbers being drawn.*
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