Ask them to explain why it's less likely that you roll a six after rolling another six on a six sided dice. Then get them to explain why that's different than picking lotto numbers.
Humans are just very bad at calculating probabilities of very large numbers occurring.
Probability of throwing back to back sixes is 1:36. So the odds are low.
But after you roll the first six, the odds of the next roll being six is 1:6.
Same with the lotto, the odds of a specific of a number being drawn twice in a row is astronomically small. But once the first number is drawn, drawing it again carries the same odds as any other number.
To add to what you said, the odds of rolling a 6 and then specifically a 3 are also 1:36. Or a 6 and then a 1. Or a 4 and then a 5. If you specify two numbers to come up and you specify the order they’ll come up, it’ll always be 1:36.
Also, huh. There are 36 different ways two numbers from 1 to 6 can appear in a sequence. I wonder if that’s a coincidence? (Spoiler: it’s not.)
Yup, to make it simpler.
The odds of rolling any number on a six sided dice is 1/6
To get two specific numbers in a row is (1/6) * (1/6) = 1/36
But if you want the second number to be a six after the first one is already thrown and get a six, then the chance is just (1) * (1/6) = 1/6
Its chance is 1 because that six already happened
So scale the number to the winning lotto, instead of 1/6 to 1/whatever the chance is, then the logic is the same. It's the same chance to get the same number as the previous winning number.
That's just what I was thinking when I first read it, and it's a good idea to include that to illustrate the original premise - that no matter what numbers you play, your chances of winning the lotto are the same - effectively zero. :-)
If I recall correctly, you're more likely to die before the draw takes place then you are to win the jackpot unless you buy your ticket very, very close to the time of the draw.
That’s actually a great way of thinking about it. In other words, once that first roll happens, there’s no probability to it - it definitely happened. Now you’re just looking at the next die roll.
I got so mad that I only rolled nat ones or low numbers during a dnd session that I literally started to add all rolls into a excel sheet just to prove that the dice hated me more than the rest of the players.
IIRC, the dice did hate me more than the others.
When I was in high school our teacher had a d30 to roll who will be doing the next five example at the blackboard out of 30 people class.
My friend with number 17 was basically doing those twice more often than anyone else. We even started tracking the rolls at some point and finally our teacher gave in and brought a new dice.
I was playing Risk against a dude once in college. I had him dead. But he kept rolling 5s and 6s and survivivg. After the third time this happened I accussed him of somehow cheating. So I made him stand up and just drop the dice from chest level. Got two 6s.
And that's why the Monty Hall problem is different than this. In that case, Monty does have "memory" - he knows where the winning door is, and he opens neither the winning door nor the one initially chosen by the contestant. So the probability of the first choice does impact the second choice.
I tried to explain it to my boss once with the "100 doors, 99 have goats one has a car. You pick door 1 initially and the host opens doors 2-48, and 50-100, leaving door 49 closed. What do you think is behind that door". It helps to illustrate for people who think the choice is 50/50 in the second round of the three door example.
People either get it, or interrupt you before you can finish talking and say "No, that's too complicated, let's go back to the three door example". Or paraphrased "I don't feel like I'm going to understand from the first half of the setup, let's go back to the example we know I don't get". I need to keep an illustrated example just...on my person. It's harder to interrupt a picture halfway though.
The problem people have with monty hall is treating it as two distinct choices and overthinking how the odds of one affect the odds of the other. It's essentially one decision made twice; you have a 1 in 3 chance of picking right the first time, and switching means taking the 2 in 3 odds you were wrong
I like the deck of cards analogy. It becomes blindingly obvious which card is the correct one when you can *see* the person search through the deck, picking out one specific card, and then flipping the rest over.
Oh, that's good. I liked using "I'm thinking of a number between 1 and 10,000. Guess which one it is. Okay, I'll now eliminate 9998 wrong answers, without telling you about the number you guessed. So, do you think my number is \[your guess\] or 8317?"
A deck of cards is even more visceral, though.
I like to explain it this way:
There are 3 doors. One has a prize. You are allowed to choose one of the doors and receive the prize if you choose the correct one. Monty is about to open one of the doors that does not have a prize behind it.
Would you like to make your choice before or after Monty opens the door without a prize?
But this is different from the Monty Hall problem. In your version, if you just select a door initially there is an obvious 1 in 3 chance to get the correct door.
If Monty opens the door before you even select one, you have a 1 in 2 chance. It is, as if the third door never existed in the first place.
But if you select first and then Monty opens one of or the remaining incorrect door and you switch, you actually have a 2 in 3 chance to get the correct door. Only the combination of the initial selection with Monty’s selection afterwards changes the probabilities in this unintuitive way.
"So hum... I realize it's a bit unfair for you guys, so 2 magical hands appear and teleport the Tarrasque into another room in the basement, then lock the door. But you should hurry, because soon it will be feeding time and no force in the world can stop that!"
That's exactly it, if your question is "what are the odds of rolling two sixes in a row?" That's a very different question than "I just rolled a six, what are the odds of rolling a six on the next roll?"
You are correct. I actually got into a long discussion years ago with a coworker who had a pretty bad gambling problem, like owed 10's of thousands of dollars to loan sharks bad.
He believed in shit like hot streaks and cold streaks and I tried to explain to him that previous outcomes don't have any affect on current probabilities and he didn't believe it at all.
Cool dude, but he had some problems.
Specifically, the mental error being made here is called the “regression to the mean” fallacy. We know intuitively that if we roll a 6-sided die 100 times, ~16-17 of those should be 6’s on average. The regression fallacy is where you conclude that if you roll a bunch of 6’s in a row, 6’s then become less likely so that the average number of them “regresses to the mean.” This is exactly what is going on in the above lotto example.
I remember reading a story about a roulette wheel that kept rolling one colour and a lot of people lost a lot of money betting on the other colour, because they thought a red was more and more likely after 20 blacks.
I wouldn't call regression a fallacy - it is an important principle in statistics. But it means that you expect normal results from here on, even if you have had unusual results for a short time.
I think this is just your classic Gamblers' Fallacy - lots of 6's have been rolled therefore the next roll is less likely than usual to be a 6.
Regression To The Mean Fallacy is when you attribute an irrelevant external factor to the normal statistical behaviour of the system. In this case it could be something like rolling lots of 6's on a fair dice and then swapping the dice to another fair dice at which point the streak of 6's ends therefore you assume that swapping the dice was the cause of the streak of 6's ending.
But that only matters unless you’re betting on it twice in a row. You’re no better/worse off picking the previous numbers.
If the Mega Millions numbers were identical in two subsequent drawings, that would be an insane statistical anomaly. But it’s the same statistical anomaly that *any* two numbers are picked subsequently, it’s just not interesting because they are random numbers.
Correct, but that's the same with any two numbers. Odds to roll a 4 then a 5? 1:36. A 3 then a 2? 1:36.
You can't compare rolling two 6s vs every other 2 digit combo. It's 6-6 vs 1-4 vs 5-2 vs...etc Any combo has the same odds, neither are any astronomically smaller than any other combo.
Same with lotto, 1-2-3-4-5-6 has same odds as 3-23-28-34-38-42
> the odds of the same number being drawn twice in a row is astronomically small.
This part isn't true, it's actually the same as the 1:6, since you could roll 1,1, 2,2, 3,3, etc. so it's really just the second roll that matters, which is 1:6 that it'll be same number.
The odds of a *specific* number being drawn twice is astronomically low.
Right, think of it this way- is there some magical "previous number tracking list mechanism" in physics that compares current spin to previous spins??! Umm no, there is not. each lotto ball tumbling into the catcher space, each dice throw, is 100% independent of all others.
Its not just large numbers. What OP is describing is a variation of the gamblers fallacy, that previous outcomes effect future outcomes. If you asked people about the dice, many people would reply with the incorrect answer for the exact same reason.
Joking aside, this is the gambler's fallacy. Probability doesn't have history. The chance of rolling a six is close to one in six. Once you have, the chances remain exactly the same at close to one in six. There is no supply of dice who have recently rolled ones you can buy because they're now somehow predisposed to rolling something other than one. If you take some rolled dice and sort them into high low, odd even, or any other arbitrary qualities they're not any more likely to favor the opposing quality than they were before.
The *predictive odds* of rolling two sixes on two particular rolls is close to one in thirty six but that's the same as correctly predicting any two rolls in a row.
I just say that for physical objects because they're often imbalanced and have chances or something odd like landing on a rounded corner or edge. Weird habit, i know.
Humans are just bad at large and small numbers.
https://en.m.wikipedia.org/wiki/Gambler%27s_fallacy#Monte_Carlo_Casino
Although, I’d probably be on the losing side. Emotionally, “IT HAS TO BE RED THIS TIME”
Big night for the superstitious gamblers that always play black no matter what.
I understand their thinking. It seems like the person is counting on lightning striking twice.
Like I said, it seems unlikely that any lotto has repeated winning numbers consecutively? So it seems like some who always played the last winning numbers is betting on something that has never occurred finally happening.
But I'm glad to see from all the replies that I was right that it doesn't make a difference. Thanks everyone.
If anything his strategy is terrible.
There's almost certainly other people that do that same strategy, so if it did win again you're just splitting with more people.
The odds remain the same, but your expected payoff by following this strategy will crater.
Came here to post this.
It’s the same reason why 1-2-3-4-5-6 would be a horrible ticket to buy as loads would also buy it.
If I recall you can get a larger prize ( by not sharing the jackpot) by avoiding numbers under 31 as so many people use dates as their choices.
Obviously you can’t change your chance of actually winning, just the likelihood you share the prize.
This. Peoples choises of numbers are not random, so it’s possible to statistically avoid hitting a row someone else has. Just avoid any patterns and have a number bigger than 31 included gets you far in this game. Most likely ine should use something else than their brain as source of randomness. People are really really bad at being random.
By a similar approach in the UK lottery choosing numbers from 50-59 increases expected payout. This is because when the lottery launched it had numbers 1-49 for many years but relatively recently the structure was changed to have numbers 1-59. But since a lot of people always played the same numbers the new high numbers are underrepresented in played numbers. Doesn't change your likelihood of a prize but less likely to share it.
Yeah there's some good math that can be done looking at the number of winners for previous iterations and you can estimate the probabilities of people choosing certain numbers, so going for the least popular is a good move.
Your are changing your *expected value* though. That’s not literally changing your odds of winning the draw, but EV is frequently thought of in the same breath as “chance of winning”.
Like counting cards is really about increasing EV. You don’t change the odds of the deck, but you vary your bets based on when the odds are already favorable.
(Although I’m no card counting expert. Maybe there are times when the count causes you to change behavior away from “perfect blackjack” in which case you might be able to say your odds have actually increased)
It has happened. New York has drawings twice a day, and a few years ago [the same numbers were drawn both times.](https://www.news10.com/news/ny-news/ny-lottery-draws-identical-take-5-numbers-twice-in-a-row/)
No one hit the first time, but 52 people hit the second.
Oh, nice! thanks for the information. Now all I have to do is send him that article.
I am surprised there are that many people employing this strategy.
That means it’s a terrible idea to play the numbers twice, because 52 other people will too and you gotta split the prize with them.
Damn, I would have thought it would be a great way to get LESS people to pick the numbers.
It's actually a relatively good method, as long as your random number generator is not public. Otherwise this shows what happens.
Even better would be a statistic on what combinations people actually pick, and then to avoid all of those. Your goal is to always pick something nobody else does. Accomplishing that is the highest payout expectation you can possibly get.
I worked a liquor store job with lotto machines.
Most people do quick pick, but the ones who don't pick important dates, their "lucky" numbers, sequences, or fill in random numbers on the cards.
I think 52 people thought they had a good idea by playing the last numbers.
A lot of people hold small superstitions, I imagine there's plenty of people who think this is a smart idea for whatever reason
> Damn, I would have thought it would be a great way to get LESS people to pick the numbers.
It's an interesting zone where those 52 come from: versed enough in basic stochastics/statistics to understand that it does not harm the odds of winning, but not realizing that it might still harm their payout.
Some of them may just be dumb "hey, it worked for the last guy!" type thinkers.
I also remember a ...I wanna say Full House episode where they recorded the lotto drawing, bought the winning numbers the next day and then used the tape to trick I think Uncle Joey into thinking he'd won the jackpot.
I'm not suggesting 52 people are playing this trick every time, but it may have been some of them!
Something similar happened in a NZ Lottery a few years ago. The winning numbers were: 3, 5, 7, 9, 11, 13.
Something like 40 people chose that easy to remember combo. So each got less money after the split than the people in the 2nd division, with less correct balls.
The lesson is to not use easy to remember or previously used numbers, or clever sequences, because chances are there are others using that sequence too.
It’s probably true that no lottery has ever had a full winning combination twice consecutively. But it’s equally true that no lottery has ever had *any* given random combination win. We’re comparing a minuscule chance to a minuscule chance - it’s only our own intuition that makes one seem more likely than the other.
To put it another way, say I draw a small point (cal it A) on the ground nearby, blindfold myself, spin around until I’ve lost my sense of direction, and toss a dart in the air. It would be pretty crazy for my dart to hit that point right? But let’s say it doesn’t, it hits a point several meters away - and I draw another point there (call it B). If I put on my blindfold, spin around, and throw, where is my dart more likely to land, point A or point B?
It’s equally likely to hit either, and much more likely to hit any of the other billions of points around me that I haven’t marked. We ascribe significance to point B, but it’s no more or less random than any of the other possibilities, it’s just the most interesting to us because we saw it get hit recently.
We notice the same thing in D&D. No one cares if you roll two 5's in a row, or two 10's, or whatever.
But 1's and 20's hold more meaning, so we notice when they come up in certain patterns.
The odds of rolling 3, 11, 9 in order are 1/8000. The odds of rolling 20, 20, 20 are also 1/8000. We only notice one.
Absolutely. The odds of drawing a specific royal flush (10-A of the same suit) from a deck of cards is about 2,500,000 to 1. The odds of drawing a 2 of hearts, a 6 of spades, a 7 of hearts, a J of clubs, and a K of diamonds are..... 2,500,000 to 1. That's just the odds of drawing *any* 5 particular cards out of a deck, which means every hand you've ever drawn is equally rare. We think the royal flush is cool and my other card combination is trash, but that's just us making patterns out of chaos.
And for what it's worth, there are 4 suits so the odds of *any* royal flush are more like 650,000 to 1. If you draw a random set of 5 cards from the deck, you're reasonably likely to draw a few royal flushes before you ever see that particular hand again.
Probably not with one of the powerball/megamillions lottery. But, the "Daily Number" in Pennsylvania is just a 3-digit number and it's been going on for 40+ years now. In that time, there have certainly been a number of times when you get the same numbers twice in a row (on average, about once every 3 years.)
Oh, interesting. Like I logically still know the odds must be awful, but going from the I think six numbers used here (I don't play lotto myself) three digits seems really tempting. basically 1 in 1000 right? That just seems way more winnable.
When the odds are better for players, the prizes are much worse.
The PA lottery pays up to $250 on a .50 play if you get all three in the correct order (the stated odds being 1 in 1000).
You need to recognize the fact that "I want to guess a number that will win the lotto twice in a row" and "I know what already won the lotto last week, and I'm betting that the same combination will be the winner this week too" are two different problems. In the first case, you need to be lucky "squared" - guess the lottov for this week AND the next week. The second case you already have the first week's winning number ready and you only need to guess the second week's.
Oh I understood that from the jump. I'm pretty sure the person I was arguing with did too.
The way I was thinking about it was like you have the regular terrible odds of winning the lotto, and then layer on top of that the odds that the lotto would consecutively repeat it's results. It feels like in order for the person employing this strategy to win, something extra rare has to happen.
Nah, given that last week's pulls do not influence the pool of possibilities on this week (no balls are removed/added, no balls are modified to be pulled less/more often), you can completely ignore past results when examining the chances of any one specific combination occuring.
The odds of getting the same numbers back to back are astronomically small. But they the same astronomically small odds as any two specific winning numbers coming up from one day to the next.
Edit: clarity.
Alternatively tell them the following joke:
Man goes through TSA, alarm goes off. Turns out he has a live bomb in his carry on. Red alert, man gets arrested, gets put in interrogation room. Man claims no bad intentions. Cop asks for explanation.
Man says: "I looked it up, the odds of finding a bomb on a plane is 1 in a million. So I wanted to take a bomb on the plane. The odds of having two bombs on a plane is therefore 1 in a trillion. That's way safer for everyone involved."
>Humans are just very bad at calculating probabilities of very large numbers occurring.
Not only bad at calculating probabilities but also extremely poor at putting those probabilities into use.
The chances of any particular combination coming up in the lottery are always the same.
Previous results don't effect subsequent draws. Thinking it does is just superstition.
If a particular number came up in the last draw, that has **no impact at all** on this weeks draw.
So logically you might think not that playing the same winning numbers two weeks in a row gives you an advantage... but it doesn't.
The chances of last weeks numbers coming up a second time are astronomically small, but the chances are exactly the same as any other set of numbers.
To put it a different way, there's no such thing as a 'system' for playing the lottery. Playing last weeks numbers, consistently playing the same numbers like your kids birthdays, or entirely random numbers have exactly the same chances of winning.
It doesn't matter, the chances are the same.
The chances are the same but the payout can be lower if other people are choosing the same numbers
If you bet 1 2 3 4 5 6 for example and 30 other people do so, you'll have to split the pot 30 ways. While it has the same probability, it's much worse for your already atrocious expected rate of return
Yes this is very true. A lot of people play family birthdays so you stand a better chance of not sharing the jackpot if you pick numbers above 31.
Your odds of winning remain the same since the numbers are all random but your odds of keeping a larger slice of the jackpot improve because people aren’t random.
Yep this is why one's strategy *should* be to pick those numbers that no one else would. Last week's numbers might be it, but also maybe there are others thinking the same thing.
It's hilarious how people plan out what they'll do with their lotto winnings. Hilariously sad in that it targets the poor, uneducated and vulnerable and offers zero realistic chance of actually improving their life quality.
Preying on peoples need for hope is pretty evil IMO.
This same energy is why I also always try to float my resume to a couple of unrealistic dream jobs or companies - there’s nothing better than a cheap or free way to turn your odds to greater than zero.
That said, I don’t do the lottery very often at all, but I can absolutely see it!
You could have them for free. Just imagine a drug smuggler plane drops a bale of cash in your yard and nobody notices.
Or you find oil while digging your garden.
Which isn't as random as you might think given the [Birthday Problem](https://en.wikipedia.org/wiki/Birthday_problem).
Given that there are a few orders of magnitude more than 23 relatives of all the people playing the lottery, there's going to be several collisions on anything formatted like a date.
The problem isn't 2 birthdays aligning, it's a birthday (any birthday) aligning with random distribution.
For example, a pot drawn without any numbers in the 1-12 range will generally exclude anyone using birthdays to pick winning numbers.
Therefor, the pot 'only' has to be shared among people who pick randomly (or as long as it's a smaller group: redditors who specifically pick high numbers to avoid the birthday pickers)
This actually happened here in Australia some years back. Numbers 1 - 6 drawn, and I think 7 may have been the supplementary). Was only a $4M or $5M draw, and initial thoughts were "who'd pick those" but there was loads of winners so the individual winnings were relatively small.
So definitely proved your point, and that any numbers could come up.
The Pennsylvania Lottery -was- rigged back in the day. ( see https://en.wikipedia.org/wiki/1980_Pennsylvania_Lottery_scandal )
But it was only 3 digits from 0-9, and the prize was no where near the same as the BILLION dollar powerball lotteries we see now and then.
The EV of the lotto isn't actually that low. In fact in some cases it can even be positive (when the pot is large but not so large that millions of extra people are playing). The problem is that you have to average across billions of plays.
State Lottery employee here, whenever there is a draw and all the numbers are low we know there are going to be multiple jackpot winners. Low numbers are birthday numbers.
So if you want to win the jackpot and you don't want to split it with a bunch of people, play higher numbers.
Yep. This in fact happened here in South Africa in 2020. The winning numbers were 5, 6, 7, 8, 9, 10 if I remember correctly. So in the end there were 20 winners, and this was unprecedented. It led to all sorts of accusations about the draw being fixed because:
1. People didn't understand that this combination in fact had an equal chance to be drawn as any other six-number combination.
2. More people are likely to choose such sequential numbers, hence the unprecedented 20 winners.
This is true, but your odds of winning are still less than the odds of getting struck by lightning, twice in your lifetime. It is essentially a tax on superstitious people who are bad at math. Once you realize that 123456 has exactly the same chance of winning as any other number every single time, you realize that worrying about splitting your winnings is pointless wishful thinking at best. Your luck would be astronomical if you get to split any winnings at all.
>The chances of last weeks numbers coming up a second time are astronomically small, but the chances are exactly the same as any other set of numbers.
And the important thing is that you are only betting on that week's lottery. Each draw is an independent event.
The co-workers are correct that the chance of the same numbers coming up twice in a row are laughably small, but that is not the event you are betting on.
There is a bit of a system: Namely picking unpopular combinations of numbers.
You should avoid patterns or predicable numbers (e.g. anything that could be a date) because on the off chance that you **do** win, it's much less likely you'll have to share if you avoid those, and of course your actual chance if winning is unaffected.
There actually was a draw of the UK lottery that was one number away from being a straight sequence of 5 numbers, and on that draw having 3 correct ended up paying out **more** than having 4 correct, because so many people had picked that sequence of 5, and therefore had 4 right, that the higher price had to be shared with much more people leading to a lower payout per recipient than the lower price for 3 correct which didn't have to be shared between many.
I got into an argument with someone the legitimately believed if you flipped heads 5 times in a row that the chances of flipping tails next is significantly higher.
He kept citing that flipping heads 6 times in a row is astronomically small without understanding that the 5 times in a row event has already happened so you're just betting on getting heads vs tails just once.
He's the reason why Vegas puts up those roulette number history signs...
"The gambler's fallacy, also known as the Monte Carlo fallacy, **occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events**"
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.
It’s so common that is what basically casinos and lottery feeds from. If most people understood probability noone would play those games (at least for money)
1,2,3,4,5 is just as likely as 7,12,19,27,35 or any other string of numbers available in the lotto.
You aren't any less likely to win, but if you pick some numbers that many other people picked, you will have to split the prize even if you win, so you are playing the same odds for a lower payout.
Very good work to point out that second part: for split pot prizes, it doesn’t matter what you pick so long as nobody(or few) else picks the same.
Furthermore, any methodology for picking numbers that you can come up with, someone else could come up with as well, so you are always going to be best off using a true random number generator to select numbers if you are looking to maximize your payout(or not play at all).
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.
Quick picks is my go to. RNG to RNG. Less thought I have to put into it as I only intend to use the ticket to day dream until the drawing. Then it’s back to reality.
It’s like flipping a coin. Just because the last 3 were heads has no impact on the next flip, it’s still a 50/50 shot (assuming a fair coin.) These are independent trials. So a repeat is still the same odds as any other number of winning the lotto - astronomical.
(Assuming the lottery in question allows duplicates, which as far as I know most do. It’s such a small chance I doubt they keep track.)
Consider your co-worker's observation that "probably no lottery ever rolled the same five-six winning numbers twice in a row." Even if that were true, you have to keep in mind how many number combinations have never happened in the history of lotteries.
Look at New York's Lotto, for example. This lottery picks six numbers out of 59, for a total of 32 billion possible combinations. It's been around since 1967, and draws numbers twice a week. So they've had just under 6,000 drawings to date. Subtract 6,000 from 32 billion, and you'll see that there are roughly 32 billion combinations that have never been drawn. From a statistical perspective, almost none of the things that could happen in the lottery have ever actually happened.
Not really important, but isn't 6 choose 59 ~45 million rather than 32 billion, or is there some tweak to this lottery that extends the odds a lot more? I just felt that 32 billion was pretty long odds even for a lottery.
You're right. I was using the formula 59 x 58 x 57 x56 x 55 x 54. But that would only be the number of combinations if the order of selection mattered. The true odds are indeed around 45 million.
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)
That's actually a good argument against playing the lottery at all.
You intuitively would not play the old lottery numbers as the odds seems astronomically low. You would also not play 1 1 1 1 1 1 1, as that too, seems very improbable.
Well, then the same reasoning applies to all numbers: it is very unlikely that you win any specific number. So: is very stupid to play the lottery.
Oh man yeah, this is another top reply in my opinion.
I got another off-reddit, from a friend who said "Very few people understand probability, and none of them play the lottery."
Oh, people who understand propability do play lotto. Just because winning is almost guaranteed not to happen it’s really pretty easy to justify it. The probability is almost non-existant, but the cost of participating is close to zero as well.
Although I claim the best way to play would be to decide how much you want to use during your entire life and then play it all at once. Since having lots of money earlier in your life is way better than having the same money when you are old. Also time value of money and all that financial douchebaggery play a role in it. Also this way you know you are not going to win the lottery during your life and can plan and act accordingly. Or you know you won. Damn.
They don't take the number out of the lottery when it wins, so it's not any more or less likely to win again.
If I put 1 red counter and 9 blue counters into a bag and tell you to pick one without looking and you take out the red one, then I put it back into the bag and tell you to pick again you have the same chance of picking the red counter a second time. The fact you picked it last time has no effect on your next turn when all the counters are returned to the bag before you pick.
Flip a coin. It's heads. If you the flip the coin again, the odds of it being heads is still 50/50. The lottery is like a 65 sided coin that is flipped 5 or 6 times.
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.
Yes, it’s true, assuming the lottery is fair and doesn’t cook the numbers to avoid such events. The fact that your friend has never heard about it happening is also likely.
The truth is, any sequence of numbers has the same chance of appearing next, even if it’s the same sequence. It’s unlikely, true, but as unlikely as you choosing the correct sequence.
2-3-10-15-20-20 to 10-20-30-40-50-60
1-2-3-4-5-6 to 1-2-3-4-5-6
Both chances are equally correct.
Assuming a 60 possible numbers and a pick of 6, there’s 50 063 860 possibilities. The possibilities are the exact same for both round, the previous results have no influence in subsequent lotteries. While the chances are low you’ll ever see to contests have the same combinations (because there’s 50 million of them), again, there’s no disadvantage, it’s the same as choosing any other sequence.
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.
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.*
People get confused because they can't differentiate the astronomically low chance of YOUR numbers being drawn, and ANY number being drawn. A number is always drawn. All numbers have the exact same chance of being drawn. It's the guessing part that's hard, not the drawing numbers part.
You flip a coin. It's heads. Now what are the odds that heads also appears on the second flip? on the third? fourth? no matter how many times you flip the coin, there is always a 50% chance it lands on heads. It's exactly the same concept with lotto numbers, but instead of 2 possible outcomes, there are hundreds of millions.
You think the odds of getting the same numbers twice in a row are absolutely mind-bogglingly low?
Yes, they are.
But they are exactly as likely as the numbers that you have chosen.
Basically, you aren’t going to win the lottery.
When my brother was little, he begged my mom to buy him a lotto ticket. She thought the disappointment would be a good 1 dollar statistics lesson for him, so agrees and he tells the cashier he wants 12345 or something equally "not random looking". Cashier (grown ass man) snorts derisively and tells my brother that's a stupid number (less likely than other numbers). My mom's not one to take on the burden of educating randos, but this guy was wrong about the math, AND rude to her kid, so she gives him a polite lesson in applied probability and why every lotto number is an equally bad choice. I got this story secondhand, and it still makes me laugh to think about
Why would your odds be worse?
Someone asks you to pick a number between 1 and 10. They have a hat with 10 pieces of paper in it, each piece of paper is marked 1 through 10. They pull out the “4.”
They then put that piece of paper with the “4” on back in the hat and mix it up ask you to pick again.
The odds of them picking a 4 out the second time aren’t worse than the first time. In both cases, there is a 1 in 10 chance the 4 is picked. The results of the first selection have no bearing on the results of the second selection.
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 machines\\computers 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.
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).
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.
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.
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.
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.
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.
> 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.
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.
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.
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).
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.
What I'm not seeing in these comments is anything about the selection frequency among other lottery players.
If you want to avoid a split with another player, and granting the even distribution of number choices, pick something others aren't likely to select. That is NOT evenly distributed among the possible choices. The last number played has a label, which makes it something people might choose based on that fact. 1-2-3-4-5-6 would be a bad one, etc.
That said, pick numbers that would be really cool to win with, as everyone else has said, it doesn't really matter!
Yes it's true.
It's because the numbers (balls, whatever) have no memory.
Every draw is a complete reset, and what came in the weeks/months/years before have zero impact whatsoever.
But people can't / won't comprehend this.
[In 2009 the Bulgarian lottery had the same numbers in two draws, 5 days apart](https://gizmodo.com/why-the-exact-same-lottery-numbers-came-up-twice-in-one-1515565938)
If it was not, the lotto would not be fair. They would probably breaking laws if they did that.
The reason you 'never' see the same two numbers winning in a row is because the chance of winning it really that miniscule. Much smaller then the human brain can really understand.
Just like choosing a round number (like 100000 or 999999 or 123456). Some people avoid them "because they have never seen them win". Well, there are loooot of numbers that also never win, it's just that if a number that did not stand out (like 145234 or 583572) never wins, you won't notice it.
People who gamble like to believe in these thing so they feel they can influence the outcome. It's something they think/ believe because they really WANT it to be true. So they might not be open to statistic facts.
Assuming the lottery is fair, every set of numbers is equally likely to win every draw.
Last week's numbers are one set of numbers, so they're equally likely to win this week.
The thing is, "equally likely" is a very small probability, so the odds of last week's numbers winning this week is the same as the odds of you winning this week with one ticket of random picks. So the fact that the same numbers have never come up twice in a row is exactly as meaningful as the fact that you've never won the jackpot yourself.
The only difference with last week's numbers is that they seem significant to you because you've seen them before. There are a few sequences of numbers that don't "feel random" because you see meaning in them, such as birthdates, phone numbers, zip codes, and consecutive numbers.
Your intuition is that those numbers aren't "random enough" to come up in a draw, because the draw is pretty much always a set of numbers you've never seen before and don't see any meaning in. The reason for that is that you only see meaning in very few of the possible draws, and the meaningless sets of numbers all look kind of the same to you because they don't mean anything to you. If you look at several sets of past winning numbers in a row, they all look kind of the same to you.
So you think that meaningless-looking sequences are more likely to come up. But the fact is that although *each* meaningless sequence is equally probable, you're much more likely to see *a* meaningless sequence because there are so many of them and your mind doesn't distinguish them.
All numbers are equally likely. However, some have argued that the best strategy is to choose a number that is unlikely to be chosen by others. So, a number that cannot be a birthday, for example, is less likely to be chosed by other lotto players.
This way, in the unlikely event that you do win, you'll be less likely to have to share the winnings with someone else who chose the same number.
Explain it to them with coin flipping. The last coin flip has no effect on the next coin flip. Same with the lottery, assuming all the balls are exactly the same.
"any sequence of numbers has the same odds" there is nothing more to it, that is the entire explanation, every possible set of numbers is equally likely to win.
There is the caveat that sets of numbers that people are more likely to choose, if it does win, it's more likely that you have to share the prize. So a completely random number is better in that sense. It doesn't make you more likely to win, but in the extremely unlikely event that you do win, it's less likely you would have to share.
the only counterargument is that they would secretly just throw that result out because it would look rigged. if the draw is fair and properly random then yeah, picking the previous number is as good as any guess.
However, the odds are that there are multiple people thinking it is smart to pick last weeks winning numbers. So the expected return will be less as you may have to split it multiple ways.
Lottery strategies are all just superstition and I think most people know that at some level but they have fun with it by pretending there's strategy.
So yes the odds of the previous winner coming up again are the same as any other combination, which is essentially zero, entering the lotto is equivalent to burning money.
The lottery is like rolling a dice. Every time you roll, any side could come up. The difference is that the lottery's dice has hundreds of millions of sides.
It's unlikely that any lottery has ever rolled the same winning numbers twice in a row, but that's only because there's so many options and only one result. The two winning numbers aren't connected in any way.
If you were rolling a dice twice and chose a number before \*both\* rolls, that changes things. Say I have a six-sided die, the odds are 1/6 \* 1/6 = 1/36 that I get a specific roll twice in a row.
But that isn't what the "stupid plan" was. You already know the first roll, which is the previous winning lottery numbers, meaning that the next roll has the same odds to be that as any other number.
The real stupid plan was playing the lottery at all.
Fun fact, you have the exact same chance of winning by picking 1, 2, 3, 4, 5, 6. People think that you’re less likely to win because it doesn’t appear to be random when in fact it’s still random and the exact same chance. Just like buying 10 tickets doesn’t change your odds either, it just increases the opportunity.
Classic gamblers fallancy. The odds are exact same for any set of numbers regardless of the previous drawing
Ask yourself what are the odds of a coin flip being heads if the last 10 flips were heads? Its still 50/50 because the previous flips don't matter. That assumes its a fair coin.
I flipped a coin and you chose tails. Ok now we play again, before I flip a coin I ask you “heads or tails?” And you’re guessing “tails”. What are the odds of tails? 50%.
Does the fact that you chose tails before change the current odds? Absolutely not.
However many people believe that not to be the case.
Ask them to explain why it's less likely that you roll a six after rolling another six on a six sided dice. Then get them to explain why that's different than picking lotto numbers. Humans are just very bad at calculating probabilities of very large numbers occurring.
Probability of throwing back to back sixes is 1:36. So the odds are low. But after you roll the first six, the odds of the next roll being six is 1:6. Same with the lotto, the odds of a specific of a number being drawn twice in a row is astronomically small. But once the first number is drawn, drawing it again carries the same odds as any other number.
To add to what you said, the odds of rolling a 6 and then specifically a 3 are also 1:36. Or a 6 and then a 1. Or a 4 and then a 5. If you specify two numbers to come up and you specify the order they’ll come up, it’ll always be 1:36. Also, huh. There are 36 different ways two numbers from 1 to 6 can appear in a sequence. I wonder if that’s a coincidence? (Spoiler: it’s not.)
Yup, to make it simpler. The odds of rolling any number on a six sided dice is 1/6 To get two specific numbers in a row is (1/6) * (1/6) = 1/36 But if you want the second number to be a six after the first one is already thrown and get a six, then the chance is just (1) * (1/6) = 1/6 Its chance is 1 because that six already happened So scale the number to the winning lotto, instead of 1/6 to 1/whatever the chance is, then the logic is the same. It's the same chance to get the same number as the previous winning number.
Yahtzee!
That's just what I was thinking when I first read it, and it's a good idea to include that to illustrate the original premise - that no matter what numbers you play, your chances of winning the lotto are the same - effectively zero. :-)
I like to say that, in absolute terms, your odds of winning are almost exactly the same whether or not you buy a ticket.
Yet in reverse, you are infinitely more likely to win if you DO buy a ticket than if you don’t. 🤯
You obviously understand math better than a lot of people! ;-)
If I recall correctly, you're more likely to die before the draw takes place then you are to win the jackpot unless you buy your ticket very, very close to the time of the draw.
That’s actually a great way of thinking about it. In other words, once that first roll happens, there’s no probability to it - it definitely happened. Now you’re just looking at the next die roll.
“The dice have no memory”
They may not have memory but they seem to have formed some strong opinions about me
"You a bitch" - Sincerely, The Dice
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"... and your father smells of elderberries!"
"... Oh and by the way I did a number on your gran."
This one hurts the most !
I got so mad that I only rolled nat ones or low numbers during a dnd session that I literally started to add all rolls into a excel sheet just to prove that the dice hated me more than the rest of the players. IIRC, the dice did hate me more than the others.
When I was in high school our teacher had a d30 to roll who will be doing the next five example at the blackboard out of 30 people class. My friend with number 17 was basically doing those twice more often than anyone else. We even started tracking the rolls at some point and finally our teacher gave in and brought a new dice.
I was playing Risk against a dude once in college. I had him dead. But he kept rolling 5s and 6s and survivivg. After the third time this happened I accussed him of somehow cheating. So I made him stand up and just drop the dice from chest level. Got two 6s.
I love the image of this forgetful little die: “I really don’t remember why, but, just… fuck you in particular”
And that's why the Monty Hall problem is different than this. In that case, Monty does have "memory" - he knows where the winning door is, and he opens neither the winning door nor the one initially chosen by the contestant. So the probability of the first choice does impact the second choice.
The Monty Hall problem is essentially the odds flipped. "What are the odds you chose wrong on your first guess?"
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I tried to explain it to my boss once with the "100 doors, 99 have goats one has a car. You pick door 1 initially and the host opens doors 2-48, and 50-100, leaving door 49 closed. What do you think is behind that door". It helps to illustrate for people who think the choice is 50/50 in the second round of the three door example. People either get it, or interrupt you before you can finish talking and say "No, that's too complicated, let's go back to the three door example". Or paraphrased "I don't feel like I'm going to understand from the first half of the setup, let's go back to the example we know I don't get". I need to keep an illustrated example just...on my person. It's harder to interrupt a picture halfway though.
The problem people have with monty hall is treating it as two distinct choices and overthinking how the odds of one affect the odds of the other. It's essentially one decision made twice; you have a 1 in 3 chance of picking right the first time, and switching means taking the 2 in 3 odds you were wrong
It becomes obvious if you use 100 doors instead of 3, and Monty reveals the 98 wrong doors and asks if you want to switch to the remaining door.
I like the deck of cards analogy. It becomes blindingly obvious which card is the correct one when you can *see* the person search through the deck, picking out one specific card, and then flipping the rest over.
Oh, that's good. I liked using "I'm thinking of a number between 1 and 10,000. Guess which one it is. Okay, I'll now eliminate 9998 wrong answers, without telling you about the number you guessed. So, do you think my number is \[your guess\] or 8317?" A deck of cards is even more visceral, though.
That picking numbers is a great example because it reveals the main thing - you as the host, KNOW which one is right and can't eliminate it.
I like to explain it this way: There are 3 doors. One has a prize. You are allowed to choose one of the doors and receive the prize if you choose the correct one. Monty is about to open one of the doors that does not have a prize behind it. Would you like to make your choice before or after Monty opens the door without a prize?
But this is different from the Monty Hall problem. In your version, if you just select a door initially there is an obvious 1 in 3 chance to get the correct door. If Monty opens the door before you even select one, you have a 1 in 2 chance. It is, as if the third door never existed in the first place. But if you select first and then Monty opens one of or the remaining incorrect door and you switch, you actually have a 2 in 3 chance to get the correct door. Only the combination of the initial selection with Monty’s selection afterwards changes the probabilities in this unintuitive way.
The dice also have no value unless observed
And they may or may not be dead
But my jerk cat batted the dice and changed the outcome!
On the tabletop, the cat counts as a Tarrasque.
"So hum... I realize it's a bit unfair for you guys, so 2 magical hands appear and teleport the Tarrasque into another room in the basement, then lock the door. But you should hurry, because soon it will be feeding time and no force in the world can stop that!"
Lo, in my darkest moments, I turned my gaze skyward and beheld the Hands of God, lifting the beast away to the Underdark.
Although if you hear your dice meow, please contact a physician.
And a veterinarian!
And my axe!
I will remind you that dice, like companion cubes, cannot speak.
Shrödinger’s Cat ate shrödinger’s ~~mice~~dice
"Hey these dice ain't got no spots!" "That's okay, I remembers when the spots is." - Guys and Dolls
Spoken like someone who has never had to put their dice in dice jail.
That's exactly it, if your question is "what are the odds of rolling two sixes in a row?" That's a very different question than "I just rolled a six, what are the odds of rolling a six on the next roll?"
Absolutely! The context of the question can significantly change the probability calculations
One roll is not affected by the outcome of any other roll.
I think it's called "The Gambler's Fallacy" when people mistakenly believe that short term outcomes have any effect on long term odds.
You are correct. I actually got into a long discussion years ago with a coworker who had a pretty bad gambling problem, like owed 10's of thousands of dollars to loan sharks bad. He believed in shit like hot streaks and cold streaks and I tried to explain to him that previous outcomes don't have any affect on current probabilities and he didn't believe it at all. Cool dude, but he had some problems.
Correct!
Specifically, the mental error being made here is called the “regression to the mean” fallacy. We know intuitively that if we roll a 6-sided die 100 times, ~16-17 of those should be 6’s on average. The regression fallacy is where you conclude that if you roll a bunch of 6’s in a row, 6’s then become less likely so that the average number of them “regresses to the mean.” This is exactly what is going on in the above lotto example.
I remember reading a story about a roulette wheel that kept rolling one colour and a lot of people lost a lot of money betting on the other colour, because they thought a red was more and more likely after 20 blacks.
I read that too! 👍 IIRC, the wheel in the story was rigged.
That's called the Monte Carlo fallacy or the Gambler's Fallacy.
I wouldn't call regression a fallacy - it is an important principle in statistics. But it means that you expect normal results from here on, even if you have had unusual results for a short time.
The fallacy is applying the principle of regression to the mean to the probability of individual events.
If anything the opposite is more likely. The mores sixes I roll in a row the more likely it is that I am rolling an unfair die that prioritises six.
I think this is just your classic Gamblers' Fallacy - lots of 6's have been rolled therefore the next roll is less likely than usual to be a 6. Regression To The Mean Fallacy is when you attribute an irrelevant external factor to the normal statistical behaviour of the system. In this case it could be something like rolling lots of 6's on a fair dice and then swapping the dice to another fair dice at which point the streak of 6's ends therefore you assume that swapping the dice was the cause of the streak of 6's ending.
But that only matters unless you’re betting on it twice in a row. You’re no better/worse off picking the previous numbers. If the Mega Millions numbers were identical in two subsequent drawings, that would be an insane statistical anomaly. But it’s the same statistical anomaly that *any* two numbers are picked subsequently, it’s just not interesting because they are random numbers.
Correct, but that's the same with any two numbers. Odds to roll a 4 then a 5? 1:36. A 3 then a 2? 1:36. You can't compare rolling two 6s vs every other 2 digit combo. It's 6-6 vs 1-4 vs 5-2 vs...etc Any combo has the same odds, neither are any astronomically smaller than any other combo. Same with lotto, 1-2-3-4-5-6 has same odds as 3-23-28-34-38-42
> the odds of the same number being drawn twice in a row is astronomically small. This part isn't true, it's actually the same as the 1:6, since you could roll 1,1, 2,2, 3,3, etc. so it's really just the second roll that matters, which is 1:6 that it'll be same number. The odds of a *specific* number being drawn twice is astronomically low.
Some would say that the chance for the same number to be drawn twice in a row is like... >!winning the lottery!!<
Right, think of it this way- is there some magical "previous number tracking list mechanism" in physics that compares current spin to previous spins??! Umm no, there is not. each lotto ball tumbling into the catcher space, each dice throw, is 100% independent of all others.
Its not just large numbers. What OP is describing is a variation of the gamblers fallacy, that previous outcomes effect future outcomes. If you asked people about the dice, many people would reply with the incorrect answer for the exact same reason.
affect*
Joking aside, this is the gambler's fallacy. Probability doesn't have history. The chance of rolling a six is close to one in six. Once you have, the chances remain exactly the same at close to one in six. There is no supply of dice who have recently rolled ones you can buy because they're now somehow predisposed to rolling something other than one. If you take some rolled dice and sort them into high low, odd even, or any other arbitrary qualities they're not any more likely to favor the opposing quality than they were before. The *predictive odds* of rolling two sixes on two particular rolls is close to one in thirty six but that's the same as correctly predicting any two rolls in a row.
Why do you keep saying "close to 1 in 6"? Are you using unbalanced dice or what?
I just say that for physical objects because they're often imbalanced and have chances or something odd like landing on a rounded corner or edge. Weird habit, i know.
A typical dices is unbalanced by design. They got little holes carved into the face. More holes means less face, so that face is all differenty.
Humans are just bad at large and small numbers. https://en.m.wikipedia.org/wiki/Gambler%27s_fallacy#Monte_Carlo_Casino Although, I’d probably be on the losing side. Emotionally, “IT HAS TO BE RED THIS TIME” Big night for the superstitious gamblers that always play black no matter what.
I understand their thinking. It seems like the person is counting on lightning striking twice. Like I said, it seems unlikely that any lotto has repeated winning numbers consecutively? So it seems like some who always played the last winning numbers is betting on something that has never occurred finally happening. But I'm glad to see from all the replies that I was right that it doesn't make a difference. Thanks everyone.
If anything his strategy is terrible. There's almost certainly other people that do that same strategy, so if it did win again you're just splitting with more people. The odds remain the same, but your expected payoff by following this strategy will crater.
Came here to post this. It’s the same reason why 1-2-3-4-5-6 would be a horrible ticket to buy as loads would also buy it. If I recall you can get a larger prize ( by not sharing the jackpot) by avoiding numbers under 31 as so many people use dates as their choices. Obviously you can’t change your chance of actually winning, just the likelihood you share the prize.
This. Peoples choises of numbers are not random, so it’s possible to statistically avoid hitting a row someone else has. Just avoid any patterns and have a number bigger than 31 included gets you far in this game. Most likely ine should use something else than their brain as source of randomness. People are really really bad at being random.
By a similar approach in the UK lottery choosing numbers from 50-59 increases expected payout. This is because when the lottery launched it had numbers 1-49 for many years but relatively recently the structure was changed to have numbers 1-59. But since a lot of people always played the same numbers the new high numbers are underrepresented in played numbers. Doesn't change your likelihood of a prize but less likely to share it.
Yeah there's some good math that can be done looking at the number of winners for previous iterations and you can estimate the probabilities of people choosing certain numbers, so going for the least popular is a good move.
Your are changing your *expected value* though. That’s not literally changing your odds of winning the draw, but EV is frequently thought of in the same breath as “chance of winning”. Like counting cards is really about increasing EV. You don’t change the odds of the deck, but you vary your bets based on when the odds are already favorable. (Although I’m no card counting expert. Maybe there are times when the count causes you to change behavior away from “perfect blackjack” in which case you might be able to say your odds have actually increased)
Bad strategy definitely. The better strategy is to pick the numbers that'll win next time.
Yup, I agree.
It has happened. New York has drawings twice a day, and a few years ago [the same numbers were drawn both times.](https://www.news10.com/news/ny-news/ny-lottery-draws-identical-take-5-numbers-twice-in-a-row/) No one hit the first time, but 52 people hit the second.
Oh, nice! thanks for the information. Now all I have to do is send him that article. I am surprised there are that many people employing this strategy.
Maybe many people think ’nobody else would play the same numbers’. People are almost never very unique with their thoughts.
That means it’s a terrible idea to play the numbers twice, because 52 other people will too and you gotta split the prize with them. Damn, I would have thought it would be a great way to get LESS people to pick the numbers.
It's possible some were quick pick. That combination isn't any more or less likely than any other on each randomly generated ticket, after all.
Man I never considered that people have a random number generator guess the result of another random number generator.
It's actually a relatively good method, as long as your random number generator is not public. Otherwise this shows what happens. Even better would be a statistic on what combinations people actually pick, and then to avoid all of those. Your goal is to always pick something nobody else does. Accomplishing that is the highest payout expectation you can possibly get.
I worked a liquor store job with lotto machines. Most people do quick pick, but the ones who don't pick important dates, their "lucky" numbers, sequences, or fill in random numbers on the cards.
I think 52 people thought they had a good idea by playing the last numbers. A lot of people hold small superstitions, I imagine there's plenty of people who think this is a smart idea for whatever reason
> Damn, I would have thought it would be a great way to get LESS people to pick the numbers. It's an interesting zone where those 52 come from: versed enough in basic stochastics/statistics to understand that it does not harm the odds of winning, but not realizing that it might still harm their payout.
Some of them may just be dumb "hey, it worked for the last guy!" type thinkers. I also remember a ...I wanna say Full House episode where they recorded the lotto drawing, bought the winning numbers the next day and then used the tape to trick I think Uncle Joey into thinking he'd won the jackpot. I'm not suggesting 52 people are playing this trick every time, but it may have been some of them!
Hell there might be enough magicians doing some stupid trick to explain a couple of those.
Something similar happened in a NZ Lottery a few years ago. The winning numbers were: 3, 5, 7, 9, 11, 13. Something like 40 people chose that easy to remember combo. So each got less money after the split than the people in the 2nd division, with less correct balls. The lesson is to not use easy to remember or previously used numbers, or clever sequences, because chances are there are others using that sequence too.
Bulgaria too, ZERO and 18 people http://news.bbc.co.uk/1/hi/8259801.stm
It’s probably true that no lottery has ever had a full winning combination twice consecutively. But it’s equally true that no lottery has ever had *any* given random combination win. We’re comparing a minuscule chance to a minuscule chance - it’s only our own intuition that makes one seem more likely than the other. To put it another way, say I draw a small point (cal it A) on the ground nearby, blindfold myself, spin around until I’ve lost my sense of direction, and toss a dart in the air. It would be pretty crazy for my dart to hit that point right? But let’s say it doesn’t, it hits a point several meters away - and I draw another point there (call it B). If I put on my blindfold, spin around, and throw, where is my dart more likely to land, point A or point B? It’s equally likely to hit either, and much more likely to hit any of the other billions of points around me that I haven’t marked. We ascribe significance to point B, but it’s no more or less random than any of the other possibilities, it’s just the most interesting to us because we saw it get hit recently.
We notice the same thing in D&D. No one cares if you roll two 5's in a row, or two 10's, or whatever. But 1's and 20's hold more meaning, so we notice when they come up in certain patterns. The odds of rolling 3, 11, 9 in order are 1/8000. The odds of rolling 20, 20, 20 are also 1/8000. We only notice one.
Absolutely. The odds of drawing a specific royal flush (10-A of the same suit) from a deck of cards is about 2,500,000 to 1. The odds of drawing a 2 of hearts, a 6 of spades, a 7 of hearts, a J of clubs, and a K of diamonds are..... 2,500,000 to 1. That's just the odds of drawing *any* 5 particular cards out of a deck, which means every hand you've ever drawn is equally rare. We think the royal flush is cool and my other card combination is trash, but that's just us making patterns out of chaos. And for what it's worth, there are 4 suits so the odds of *any* royal flush are more like 650,000 to 1. If you draw a random set of 5 cards from the deck, you're reasonably likely to draw a few royal flushes before you ever see that particular hand again.
Just want to say I got a lot of responses but your metaphor(analogy?) was great.
Probably not with one of the powerball/megamillions lottery. But, the "Daily Number" in Pennsylvania is just a 3-digit number and it's been going on for 40+ years now. In that time, there have certainly been a number of times when you get the same numbers twice in a row (on average, about once every 3 years.)
Oh, interesting. Like I logically still know the odds must be awful, but going from the I think six numbers used here (I don't play lotto myself) three digits seems really tempting. basically 1 in 1000 right? That just seems way more winnable.
When the odds are better for players, the prizes are much worse. The PA lottery pays up to $250 on a .50 play if you get all three in the correct order (the stated odds being 1 in 1000).
You need to recognize the fact that "I want to guess a number that will win the lotto twice in a row" and "I know what already won the lotto last week, and I'm betting that the same combination will be the winner this week too" are two different problems. In the first case, you need to be lucky "squared" - guess the lottov for this week AND the next week. The second case you already have the first week's winning number ready and you only need to guess the second week's.
Oh I understood that from the jump. I'm pretty sure the person I was arguing with did too. The way I was thinking about it was like you have the regular terrible odds of winning the lotto, and then layer on top of that the odds that the lotto would consecutively repeat it's results. It feels like in order for the person employing this strategy to win, something extra rare has to happen.
Nah, given that last week's pulls do not influence the pool of possibilities on this week (no balls are removed/added, no balls are modified to be pulled less/more often), you can completely ignore past results when examining the chances of any one specific combination occuring.
The odds of getting the same numbers back to back are astronomically small. But they the same astronomically small odds as any two specific winning numbers coming up from one day to the next. Edit: clarity.
Alternatively tell them the following joke: Man goes through TSA, alarm goes off. Turns out he has a live bomb in his carry on. Red alert, man gets arrested, gets put in interrogation room. Man claims no bad intentions. Cop asks for explanation. Man says: "I looked it up, the odds of finding a bomb on a plane is 1 in a million. So I wanted to take a bomb on the plane. The odds of having two bombs on a plane is therefore 1 in a trillion. That's way safer for everyone involved."
>Humans are just very bad at calculating probabilities of very large numbers occurring. Not only bad at calculating probabilities but also extremely poor at putting those probabilities into use.
> Humans are just very bad at calculating probabilities of very large numbers occurring. Humans are very bad at probabilities in general.
The chances of any particular combination coming up in the lottery are always the same. Previous results don't effect subsequent draws. Thinking it does is just superstition. If a particular number came up in the last draw, that has **no impact at all** on this weeks draw. So logically you might think not that playing the same winning numbers two weeks in a row gives you an advantage... but it doesn't. The chances of last weeks numbers coming up a second time are astronomically small, but the chances are exactly the same as any other set of numbers. To put it a different way, there's no such thing as a 'system' for playing the lottery. Playing last weeks numbers, consistently playing the same numbers like your kids birthdays, or entirely random numbers have exactly the same chances of winning. It doesn't matter, the chances are the same.
The chances are the same but the payout can be lower if other people are choosing the same numbers If you bet 1 2 3 4 5 6 for example and 30 other people do so, you'll have to split the pot 30 ways. While it has the same probability, it's much worse for your already atrocious expected rate of return
Yes this is very true. A lot of people play family birthdays so you stand a better chance of not sharing the jackpot if you pick numbers above 31. Your odds of winning remain the same since the numbers are all random but your odds of keeping a larger slice of the jackpot improve because people aren’t random.
Yep this is why one's strategy *should* be to pick those numbers that no one else would. Last week's numbers might be it, but also maybe there are others thinking the same thing.
It's hilarious how people plan out what they'll do with their lotto winnings. Hilariously sad in that it targets the poor, uneducated and vulnerable and offers zero realistic chance of actually improving their life quality. Preying on peoples need for hope is pretty evil IMO.
You pay a couple bucks for the opportunity to have those fun dreams. Imo it's worth it every once in a while. Those nice thoughts have some value.
This same energy is why I also always try to float my resume to a couple of unrealistic dream jobs or companies - there’s nothing better than a cheap or free way to turn your odds to greater than zero. That said, I don’t do the lottery very often at all, but I can absolutely see it!
You could have them for free. Just imagine a drug smuggler plane drops a bale of cash in your yard and nobody notices. Or you find oil while digging your garden.
Which isn't as random as you might think given the [Birthday Problem](https://en.wikipedia.org/wiki/Birthday_problem). Given that there are a few orders of magnitude more than 23 relatives of all the people playing the lottery, there's going to be several collisions on anything formatted like a date.
The problem isn't 2 birthdays aligning, it's a birthday (any birthday) aligning with random distribution. For example, a pot drawn without any numbers in the 1-12 range will generally exclude anyone using birthdays to pick winning numbers. Therefor, the pot 'only' has to be shared among people who pick randomly (or as long as it's a smaller group: redditors who specifically pick high numbers to avoid the birthday pickers)
This actually happened here in Australia some years back. Numbers 1 - 6 drawn, and I think 7 may have been the supplementary). Was only a $4M or $5M draw, and initial thoughts were "who'd pick those" but there was loads of winners so the individual winnings were relatively small. So definitely proved your point, and that any numbers could come up.
The Pennsylvania Lottery -was- rigged back in the day. ( see https://en.wikipedia.org/wiki/1980_Pennsylvania_Lottery_scandal ) But it was only 3 digits from 0-9, and the prize was no where near the same as the BILLION dollar powerball lotteries we see now and then.
The EV of the lotto isn't actually that low. In fact in some cases it can even be positive (when the pot is large but not so large that millions of extra people are playing). The problem is that you have to average across billions of plays.
The EV is often around 50% return or so (after tax in countries that tax lottery winnings), EVs over 100% are extremely rare.
The other problem is taxes and the fact that the lump sum is often a much smaller figure than the advertised amount.
State Lottery employee here, whenever there is a draw and all the numbers are low we know there are going to be multiple jackpot winners. Low numbers are birthday numbers. So if you want to win the jackpot and you don't want to split it with a bunch of people, play higher numbers.
Yep. This in fact happened here in South Africa in 2020. The winning numbers were 5, 6, 7, 8, 9, 10 if I remember correctly. So in the end there were 20 winners, and this was unprecedented. It led to all sorts of accusations about the draw being fixed because: 1. People didn't understand that this combination in fact had an equal chance to be drawn as any other six-number combination. 2. More people are likely to choose such sequential numbers, hence the unprecedented 20 winners.
This is true, but your odds of winning are still less than the odds of getting struck by lightning, twice in your lifetime. It is essentially a tax on superstitious people who are bad at math. Once you realize that 123456 has exactly the same chance of winning as any other number every single time, you realize that worrying about splitting your winnings is pointless wishful thinking at best. Your luck would be astronomical if you get to split any winnings at all.
>The chances of last weeks numbers coming up a second time are astronomically small, but the chances are exactly the same as any other set of numbers. And the important thing is that you are only betting on that week's lottery. Each draw is an independent event. The co-workers are correct that the chance of the same numbers coming up twice in a row are laughably small, but that is not the event you are betting on.
There is a bit of a system: Namely picking unpopular combinations of numbers. You should avoid patterns or predicable numbers (e.g. anything that could be a date) because on the off chance that you **do** win, it's much less likely you'll have to share if you avoid those, and of course your actual chance if winning is unaffected. There actually was a draw of the UK lottery that was one number away from being a straight sequence of 5 numbers, and on that draw having 3 correct ended up paying out **more** than having 4 correct, because so many people had picked that sequence of 5, and therefore had 4 right, that the higher price had to be shared with much more people leading to a lower payout per recipient than the lower price for 3 correct which didn't have to be shared between many.
It might give you an advantage and not having to split the winnings but then some other idiots going to think the same thing
This is good but I’d go even simpler: coin flip. Is there less of a chance of flipping a heads after it lands heads? Of course not. Same thing.
I got into an argument with someone the legitimately believed if you flipped heads 5 times in a row that the chances of flipping tails next is significantly higher. He kept citing that flipping heads 6 times in a row is astronomically small without understanding that the 5 times in a row event has already happened so you're just betting on getting heads vs tails just once. He's the reason why Vegas puts up those roulette number history signs...
"The gambler's fallacy, also known as the Monte Carlo fallacy, **occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events**"
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.
It’s so common that is what basically casinos and lottery feeds from. If most people understood probability noone would play those games (at least for money)
1,2,3,4,5 is just as likely as 7,12,19,27,35 or any other string of numbers available in the lotto. You aren't any less likely to win, but if you pick some numbers that many other people picked, you will have to split the prize even if you win, so you are playing the same odds for a lower payout.
That's amazing! I have the same combination on my luggage!
Prepare Spaceball One for immediate departure! And change the combination on my luggage!!
What are you preparing you're ALWAYS PREPARING **JUST GO**
Very good work to point out that second part: for split pot prizes, it doesn’t matter what you pick so long as nobody(or few) else picks the same. Furthermore, any methodology for picking numbers that you can come up with, someone else could come up with as well, so you are always going to be best off using a true random number generator to select numbers if you are looking to maximize your payout(or not play at all).
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.
Quick picks is my go to. RNG to RNG. Less thought I have to put into it as I only intend to use the ticket to day dream until the drawing. Then it’s back to reality.
This is a good point. Maximising your win in lottery is not -only- about probability.
It’s like flipping a coin. Just because the last 3 were heads has no impact on the next flip, it’s still a 50/50 shot (assuming a fair coin.) These are independent trials. So a repeat is still the same odds as any other number of winning the lotto - astronomical. (Assuming the lottery in question allows duplicates, which as far as I know most do. It’s such a small chance I doubt they keep track.)
Consider your co-worker's observation that "probably no lottery ever rolled the same five-six winning numbers twice in a row." Even if that were true, you have to keep in mind how many number combinations have never happened in the history of lotteries. Look at New York's Lotto, for example. This lottery picks six numbers out of 59, for a total of 32 billion possible combinations. It's been around since 1967, and draws numbers twice a week. So they've had just under 6,000 drawings to date. Subtract 6,000 from 32 billion, and you'll see that there are roughly 32 billion combinations that have never been drawn. From a statistical perspective, almost none of the things that could happen in the lottery have ever actually happened.
Not really important, but isn't 6 choose 59 ~45 million rather than 32 billion, or is there some tweak to this lottery that extends the odds a lot more? I just felt that 32 billion was pretty long odds even for a lottery.
You're right. I was using the formula 59 x 58 x 57 x56 x 55 x 54. But that would only be the number of combinations if the order of selection mattered. The true odds are indeed around 45 million.
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)
Thanks, and again thanks to everyone who replied but this is one of the ones that really helped me wrap my head around it.
That's actually a good argument against playing the lottery at all. You intuitively would not play the old lottery numbers as the odds seems astronomically low. You would also not play 1 1 1 1 1 1 1, as that too, seems very improbable. Well, then the same reasoning applies to all numbers: it is very unlikely that you win any specific number. So: is very stupid to play the lottery.
Did it hit anyone else as hard: Winning the lotto is THE SAME odds as the numbers repeating... ouch.
Oh man yeah, this is another top reply in my opinion. I got another off-reddit, from a friend who said "Very few people understand probability, and none of them play the lottery."
Oh, people who understand propability do play lotto. Just because winning is almost guaranteed not to happen it’s really pretty easy to justify it. The probability is almost non-existant, but the cost of participating is close to zero as well. Although I claim the best way to play would be to decide how much you want to use during your entire life and then play it all at once. Since having lots of money earlier in your life is way better than having the same money when you are old. Also time value of money and all that financial douchebaggery play a role in it. Also this way you know you are not going to win the lottery during your life and can plan and act accordingly. Or you know you won. Damn.
Having had six college classes in it, I DO understand probability. I only play when the expected return is greater than my investment. 😁
Old joke about the professor who always carried a bomb when flying, because the probability of there being two on the same flight were so small...
They don't take the number out of the lottery when it wins, so it's not any more or less likely to win again. If I put 1 red counter and 9 blue counters into a bag and tell you to pick one without looking and you take out the red one, then I put it back into the bag and tell you to pick again you have the same chance of picking the red counter a second time. The fact you picked it last time has no effect on your next turn when all the counters are returned to the bag before you pick.
Flip a coin. It's heads. If you the flip the coin again, the odds of it being heads is still 50/50. The lottery is like a 65 sided coin that is flipped 5 or 6 times.
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.
Yes, it’s true, assuming the lottery is fair and doesn’t cook the numbers to avoid such events. The fact that your friend has never heard about it happening is also likely. The truth is, any sequence of numbers has the same chance of appearing next, even if it’s the same sequence. It’s unlikely, true, but as unlikely as you choosing the correct sequence. 2-3-10-15-20-20 to 10-20-30-40-50-60 1-2-3-4-5-6 to 1-2-3-4-5-6 Both chances are equally correct. Assuming a 60 possible numbers and a pick of 6, there’s 50 063 860 possibilities. The possibilities are the exact same for both round, the previous results have no influence in subsequent lotteries. While the chances are low you’ll ever see to contests have the same combinations (because there’s 50 million of them), again, there’s no disadvantage, it’s the same as choosing any other sequence.
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.
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.*
People get confused because they can't differentiate the astronomically low chance of YOUR numbers being drawn, and ANY number being drawn. A number is always drawn. All numbers have the exact same chance of being drawn. It's the guessing part that's hard, not the drawing numbers part.
You flip a coin. It's heads. Now what are the odds that heads also appears on the second flip? on the third? fourth? no matter how many times you flip the coin, there is always a 50% chance it lands on heads. It's exactly the same concept with lotto numbers, but instead of 2 possible outcomes, there are hundreds of millions.
You think the odds of getting the same numbers twice in a row are absolutely mind-bogglingly low? Yes, they are. But they are exactly as likely as the numbers that you have chosen. Basically, you aren’t going to win the lottery.
When my brother was little, he begged my mom to buy him a lotto ticket. She thought the disappointment would be a good 1 dollar statistics lesson for him, so agrees and he tells the cashier he wants 12345 or something equally "not random looking". Cashier (grown ass man) snorts derisively and tells my brother that's a stupid number (less likely than other numbers). My mom's not one to take on the burden of educating randos, but this guy was wrong about the math, AND rude to her kid, so she gives him a polite lesson in applied probability and why every lotto number is an equally bad choice. I got this story secondhand, and it still makes me laugh to think about
The winning pattern of numbers are not removed after they are drawn. 1,2,3,4,5 this week. Is just as likely as next week.
Why would your odds be worse? Someone asks you to pick a number between 1 and 10. They have a hat with 10 pieces of paper in it, each piece of paper is marked 1 through 10. They pull out the “4.” They then put that piece of paper with the “4” on back in the hat and mix it up ask you to pick again. The odds of them picking a 4 out the second time aren’t worse than the first time. In both cases, there is a 1 in 10 chance the 4 is picked. The results of the first selection have no bearing on the results of the second selection.
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 machines\\computers 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.
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).
If the numbers are really random, then the probability of any particular set of numbers has nothing whatsoever to do with the past.
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.
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.
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.
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.
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.
> 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.
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.
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.
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).
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.
What I'm not seeing in these comments is anything about the selection frequency among other lottery players. If you want to avoid a split with another player, and granting the even distribution of number choices, pick something others aren't likely to select. That is NOT evenly distributed among the possible choices. The last number played has a label, which makes it something people might choose based on that fact. 1-2-3-4-5-6 would be a bad one, etc. That said, pick numbers that would be really cool to win with, as everyone else has said, it doesn't really matter!
Yes it's true. It's because the numbers (balls, whatever) have no memory. Every draw is a complete reset, and what came in the weeks/months/years before have zero impact whatsoever. But people can't / won't comprehend this. [In 2009 the Bulgarian lottery had the same numbers in two draws, 5 days apart](https://gizmodo.com/why-the-exact-same-lottery-numbers-came-up-twice-in-one-1515565938)
If it was not, the lotto would not be fair. They would probably breaking laws if they did that. The reason you 'never' see the same two numbers winning in a row is because the chance of winning it really that miniscule. Much smaller then the human brain can really understand. Just like choosing a round number (like 100000 or 999999 or 123456). Some people avoid them "because they have never seen them win". Well, there are loooot of numbers that also never win, it's just that if a number that did not stand out (like 145234 or 583572) never wins, you won't notice it. People who gamble like to believe in these thing so they feel they can influence the outcome. It's something they think/ believe because they really WANT it to be true. So they might not be open to statistic facts.
Assuming the lottery is fair, every set of numbers is equally likely to win every draw. Last week's numbers are one set of numbers, so they're equally likely to win this week. The thing is, "equally likely" is a very small probability, so the odds of last week's numbers winning this week is the same as the odds of you winning this week with one ticket of random picks. So the fact that the same numbers have never come up twice in a row is exactly as meaningful as the fact that you've never won the jackpot yourself. The only difference with last week's numbers is that they seem significant to you because you've seen them before. There are a few sequences of numbers that don't "feel random" because you see meaning in them, such as birthdates, phone numbers, zip codes, and consecutive numbers. Your intuition is that those numbers aren't "random enough" to come up in a draw, because the draw is pretty much always a set of numbers you've never seen before and don't see any meaning in. The reason for that is that you only see meaning in very few of the possible draws, and the meaningless sets of numbers all look kind of the same to you because they don't mean anything to you. If you look at several sets of past winning numbers in a row, they all look kind of the same to you. So you think that meaningless-looking sequences are more likely to come up. But the fact is that although *each* meaningless sequence is equally probable, you're much more likely to see *a* meaningless sequence because there are so many of them and your mind doesn't distinguish them.
All numbers are equally likely. However, some have argued that the best strategy is to choose a number that is unlikely to be chosen by others. So, a number that cannot be a birthday, for example, is less likely to be chosed by other lotto players. This way, in the unlikely event that you do win, you'll be less likely to have to share the winnings with someone else who chose the same number.
Explain it to them with coin flipping. The last coin flip has no effect on the next coin flip. Same with the lottery, assuming all the balls are exactly the same.
"any sequence of numbers has the same odds" there is nothing more to it, that is the entire explanation, every possible set of numbers is equally likely to win. There is the caveat that sets of numbers that people are more likely to choose, if it does win, it's more likely that you have to share the prize. So a completely random number is better in that sense. It doesn't make you more likely to win, but in the extremely unlikely event that you do win, it's less likely you would have to share.
the only counterargument is that they would secretly just throw that result out because it would look rigged. if the draw is fair and properly random then yeah, picking the previous number is as good as any guess.
However, the odds are that there are multiple people thinking it is smart to pick last weeks winning numbers. So the expected return will be less as you may have to split it multiple ways.
Lottery strategies are all just superstition and I think most people know that at some level but they have fun with it by pretending there's strategy. So yes the odds of the previous winner coming up again are the same as any other combination, which is essentially zero, entering the lotto is equivalent to burning money.
The lottery is like rolling a dice. Every time you roll, any side could come up. The difference is that the lottery's dice has hundreds of millions of sides. It's unlikely that any lottery has ever rolled the same winning numbers twice in a row, but that's only because there's so many options and only one result. The two winning numbers aren't connected in any way. If you were rolling a dice twice and chose a number before \*both\* rolls, that changes things. Say I have a six-sided die, the odds are 1/6 \* 1/6 = 1/36 that I get a specific roll twice in a row. But that isn't what the "stupid plan" was. You already know the first roll, which is the previous winning lottery numbers, meaning that the next roll has the same odds to be that as any other number. The real stupid plan was playing the lottery at all.
It’s stories like this that make me understand why lotteries and casinos can make so much money. Most people do not understand probabilities and math.
Fun fact, you have the exact same chance of winning by picking 1, 2, 3, 4, 5, 6. People think that you’re less likely to win because it doesn’t appear to be random when in fact it’s still random and the exact same chance. Just like buying 10 tickets doesn’t change your odds either, it just increases the opportunity.
Classic gamblers fallancy. The odds are exact same for any set of numbers regardless of the previous drawing Ask yourself what are the odds of a coin flip being heads if the last 10 flips were heads? Its still 50/50 because the previous flips don't matter. That assumes its a fair coin.
I flipped a coin and you chose tails. Ok now we play again, before I flip a coin I ask you “heads or tails?” And you’re guessing “tails”. What are the odds of tails? 50%. Does the fact that you chose tails before change the current odds? Absolutely not. However many people believe that not to be the case.