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
You’re correct. Assuming the lottery drawing is fair (eg: balls in a machine), there is no memory in the machine or balls to what was drawn last, and hence avoid being drawn the next time. Any set of numbers is just as likely as any other set of numbers, no matter what day they are drawn, or what the last or next drawing will be. It’s not like they’re removing balls from the machine after they’ve come up before – they go right back and are just as likely as any other…
Hell, if the machine did have any kind of bias to certain balls (which it shouldn’t, but just for the sake of argument let’s imagine it did), selecting the last winning lottery numbers might be a good idea since if there is a bias towards certain numbers, the last winner’s might be some of those unfair balls and hence worth picking again.
> They thought I was crazy, pointing out that probably no lottery ever rolled the same five-six winning numbers twice in a row.
This might be true, but it’s also such a rare event in the first place to even win a lottery by itself. Millions of people play the lottery every week and even then, often there are zero winners. So what are the odds of getting two back-to-back numbers when you have a few lotteries do one draw a week?
(The actual odds in any single drawing are the same as simply winning the lottery – nailing 5 or 6 exact number requirements).
Theoretically, no number becomes more or less likely, even compared to prior performance, in a completely random environment. Even if you flip a quarter 11 times and it comes up heads every time, unless the quarter is rigged then it doesn’t make another heads any more likely. To think otherwise is called the Gambler’s fallacy. Looking up the gambler’s fallacy, and why it’s basically completely imaginary bias, might be the most direct answer your friend needs.
By that measure, the same winning numbers could happen twice in a row. Or more. It doesn’t make it something to count on. Any numerical sequence is as likely, in a completely random environment, within the range of the possible numbers.
There would have to be other, internal rules not publicly advertised, to change the possibility, yet for the most part the lottery commissions are required to advertise odds and criteria, depending on the state and country. It’s possible that behind the scenes, the lottery commissions would see a result and think it too… ridiculous, and redo a rolling. But this would be incredibly problematic to do.
There’s always going to be things going on under the hood. Minutia, like rolling machinescomputers replaced, lottery balls, tokens, etc., replaced, making minute changes in odds in reality, but you’re never going to be able to find out about all factors. So just choose what you want.
If the numbers are really random, then the probability of any particular set of numbers has nothing whatsoever to do with the past.
The two draws are entirely unconnected.
Humans are very, very bad at understanding unlikely events. And a particular sequence of numbers is unlikely. So let’s not do big numbers.
You have a black sack. It contains a red and a blue ball. Reach in and pull one out. What’s the chance of blue? 50/50 right?
Put it back. Leave it until tomorrow. Now pick out a ball. What’s the chance of blue now? Still 50/50 isn’t it? How could it be anything else? It can’t!
If the number 25 is drawn today, the only way it could be less likely to come up next time is if that information “I was drawn last week” was somehow passed on to the next draw. There is no way to do that. The ball has no idea it came out a week ago.
The lottery also plays on our feeling that numbers are somehow special and mathematical. But the numbers on the balls have no meaning. You could use symbols. Boat, horse, house, dog, tomato, scissors and car come out. Without numbers we don’t do things like “ooh, they drew 13 and I had 14! So close” when, of course, it isn’t close at all.
It’s also clear that if boat comes out every week well, that’s ok, it’s just a symbol.
The reason no particular lottery has ever done the same numbers twice is the same reason they’ve never drawn *your* numbers. Any particular set of numbers is tens of millions to one. It’s just that each week the numbers you’re talking about aren’t ones in a ticket, they’re the ones printed in the paper last week.
Well, it is probably stupid but not for the reason your co-worker thinks it is. It’s disadvantegeous because picking last weeks winning numbers is a common strategy so in case they do hit twice in a row, you’ll likely share the win with thousands of people and your payday is much smaller. So your odds don’t get any smaller, but potential winnings almost certainly do.
You are asking about dependent probability.
What are the odds of picking 3 winning numbers (1-10) in order?
1 in 1000
What are the odds of picking tomorrow’s numbers?
1 in 1000
What are the odds that I will pick win the same numbers two times in a row?
1 in 1,000,000.
What tomorrow’s lottery numbers are is independent of yesterdays.
However, since with the lotto, it’s like 1 in 100 million chance, it’s probable we won’t see this happen in our lifetime. 150 draws a year is not av lot of attempts to hit one in 10 million billion.
Humans suck at probability because we think things are connected when they are not.
The chance to roll a 6 is 1/6. The chance to roll a 6, after you have rolled 6, 6’s in a row is still, 1/6.
The chance you actually roll 6 6’s in a row, is 1/(6^6), but that’s only because we put the stipulation in a row. In a set of independent rolls, every number has a 1/6 chance, every time.
Every lotto number has a 1/(total #’s) chance to get pulled. Every lotto event is an independent event from the previous one or the next one as the results do not depend any other drawing so the chances to win remain soley based upon the # of tickets you purchased for that 1 event, not the # of events you participate in, i.e., its better to play 10 numbers 1 time, than 1 number 10 times.
Exactly. People confuse “what are the chances of the lottery numbers being the same twice” with “given a winning set of numbers, what are the chances the next draw will be the same.”
One way that helped me explain it, is let’s say I asked what the odds are of the winning numbers being 1,4,18,19,23,28,29? Is that arrangement more likely than any other? The answer should be no, but those numbers are literally the last winning numbers for lotto max. I used a lottery to develop the question, and it didn’t affect the probability. Sometimes new information changes a probability, sometimes it doesn’t. In this case it doesn’t.
No one has addressed yet the point your coworker seems to be using to justify their (incorrect) belief: that there has never been a repeat on numbers that wins.
Your coworker is probably right about that. But your coworker is also ignoring that there are comparatively very few drawings compared to possible outcomes.
Consider if there were three balls, each 1-10. Week 1 is 1, 5, 8. Week two is 2, 7, 8. Week three is 1, 4, 5. And that’s all the drawings we’ve done. Now, it’s true we’ve never had back-to-back identical, but we’ve also not had nearly 1000 possible two-week-combinations. But not having any history of going 1,5,8 to 2,3,4 is not something the human brain sees as a pattern, even though it’s exactly as much of a pattern as not ever having 1,5,8 feed into 1,5,8.
Basically your coworker has seen one true pattern but missed the millions of other patterns. So they’re fixating on something that isn’t actually worth fixating on.
The odds of the same number hitting twice in a row ARE low. but you don’t need the same number to hit twice in a row to hit the lotto. Only once. And in each individual drawing, the odds of any combination hitting are the exact same.
The reason it’s very unlikely the numbers would hit again are because it’s very unlikely that any number hits in the first place.
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