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 technically not, it’s just that we have a poor sense of what IS likely.
It’s the same random choice between the same huge set of random numbers. *Generally*, repeating the same number this way is unlikely, but it is not made cosmically less likely EACH time.
For example, flipping a single coin has an exactly 50% chance of landing on heads. Every time I flip it, it still has a 50% chance of landing on heads. Nothing about the coin itself changes between flipping, so it’s no less likely *each separate time* to land on heads.
But it’s only 50% when YOU the human observer are predicting it as single time. When YOU attempt to predict MANY flips, you are adding to the likelihood that YOU will guess it wrong. Because it truly is random EACH time.
There is nothing “special” about a number that wins. But we assign significance to things all the time. It’s just how our brains work.
The odds of an event happening are 1 in (the number of different possible outcomes). To make it simple, use coins.
The odds of you flipping 3 heads in a row are 1 in 8, because the possible outcomes are:
H h h
H h t
H t h
H t t
T h h
T h t
T t h
T t t
And only one of those is H H H.
But if you have already flipped two heads, what are the odds that the next flip will be heads? 1 in 2. Because the possible outcomes are
H h t
And
H h h
And only one of those is h h h.
What came before doesn’t matter, because it’s a part of the outcome that can’t change anymore, so it is part of ALL future outcomes. So it has no effect on the odds of the next outcome.
Although the odds of any particular numbers being drawn are the same, it is still a bad strategy to use well known numbers like dates and sequences such as 1234567 (or the previous numbers that were drawn). This is because it is more likely that other people chose the same numbers so if you do win you will be sharing the prize.
> They thought I was crazy, pointing out that probably no lottery ever rolled the same five-six winning numbers twice in a row.
That’s because the odds of any specific combination is astronomically low.
It seems like close to impossible because it is. But any other pick is exactly equally close to impossible.
It not that they are wrong thinking it is nearly impossibly unlikely. It is just that our “gut feel” just waaaaay overestimates how likely every other combo is. Our brains don’t easily conceptualize how unlikely “1 in a million” actually is.
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.*
Any well defined number probably is worse that a non-well defined number.
Number consists only of dates? Worse.
Number is a numercization of some name? Worse.
Number is the most recent number played? Worse.
All numbers have the same probability of being picked, BUT special number are more likely to be picked by multiple people, so the odds of winning on special numbers is the same, but the expected payout is lower (cause the odds of someone else picking that special number are higher).
There’s also (probably) never been a case where the winning numbers are exactly 100 greater than the previous lotto’s numbers. Or 5000 greater. Or 2000 less. Yet your coworker seems to think that choosing a ticket that’s 1,234 greater than the previous lotto or whatever is somehow smarter than picking a number that’s equal to the previous lotto despite there being no evidence that that’s ever worked. (I mean, obviously there’s still a chance that whatever random number you pick has been a previous gap between two adjacent lottery numbers, but my point is that the logic is insanely arbitrary)
Your co-worker operates under the Gambler’s fallacy ( [https://en.wikipedia.org/wiki/Gambler%27s_fallacy](https://en.wikipedia.org/wiki/Gambler%27s_fallacy) ). It’s so common that it has it’s own wiki page.
The mistake is made in thinking that previous draws affect future ones. Betting on whether the same drawing occurs twice is very different from betting on a drawing that has occurred already before; it doesn’t click right away, but careful consideration will reveal the faulty logic.
This is the [Gambler’s Fallacy.](https://www.investopedia.com/terms/g/gamblersfallacy.asp#:~:text=The%20gambler’s%20fallacy%2C%20also%20known,event%20or%20series%20of%20events.)
The odds of any specific number from 1-10 being drawn are one in ten every time. The odds of a 7 being drawn after a seven are therefore one in ten. BUT the odds of two sevens being drawn in a row before either of them are drawn is actually 1 in 100. People conflate the odds of the whole series occurring with the odds of just the next step in the series occurring, which creates this fallacy.
Just to put a point on it: If you flip a coin 1,000 times, the odds of what it lands on the thousandth time are not affected by what happened in all of the previous flips. Even if the previous 999 were all heads.
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