It’s the same likelihood to draw the numbers, however more people are likely to buy that sequence of numbers as it is a very common sequence that people think of.
However, the probability of ending up with a sequence like this is still quite low - probability of coming up with six consecutive numbers is 40 : 42,375,200 i.e. less than one in a million.
If it's done properly, it's the same as any other sequence, right?
I don't know how many balls they have and whether there is replacement to tell you the actual number, but there shouldn't be anything special about this one among all the other possible sequences, except that it's more likely to be guessed.
1,2,3,4,5,6 and 10,11,12,13,14,15 and even 2,4,6,8,10,12 would have had the same amount of attention and scruitny.
So "what are the odds that a sequence of numbers would come out that would look 'funny' to many people" is now not one out of n, it's several hundred out of n.
I was thinking what's the odds that any number drawn will have a special relationship to the number drawn before, where the degree of specialness is determined by how many people hearing the number think "huh, that's weird"
The question most people are probably thinking of is "What are the chances of any sequence of numbers being drawn?", not just this specific one in the article.
Actually no, because this lottery picks five balls from a pool of 50 and then one ball from a pool of 20. So there are only 15 possibilities where the whole draw is six consecutive numbers (from 1-2-3-4-5/6 to 15-16-17-18-19/20).
No, in fact the numbers were not drawn sequentially but arranged in order after. The only exception is the powerball, the 10 in this case, which always is last in the draw and positioned last in the final numbers.
Yes, as others pointed out, this particular sequence is the same as every other sequence. Or, the one person who said 100% is referring to the probability of something that already happened.
To give you a more charitable interpretation, the South African lottery Powerball can be 1-20 so there are 20 straights possible so 20 in 42,375,200. Or roughly 1 in 2,000,000 or roughly 40,000 years of weekly draws to see a straight.
Yes, you're right. In this case, the Powerball comes last. So increasing straights can't end with 1, 2, 3, 4, or 5. However, you could have wrap around straights. So 15 or 20 depending if you allow the wraparound.
Many repliers are computing the probability of this exact draw, but probably a more relevant consideration of "this" is "the odds of a 'suspiciously regular' combination being drawn". The probability of one of those occurring is (the number of such sequences you name):42,375,200, or that number over 42,375,200.
There is some inherent fuzziness in what you consider a "suspicious sequence", obviously. If you stick to entire sequences you don't get very many; however, if you consider "1 2 3 4 5" in the original numbers to be suspicious regardless of the bonus ball draw, then the number of such sequences starts going up fairly quickly. (Include things like [1,3,5,7,9], [2,4,6,8,10], [3,6,9,12,15], etc.)
It's pretty easy to get up to a couple thousand "suspicious sequences". For the sake of roundness and being a bit conservative, let's say there are 423 "suspicious sequences", in which case the odds of hitting one are roughly 1 in 100,000. You may choose to add another order of magnitude of "suspicious sequences" pretty easily, in which case it goes to 1 in 10,000. Given the number of draws done for this sort of lottery (dozens or hundreds a day, I'd guess), it's inevitable that sooner or later one would be hit on lotteries of this size.
Some of the challenge in weighting the number of sequences is they aren't all equally "suspicious". [1,2,3,4,5] is what most people would consider a "dead giveaway" (right or wrong), whereas [1,2,4,8,16,32] would probably bother fewer people. Some people might still find even [1,2,3,4,18,bonus 6] suspicious ("look how 'close' it was to 12345!"). So there's just some intrinsic fuzziness to the answer of how likely this is.
It depends on how many samples. The odds that this specific drawing would yield this result should be one in 42 million, but the odds that a lottery somewhere would yield this result in our lifetime is substantially greater.
Isn't the real question "what are the odds of the lottery being random if this suspicious sequence comes up so soon"? I.e. given a specific sequence, how many weeks should you expect to wait before you see it? In the extreme if you would expect to see 1,2,3,4,5,6 after 500,000 weeks, but you see it in the first week, then probably the lottery is not random, right?
If the probability distribution gives equal weight to all the numbers, then yes. But the fact that a sequence that is semantically meaningful to humans (in such a profound way) came up should raise some questions, because there may be some funny business going on. At the very least, it you want to audit the lottery just to give people confidence it isn't rigged.
if you're a completely logic person then yes. I guess the problem here is that a lot of people will always think this was a scam as they do not understand that 1 2 3 4 5 6 7 8 9 is as likely to happen as 2 1 3 4 5 6 7 8 9. And there's there's the other step... if we can make people have this kind of thinking then very easily this kinds of games would end as people would figure out it's just a waste of money.
I believe that the lottery in question picks a combination, not a permutation, and writes the combination in ascending order. But it's not particularly clear from the documentation.
I don't think you're correct. Imagine you code a random number generator and run it ten times and get the same number every time. A "completely logical" person would probably assume there's a bug in their program. In fact, this is basic Bayesian reasoning.
Yes, but the outcome 5 6 7 8 9 10 is also evidence that something is amiss. If you can discern some structure in some random sequence of numbers, that's evidence that it's not random.
Your comment is basically correcet, but not as a refutation of mine. Your point is the same as mine: certain "special" outcomes at certain rates are evidence of implementation flaws in our random number generator even though they're not any more or less likely given an actually perfect RNG.
Not really, no. Humans are good at spotting patterns, even when none exist. AND.... Given a truly random number generator, there WILL be patterns in various subsets of the numbers.
The thing is that the lottery is not a truly random number generator. It's a physical process implemented by humans, subject to design flaws. So how can we detect whether or not the random number generator we've built has any flaws? By using sound Bayesian reasoning and experiment. If we run the process and it gives us the same number 100 times in a row in the first 100 results, we should adjust our priors and assume what we've built is not in fact a random number generator.
In a long enough random sequence of numbers, small scale patterns are inevitable, as their absence would in itself constitute a (large scale) pattern.
The small scale is only logarithmic in the sequence length though...
Of course. In this case I think it's plenty likely that in fact the 5678910 sequence is in fact just a random event. It's not strong evidence, it's just evidence.
I'm looking at the first 100,000 digits of pi. Lo and behold, 00000 shows up once. So does 11111. What are the odds of each of those happening? It's 1:100,000!
Absolutely astonishing.
As an aside, the inevitability of weird flukes in large sample sizes really sinks in if you've ever wasted part of a year multi-tabling online poker. You'll see some hands play out in totally WTF fashion, as 1:100 and 1:1,000 probabilities come good.
The lesson, of course, is that when you play thousands of hands, encountering such oddities with your money at stake is no longer nearly impossible. It's moved into the zone of nearly certain.
Assuming pi is normal, the odds are 59.3% for any run of 5. The odds of two specific runs of 5 in 100,000 digits is (rough guess) between 3.5% and 10%.
This snarky response unfortunately misses my point, and your point is trivial to anybody who has taken even a remedial course in probability. The key detail is that we know the "RNG" in question might be flawed. If I tell you I implemented a RNG and you run it and find that it imediately spits out the ASCII codes for DONTBEADOUCHE in binary, you might rightly assume you've been duped.
Such a sequence, assuming a low total number of draws, is pretty strong evidence in favor of the theory that the balls were put in sequentially and were supposed to be randomized but the randomization didn't actually happen.
"Over here we have our random number generator."
"Nine nine nine nine nine nine"
"Are you sure that's random?"
"Thats the problem with randomness: you can never be sure."
Randomness is a weird concept, because if you roll a die it's random right? Unless you have all the physical variables - roll speed, angular velocity, height, shape of die, air resistance, air movement, temperature, etc to work out where it will land. So randomness is more a lack of knowledge. Randomness is that you are not sure.
And I don't know enough about quantum mechanics to even comment on that, but that's some weird shit too!
Poe's law is at work here for me. I have no idea if you're sarcastic or joking around because there are a lot of crazy people that actually would believe something this ridiculous.
Scott Adams went fully, publicly, into the Trumpian regime's alternate reality. It is a disappointment, to say the least. But using the t-word should be reserved for extreme scenarios, including some current politicians in American politics, though I will refrain from naming them.
Entirely genuine. Look at his Twitter. He's gone off the deep end and is explicitly supporting a coup and spreading obvious lies. It gives you a perspective on how deeply negative the cynical intent behind his comics is. They're forever ruined.
This isn't a controversial take anywhere in civil society. The fact that Hacker News collects so many conspiracy-minded anti-intellectuals these days should be a warning to PG about the culture he's fostered...
--
reply-via-edit since I'm being rate limited:
> Trump trying to usurp power like crazy people said was going to happen.
He's literally been calling the governors and secretaries of state pressuring them to appoint electors directly instead of as a result of the election. How is that not "trying to usurp power" in an unprecedented way?
"Both sides" are not equivalent here, and it is disingenuous to pretend so.
The fact that Trump and his supporter are so incompetent that they can't actually accomplish it is a blessing, but that doesn't make their supporters any less guilty, just more pathetic.
I had no doubt that if Trump would lose the election, he would not be a gracious loser and would be on Twitter bitching about it until the day he dies. Lo and behold, Trump lost the election, and he's on Twitter bitching about it.
What I don't see is any evidence of Trump supporters rioting, or engaging in violence, or Trump trying to usurp power like crazy people said was going to happen.
Perhaps you should take a chill-pill? States are certifying election results (including Republican majority states). Trump is pursuing legal options, as he is entitled to. Pretty clear that Biden will officially become President-elect when the Electoral College meets later this month (By the way, remember when crazy people in 2016 were trying to get electors to not vote for Trump even though he won [1]?).
So what's the problem? That Scott Adams is calling this election fraudulent? That's par for course. For example, every election that Democrats lose, is also labeled fraudulent, due to 'voter suppression', or Russian meddling or Diebold machines being hacked (remember that one from 2004? [2]). It's a 'meh'.
re [1]. Yes, there are crazy people on both sides. But they didn't include any top officials in the party. Clinton most more electoral votes to faithless electors in 2016 than Trump, so that's a really bad example.
[2] Notice how in 2020 all voting machines include a properly auditable paper trail? The 2004 concerns were very real.
Yeah, he's a Trump supporter. That he labels this past election as 'fraud' is 'meh'. There are plenty of people (on the right, but especially on the left) that call out election fraud (from voter suppression, to illegals voting, to Russians hacking voting machines etc.) after every election.
To be a Trump supporter in December 2020 is be ignorant or to be a traitor, as Trump is currently in the midst of a (failed) coup attempt, and his lieutenants have been trying to float the idea of of martial law.
Most Trump supporters are just ignorant, but Scott Adams is no isolated fool, so unfortunately his continued support for Trump is, yes, willfully seditious.
Matters are very rarely black and white, but when you have someone openly attempting to retroactively cancel an election after he lost, while undermining efforts to secure it beforehand, the contrast is at a maximum, and the choice should be easy.
In America, it isn't possible to commit treason unless there is a legally declared war going on (there hasn't been one for decades.) Otherwise, 'traitor' is nothing more than an insult.
>To be a Trump supporter in December 2020 is be ignorant or to be a traitor,
Geez Louise.
>Most Trump supporters are just ignorant
A little under 50% of the population supports Trump. All of them are ignorant? Uh huh.
> but Scott Adams is no isolated fool, so unfortunately his continued support for Trump is, yes, willfully seditious.
Geez Louise.
>but when you have someone openly attempting to retroactively cancel an election after he lost,
Let me fix that for you to add some context: "but when you have someone OPENLY AND LEGALLY attempting to retroactively cancel an election after he lost".
Trump is going through the court system. He has a right to do that. Do you want to live in a country where candidates are not allowed to challenge election results in court?? Really really? So far outcomes of the lawsuits resulted in some votes that were missed to be counted (like the flash cards in Georgia), some re-counts that resulted in Biden getting a bigger voter-share, and a number of lawsuits being thrown out. Seems like the system is working as intended. WHAT'S THE PROBLEM?
Scott Adams has long been an opponent of the theory of evolution. That seems considerably more wrongheaded than any view he may hold on election fraud.
From a quick look at his twitter, he seems fully on-board the “election fraud” conspiracy train.
As best I can tell, everyone on that train is 99.9% full of shit and acting in a pretty dangerous manner. I’m no history buff, but I have never heard of any previous presidential election where utterly depraved lies and the filthiest of propaganda were so prevalent, especially coming from people in the highest positions of power.
"Eschew flamebait. Don't introduce flamewar topics unless you have something genuinely new to say. Avoid unrelated controversies and generic tangents."
On this site, let's try to avoid the online shaming culture. One of its properties is to link everything anybody ever said or did to the worst thing about them. If all we do is rush along the edges of that directed graph, discussion soon implodes into a high-activation-low-information state. That may be the game on much of the internet, but it's obviously not consistent with curious conversation, which is the mandate of this site, so please let's play a different game here.
This is a good policy in general, but this is one of the most pivotal moments in American history, so much is at stake, and a line must be drawn. The YC community in particular, is full of people who are complicit or explicitly supportive of these efforts, and they need to be shown that they are not welcome.
Except, that they are welcome. Y Combinator has fostered a community with a lot of anti-democratic sentiments.
It's sick, and history will look upon you all with pity and contempt. You should resign and get out.
So there are a few people mentioning that the chances of this happening are equal to the chance of any other set of 6 numbers coming up, but something I like to think about is how to estimate the size of the set of winning combinations that would trigger this kind of reaction, and what the chances of one member of that set being the winning numbers would be.
So let say, a set of:
- sequential numbers.
- sequential primes.
- sequential even or odd.
- a commonly memorized multiplication table 3,6,9,12...
- squares 2,4,8,16,32...
- other famous sequences - eg fibonacci
- famous numbers - eg 4,8,15,16,23,42
- the same numbers being picked multiple days in a row
As a bonus, I like to think of the number of lotteries important enough to warrant making the news. Then you can calculate how frequently you can expect to see a 'crazy lottery winning combination' story.
Ha, you're right. Leaving the mistake in. Appreciate the correction. I was going to do perfect squares but switched to powers and didn't relabel. :facepalm:
Depending on how you count, famous numbers isn't exactly a well defined category, the number of special sequences will be less than 100 and certainly less than 1000. Regardless, very small compared to the overall number of sequences.
I’m not great at maths, but back of fag packet let’s say there are 100 suspicious sequences, and there is a 1 in 15 million chance of winning the lottery - that’s 100/15000000 or 1/150000.
Let’s assume that there are on average 2 lottery drawings per week per country, which means c400 lotteries.
So 400/150000 = 1/375 chance per week, so it’s going to happen every 10 or so years.
Your math is correct. I would say two draws per week is wrong but I'm not a lottery expert. Every 10 years may seem surprisingly often, but we are including sequences like 2,3,5,7,11,13 which most people wouldn't find special. Even 10,12,14,16,18,20 (double of this "special" sequence) I think a lot of people wouldn't care as much.
Do you think two draws a week is a little on the high side or the low side?
The U.K. has 7 draws per week, and I assume the USA has draws in every state, so it could add up fast. I’m assuming most lotteries are weekly, but they could be much more infrequent.
I assume there are other funky possibilities like the crazy thought that someone could get their own phone number as a result, or the sequence 10,20,30,40,50,60 etc so I suspect there are a few other notable sequences hidden in there.
I think this is an important point. I think someone asked "what's the probability this number is chosen?" and many people respond with 1 in 42 million or something like that. But in fact this is only true under the assumption the lottery is implemented perfectly. But this assumption is what is under scrutiny here. Because the lottery is not some ideal process in the mathematical universe, it's a process in the physical universe implemented by humans. Because it's a real process implemented by humans, there's all sorts of ways we can imagine the results could be skewed by the implementation details, and we can imagine all sorts of outputs that might be more likely given the most likely flaws in the implementation.
True, but it’s random enough to make analysis difficult.
I’d be more worried about lack of transparency and poor controls on the part of the game administration. The secretive organization that runs one of the big lotteries requires NDAs for everything and is super secretive, but lacked internal controls to prevent an insider from rigging the game.
Can we define an order of "specialness" on the set of sequences? Because in this case, you have a subset of the non-special sequences which are the least special of all. Which makes them special.
The “interesting number paradox.”[0] Basically, if one were to classify numbers into two categories: “interesting” and “uninteresting”, you’d end up with a contradiction as the smallest “uninteresting” number is itself “interesting” for being the smallest in the set.
Even if these "noticeable" sequences make up only a tiny fraction of all possible sequences, the probability that they show up at least once in a while among all of the world lotteries is actually high.
In general the probability that some unlikely events occur is high.
If you take OEIS as a database of “interesting sequences” (some of them are only interesting to mathematicians), and pull out all of the running groups of 6 (in the sequence as provided, which of course doesn’t include the full version of very long or infinite sequences) that could be a powerball number, you get 1,097,698; or about a 2.6% chance; just the first 6 digits of each sequence gives a mere 32,110; or about 0.076%. Of course most of these aren’t actually very interesting, after all; but it does provide a rough approximation.
I would think it more likely people pick days of the month and month numbers (birthday, wedding day, etc). That hypothesis can be tested by looking at the number of winners vs the winning numbers. Draws where all numbers are over 31 should have relatively fewer winners.
Also, if the numbers have to be picked from a grid, the layout of the form may drive what people pick (similar to why 2580 is a relatively popular security pin. See https://www.datagenetics.com/blog/september32012/)
I used to work at a lottery company and I can confirm your hypothesis. Numbers below 31 and magical numbers like 7 or 13 are picket more frequently. In a game where we draw 5 numbers out of 90 the combination 1,2,3,4,5 was played 4-5000 times a week on average, which means 1 lottery ticket in every 3000. Which is a bad strategy in games where the pot is splitted up equally between the winners. You could have statistically duoble your expected win (return on investment) picking unusual numbers. But ROI was still at 70%.
[Edit] We had a lot of funny stories dealing with obsessed players. One of them accused us of cheating because he found the winning numbers in the newspapers of the last week, in the section of financial news. He also sent us copies of the newspapers, filled with encirceld numbers. It remembered me of one scene in the movie A beautiful mind where John Nash does the same with words.
Wow, glad you got to draw attention to yourself through needless digressions about charged topics. I'm so glad you brought up the concept of gamlbing addiction. No one in all of history has thought of or mentioned it before. You're so amazing.
Or, rather, kindly take your clickbaity comments and shove them 'you know where'
I've done the math on my local lotteries and the EV tips into the players favour when the jackpot gets a bit bigger than 30 million, even if you share a jackpot with one other. This is due to the return of 3,4,5,6 and 7 numbers all adding up, combined with the fact that the jackpot is largely from what others have spent in previous weeks.
If I was completely rational I'd bet my house on it when it tips into my favour. I am not completely rational.
>If I was completely rational I'd bet my house on it when it tips into my favor. I am not completely rational.
It would be rational to bet your house on it if you could repeat the draw an infinity of times, so that the outcome would converge to the expected value.
Not wanting to protect the company, but it's called the National Gambling Company, so it's pretty obvious for everyone what its products are, the participation in the games is anonymous, the customers have the opportunity to opt out (not buying lottery tickets) and it is owned by the government therefore it's profit is nothing more than a special form of tax. Their games are supervised directly by the Ministry of Finance.
I could came up easily with a bunch of well know companies/industries breaking all these rules at once, but that's an other topic.
I think it's still not that frequent. More frequent than I expected before running the numbers, though. Let's say you have a five number interesting sequence starting at N. If the highest number that you can draw is M, then at most, you will have M-5 of these possible. Call it M of them. But we probably don't have sequences starting at each N.
Let's say we've got k of these different kinds of interestingnesses, and an average sequence can start at like a quarter of the numbers. Then the number of draws that we would consider interesting are no more than 0.25 * k * M. So the probability of an interesting draw is 0.25 * k * M / (M choose 5). If M = 69 (apparently the PowerBall rules), then it's 0.25 * k * 69 / 11238513 = k / 651508.
The probability of drawing one of these in c draws is 1 - (1 - k / 651508)^c. For a draw to be at least 50-50 (where it becomes more surprising to not have seen one, that's at least -log(2)/log(1 - k/651508) draws.
For 5 interesting sequences, that's about 90k draws. For 10 interesting sequences, that's about 45k draws. For 100 interesting sequences, it's about 4.5k draws. By 100 sequences, I think the number of numbers the sequence is eligible to start at will drop by a ton. Even having a quarter of numbers be eligible start positions with 10 really interesting sequences seems like a tall order.
So I'd guess the number of draws for a "real" answer is between 5k and 100k draws.
Looks like about 50 U.S. states and territories do it 2x / week. I don't know internationally, but let's double that number to 100 places, 2x per week: 200 draws per week.
5k/200-100k/200 = 25 - 500 weeks = 6mo to a decade before this isn't surprising. I'm leaning more toward the decade end.
Just realized it’s six balls drawn not five, so it’s one in about 7M per draw, nearly 10x less likely, so it would take about 10x longer, somewhere between 5 and 90 years before it’s unsurprising. So if the number of draws per week is accurate, this is reasonably suspicious.
It's hilarious that people assume this must be a scam. If someone figured out how to fix the lottery, why on earth would they pick such a distinctive sequence and split it 20 ways? They could have picked a more "random-looking" sequence, walked away with 100% of the jackpot, and no one would have batted an eye.
It's reckoned in the UK that about 10,000 people every week choose 1, 2, 3, 4, 5, 6 as their lottery numbers. So it'd be really stupid to enter the lottery with those as your own numbers because you'd only win 1/10,000th of the jackpot. In this story 20 people shared the jackpot because of a common sequence.
This seems to indicate that if you are going to enter, you should choose high numbers that aren't, for example, part of memorable sequences, dates, etc. So all numbers > 31. Avoid all even or all odd, progressions, etc.
Yep, the same concept applies to Daily Fantasy Sports. Where you don't necessarily want to pick the best players. You want to pick the best players that no one else will pick. This is for the DFS games that have one player take all.
The best rule to follow to avoid getting duplicate numbers is to just not pick them at all. Quick Pick is a common lottery feature that just gives you random numbers, and should give the best odds of choosing a number which no one else has. Any system your brain can come up with to choose “random” numbers is probably one that someone else came up with too!
A trivially constructed strategy with higher expected value: A surprising number of people choose 1, 2, 3, 4, 5, 6 as their numbers. So, instead of a strategy of using Quick Pick, you could use a strategy of starting with Quick Pick and discarding the result until it's something other than 1, 2, 3, 4, 5, 6, which you then use. That has a higher expected value than Quick Pick by itself. The number of people using this strategy is dwarfed by the number of people using the "1, 2, 3, 4, 5, 6" strategy.
This could be expanded to avoiding months, birthdays, etc.
The odds of a quick pick coming up as 1, 2, 3, 4, 5, 6 are roughly equivalent to winning the lottery in the first place, so “repeat the quick pick until you don’t get this particular combination” seems rather silly, no?
I think you're missing the point. The sequence 1, 2, 3, 4, 5, 6 is just one of many common sequences people play. If you have a primitive bool IsCommonSequence(sequence), then you can do better than random by re-rolling whenever IsCommonSequence returns true. As illustrated by some of the other posts on the thread, your odds of getting a common sequence aren't totally astronomical
This is why I tell people it’s inadvisable to buy a ticket with a special date or similar.
You are no less likely to win, but you are more likely to split any winnings with another player who also bought that number, lowering the expected value of the ticket.
That's not true, it's pretty common in the finance/trading for the office to go spend tens or even hundreds of thousands when the lottery has a positive EV. I've seen brilliant people throw down thousands of dollars. Mostly because it's fun, but also because it's rational.
While every outcome is equally likely, one can say that, a-priori, the odds of an easily described outcome is small. This is formalized in Algorithmic Information Theory [1] [2].
For instance, when flipping a coin 100 times, the odds of the outcome being describable by a 40-bit program in a predetermined language are only 1 in 2^60.
Yes, good point. It's also formalized in basic probability theory. The set of number sequences a human would find interesting or surprising is smaller than the set of all number sequences. If all number sequences are equally likely, by the third axiom of probability you're more likely to draw an uninteresting number sequence than an interesting number sequence.
However that does change the problem statement; we do still expect "123456" to occur equally as often as any other sequence, interesting or not.
The news report quotes the lottery official as saying the numbers were generated by a computer algorithm that is used world wide. Maybe it was in test mode by mistake?
The fact that it was using a known-good computer algorithm means little. Suppose an actor can set the algo seed and thus the generator can give you whatever results you want. Or the output is intercepted. So many possibilities.
I suspect this to be a genuine random event rather than a 'fix'. If you were able to set the numbers and let your stooge know what the winning numbers were going to be...
Why on earth would you pick numbers that were certain to draw attention?
So to prevent attention, choose “non-obvious” sequences. But then those end up being investigated more than “obvious” ones like this. So you would actually want to choose “obvious” ones to avoid suspicion!
There’s a paradox related to this train of thought: the “unexpected hanging paradox.”[0]
> Why on earth would you pick numbers that were certain to draw attention?
Not only that, but sequences like this are significantly more likely to have many winners (assuming the lottery allows ticket purchasers to select their own numbers).
What if you fixed the lottery with a PRNG where if you knew the IV then you would know the output, but then someone forgot to set the IV or some other human error, leading to the PRNG simply incrementing numbers from 5?
So because the chances of something happening are so infinitesimally small, it’ll never happen? Airplanes are orders of magnitude safer than cars, yet planes still crash. The “law of large numbers” and all.
The probability is roughly one in a million. The problem is that people underestimate how often one-in-a-million chances happen, because they don't think about how many times you actually roll for that one-in-a-million chance.
Take the Bulgaria example. How many lotteries are run around the world, such that we'd hear about a rare coincidence like this? Probably about a 1000 a week. So now the one-in-a-million chance is a one-in-a-thousand chance on a weekly basis, or put differently, we should expect to see it happen about every 20 years.
That's not how probability works. Each draw is an independent event from every previous draw, doing a draw with a 1 in 20 million chance of a given sequence 20 million times will not draw every sequence once.
Probability tricks us. I'm not an expert but this is what I think.
Follow one lottery, and then watch it this weekend. If the same numbers come up this weekend as last - it is probably fixed.
Now follow every lottery, and watch them all over a few years. If the same numbers come up one week as last, it could be fix (maybe higher probability than normal) but it's most likely a fluke.
I don't know how often the Bulgarian lottery runs, and how many number there are, but I expect the probability of it happening during the life of the lottery would be about 1 in thousands. That's low, but not unbelievably so.
We need to consider all the "interesting" things that can happen. It can be sequential numbers like in the article, or anything that strikes you when it happens but didn't think about before.
There is still a chance for a mistake. Fraud is unlikely: why would a fraudster do that? It is extremely noticeable and is likely to make the earnings shared.
The probability is exactly the same as the probability of any one ticket holder winning the lottery.
It's a very simple argument: the draw from the week before is the ticket. The next draw, which is completely independent, either matches the ticket, or it doesn't.
The probability of that happening is much much negligible though (the probability of it happening once is 1/N, the probability of it happening twice is 1/N^2)
That only applies if those particular numbers are somehow significant. The chance of picking last week's numbers are the same as picking any other combination.
But I can assure you this is not fraud, because our fraudsters aren't dumb enough to pick sequential numbers and draw even more attention to themselves.
Maybe they are bored of getting away with it? I think the main other necessary data point is that this was an "electronic" lottery. There was a video somewhere (can't find it) where the National Lottery supposedly explains why "this isn't unusual".
In the video they must have mentioned the phrase "random number generator" at least 5 times and never explained why the numbers aren't unusual.
Brings to mind the people in the 2000s that built dice throwing machines and then piped the results to online random number services. Whatever was wrong with our classic lottery ball machine?
not to mention that they are sharing the prize with 19 other people. Would be much better to pick numbers that others are unlikely to have if you are trying to run a scam.
Hmmmm given that a few years ago Zuma had a pool built at his house on the taxpayers dime and tried to say it was a fire pool nothing would surprise me.
My concern is Why is the winner of the US lottery always in some out-of-the-place town in the middle of nowhere? The chances per-capita of the dart landing in a small town are microscopic, yet it happens all the time. Because its fixed. Somebody's relative.
Small towns make up about 50% of the population in the US. Couple that with the fact that small towns also typically have lower income households which are more likely to buy lottery tickets, and you end up with basically every winner being in that demographic.
As someone who lives in a small rural town I highly doubt that. The percent has been consistently going down over time, not up and covid housing movement is nowhere near enough for that large a shift in one year.
Suburbs are significantly more people than small towns, and large metro areas in general hold vast majority of population.
Yeah, but all the mid-sized cities (and suburban towns) on the news that aren't in my area are indistinguishable from small towns in the middle of nowhere.
Small town winner news stories resonate more with a wider audience so will feature much more than big city winners. People can also work out who won in a small community as opposed to a large metropolis so higher chance of nabbing a story there too. Being more newsworthy is not a representative selection when reporters are looking for the most rags-to-riches (Willy Wonka) heart-warming story.
Lottery should be illegal. It is a luck-based system to concentrate and redistribute wealth from individuals (often lower class) to a single member of the society; propelling one person from the lower echelons of the society to the top at the expense of others. We want to align some kind of a productive output and reasonable incentives for a person to justify amassing so much wealth.
Which is why in the US at least, most states take about 40-50% of the lottery winnings to fund education programs. In Georgia, we have the HOPE scholarship which is funded by the Georgia Lottery. If you have a good GPA in high school, and you maintain it in college, you basically get a free ride and don't have to pay tuition. While the HOPE scholarship can probably be tailored, more towards the household income, from a distribution perspective, it still works well.
It allowed myself and many of my peers to graduate with significantly less debt than if we had to pay for college ourselves.
The cynic in me notes that the stock exchange amounts to where moderate to middle class does all of their gambling. With most of the proceeds just consolidating up the wealth chain. At least in lotteries the programs are progressive. :D
However OPs point about mostly lower socioeconomic groups funding the lottery is still relevant as it raises questions about whether this pseudo-regressive “tax” is a fair way to fund a public good like education.
In all fairness, in the US--at least where I live--the bulk of education funding comes from property taxes which is presumably progressive. (There is a different criticism that this leads to wealthier towns having better education. Which is probably true at some level although there isn't a lot of correlation between per pupil spend and educational outcomes in a given area.)
Property taxes aren't progressive: although they're levied on individuals who tend to be well-off, a significant proportion of those costs end up passed on to renters. Additionally, poorer people tend to spend a larger portion of their income on housing (be it rent or otherwise) than the rich.
That's fair enough and probably depends on the housing prices in a location. Wealthier people tend to own more house but it may still be a smaller portion of their income, depending upon where they live.
States do this when they pass gambling laws to make it seem less scummy in my opinion.
My state recently made certain slot machine games legal. I found myself overlooking the parking lot of one of the casinos at 8am while waiting for my grocery pickup. The addicts were already arriving. Somehow every car seemed to have been in an accident and not been repaired. The parking lot was covered in oil stains.
When the casinos opened I imagined people going out occasionally for a fun night gambling. This was far from that.
The trouble with earmarking like this is that the legislature takes it into account when distributing funds, so you can easily have a situation where "all proceeds from the lottery go to education" but you don't actually have any more education funding than you did before.
A specific, new, fully funded program like a scholarship is actually possibly a better form of this than just general funding for the school system.
In a fair number of states, its funny math. They don't increase the size of the budget, they just shift the money around. So if lottery revenue goes up for the state, more of the education budget may come from lottery money vs taxes, but the overall budget remains the same.
> most states take about 40-50% of the lottery winnings to fund education programs. In Georgia, we have the HOPE scholarship which is funded by the Georgia Lottery.
My father and I once debated the merits of this, and he made a point that stuck with me: the overall funding for education didn't change. It's just that the money that used to come from the government now comes from lotteries instead.
Meaning the burden of that cost has shifted from the collected taxes, which is more proportionally paid by the rich, to the lottery system which is more proportionally paid by the poor.
Did the amount of money the poor invest in gambling change? Or are the gambling losses just being re-targeted to fund education, instead whatever they used to end up in previously.
HOPE scholarships are great PR but awful policy. Basically, the poorest people in Georgia are paying for the children of mostly middle and upper-class residents to go to UGA and Ga Tech for free. Of course the state points out the handful of low-income students who also benefited from a HOPE scholarship, but these are the minority of recipients, and they would almost all have qualified for significant grants and financial aid anyway. The most offensive aspect, I'll state again, is the fact that the poorest residents overwhelmingly purchase lottery tickets while the wealthiest residents overwhelmingly receive the scholarships.
It also makes the state university (UGA) much, much harder to gain admission to, since demand for a free college education is high. Applications (and thus necessary GPA/SAT scores) are through the roof... Ivy-qualified students (again, often from wealthy families) are often encouraged to go to UGA for free instead.
HOPE already vastly exceeded its budget once, leading to cutbacks and reforms about a decade ago, with many students losing scholarships or suddenly not qualifiying. A more recent report says it is likely to run out of funds again in 2028. https://www.11alive.com/article/news/local/new-analysis-show...
It would seem to me that all wealth is at the expense of others. I like your comment, but I think it needs to account for the fact that non-lottery wealth comes from either being lucky (born into it, or first to market) or by taking from other people.
Looked at individual transactions within the economy - i.e. how this thread is looking at the lottery - those do appear to be zero sum in the same way.
It's usually other people voluntarily give it to them, not that they take it.
First to market isn't just luck. It's often the result of work harder and faster and taking more risk than others. It's not as if Bill Gates just sat around and told people to make software.
That is true only if making lotteries illegal made them nonexistent. In the United States, the legal lottery is arguably better than the widespread (illegal) "numbers game" it replaced.
It's also arguably worse. It adds a conflict of interest that the "numbers game" never had. The same government that is responsible for providing an education that makes people resistant to the lottery has an interest in people being vulnerable to the lottery.
In my home state of Florida, it's pretty nefarious because they often advertise that the proceeds are used to support education. While that is true, they also removed other sources of funds such as taxes. So in the end the funding level is about the same while less of it comes from taxes. This means Florida can tax people less to pay for education but as other have pointed out, the lottery is essentially a tax on stupidity or at least innumeracy. I guess using an innumeracy tax to fund education is kind of poetic but what Florida has done is tax the uneducated to give tax cuts to everyone else.
>It's rational to play the lottery if you believe that it's the only way to make a significant economic change to your life.
But that belief is irrational. There are a ton of better ways to make a significant economic change to your life with $1 each week than through playing the lottery. $1 each week is $52 a year, you can buy classes, learn skills, etc. with that money and the time you spend watching numbers get called out.
But everyone involved in the illegal lottery is committing a crime (knowingly, I might add). Legalizing and regulating the lottery might be better than the numbers game, but it's also making the government condone and even encourage an activity which is very addictive to individuals and destructive to society: gambling.
Governments shouldn't regulate gambling just because people will illegally gamble if they can't legally gamble. Governments should always weigh the morality of what they promote with the profit it will generate.
Illegal numbers would never reach 5% of the revenue of legal state lotteries. Probably not even 1%. Plenty of law-abiding people with little or no connection to any underworld activity are nevertheless bombarded with legal state-run lottery ads out in the open and available to play at the grocery or convenience store they visit frequently, even daily -- illegal games wouldn't have ads, wouldn't be at 7-11, drawings wouldn't be televised. Further, all numbers games are low-stakes... there is no crime syndicate which could ever afford to run a Powerball or MegaMillions game with 9-figure prizes. Even 6-digit prizes wouldn't be affordable, even if it was, who would ever trust an underground game with that kind of money?
Fortunately, we can always rely on crime syndicates to provide unrestricted access to vices (either gambling, sex, booze, or drugs) for as long as people will want it, no matter what Rulers and other "pezzonovante" think of such a vices.
Said otherwise, you can not change, and will not change, human nature.
It's a high risk and very high variance bet. The odds are terrible but for 99.999% of people it's the only bet you can make with "instantly project me into the top echelon of wealth" levels of upside. There's value in that which is not captured by the negative expected value.
Finance professionals have access to this kind of bet outside the lottery via leverage and complex derivatives and they place bets all the time. Earlier this year Bill Ackman made 2.6B on a really wacky bet against corporate debt [0].
The lottery is absolutely a waste of money for most people, but if you're rational about it you can see it as an opportunity that has no replacement.
> We want to align some kind of a productive output and reasonable incentives for a person to justify amassing so much wealth.
Or maybe it's just fun to play, and people can make their own choices?
Frankly, I think governments should not be in the business of attempting to engineer "desirable" outcomes through coercion. Invest the money that would have been spent on coercion/crackdowns on education and then let people live with the consequences of their actions.
If this were a true random event, then near misses with 5 out of 6 sequential digits would be far more frequent, but I have never heard of one. So that says this is non-random somehow.
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[ 2.9 ms ] story [ 364 ms ] threadHowever, the probability of ending up with a sequence like this is still quite low - probability of coming up with six consecutive numbers is 40 : 42,375,200 i.e. less than one in a million.
> The chances of winning South Africa's PowerBall lottery are one in 42,375,200
I don't know how many balls they have and whether there is replacement to tell you the actual number, but there shouldn't be anything special about this one among all the other possible sequences, except that it's more likely to be guessed.
1,2,3,4,5,6 and 10,11,12,13,14,15 and even 2,4,6,8,10,12 would have had the same amount of attention and scruitny.
So "what are the odds that a sequence of numbers would come out that would look 'funny' to many people" is now not one out of n, it's several hundred out of n.
This can be seen in the official announcement: https://youtu.be/11RN1pEnrTo
To give you a more charitable interpretation, the South African lottery Powerball can be 1-20 so there are 20 straights possible so 20 in 42,375,200. Or roughly 1 in 2,000,000 or roughly 40,000 years of weekly draws to see a straight.
There is some inherent fuzziness in what you consider a "suspicious sequence", obviously. If you stick to entire sequences you don't get very many; however, if you consider "1 2 3 4 5" in the original numbers to be suspicious regardless of the bonus ball draw, then the number of such sequences starts going up fairly quickly. (Include things like [1,3,5,7,9], [2,4,6,8,10], [3,6,9,12,15], etc.)
It's pretty easy to get up to a couple thousand "suspicious sequences". For the sake of roundness and being a bit conservative, let's say there are 423 "suspicious sequences", in which case the odds of hitting one are roughly 1 in 100,000. You may choose to add another order of magnitude of "suspicious sequences" pretty easily, in which case it goes to 1 in 10,000. Given the number of draws done for this sort of lottery (dozens or hundreds a day, I'd guess), it's inevitable that sooner or later one would be hit on lotteries of this size.
Some of the challenge in weighting the number of sequences is they aren't all equally "suspicious". [1,2,3,4,5] is what most people would consider a "dead giveaway" (right or wrong), whereas [1,2,4,8,16,32] would probably bother fewer people. Some people might still find even [1,2,3,4,18,bonus 6] suspicious ("look how 'close' it was to 12345!"). So there's just some intrinsic fuzziness to the answer of how likely this is.
If it produces pretty sequences at significantly greater than expected rates, that would be suspicious.
Absolutely astonishing.
As an aside, the inevitability of weird flukes in large sample sizes really sinks in if you've ever wasted part of a year multi-tabling online poker. You'll see some hands play out in totally WTF fashion, as 1:100 and 1:1,000 probabilities come good.
The lesson, of course, is that when you play thousands of hands, encountering such oddities with your money at stake is no longer nearly impossible. It's moved into the zone of nearly certain.
Such a sequence, assuming a low total number of draws, is pretty strong evidence in favor of the theory that the balls were put in sequentially and were supposed to be randomized but the randomization didn't actually happen.
And I don't know enough about quantum mechanics to even comment on that, but that's some weird shit too!
...for the curious.
Because the scene is priceless
So lost I was. Never heard of Spaceballs.
Scott Adams went fully, publicly, into the Trumpian regime's alternate reality. It is a disappointment, to say the least. But using the t-word should be reserved for extreme scenarios, including some current politicians in American politics, though I will refrain from naming them.
This isn't a controversial take anywhere in civil society. The fact that Hacker News collects so many conspiracy-minded anti-intellectuals these days should be a warning to PG about the culture he's fostered...
--
reply-via-edit since I'm being rate limited:
> Trump trying to usurp power like crazy people said was going to happen.
He's literally been calling the governors and secretaries of state pressuring them to appoint electors directly instead of as a result of the election. How is that not "trying to usurp power" in an unprecedented way?
"Both sides" are not equivalent here, and it is disingenuous to pretend so.
The fact that Trump and his supporter are so incompetent that they can't actually accomplish it is a blessing, but that doesn't make their supporters any less guilty, just more pathetic.
I had no doubt that if Trump would lose the election, he would not be a gracious loser and would be on Twitter bitching about it until the day he dies. Lo and behold, Trump lost the election, and he's on Twitter bitching about it.
What I don't see is any evidence of Trump supporters rioting, or engaging in violence, or Trump trying to usurp power like crazy people said was going to happen.
Perhaps you should take a chill-pill? States are certifying election results (including Republican majority states). Trump is pursuing legal options, as he is entitled to. Pretty clear that Biden will officially become President-elect when the Electoral College meets later this month (By the way, remember when crazy people in 2016 were trying to get electors to not vote for Trump even though he won [1]?).
So what's the problem? That Scott Adams is calling this election fraudulent? That's par for course. For example, every election that Democrats lose, is also labeled fraudulent, due to 'voter suppression', or Russian meddling or Diebold machines being hacked (remember that one from 2004? [2]). It's a 'meh'.
[1] https://www.youtube.com/watch?v=0z0iuWh3sek [2] https://www.motherjones.com/politics/2004/03/diebolds-politi...
re [1]. Yes, there are crazy people on both sides. But they didn't include any top officials in the party. Clinton most more electoral votes to faithless electors in 2016 than Trump, so that's a really bad example.
[2] Notice how in 2020 all voting machines include a properly auditable paper trail? The 2004 concerns were very real.
https://news.ycombinator.com/newsguidelines.html
titled:
Episode 1205 Scott Adams: I Tell You How Democrats Pulled off the Perfect (Alleged!) Crime, With Whiteboard
with hashtags such as ElectionFraud.
Posted December 2, 2020 in: #CNN Fake News, #Doctrine of Laches, #Election Fraud, #Joe Biden, #politics, #president trump, #Project Veritas, #Sarcasm Guppy, #Scott Adams, #ted cruz, #The Fourth Turning, #tucker carlson
Where is this coup support?
Most Trump supporters are just ignorant, but Scott Adams is no isolated fool, so unfortunately his continued support for Trump is, yes, willfully seditious.
Matters are very rarely black and white, but when you have someone openly attempting to retroactively cancel an election after he lost, while undermining efforts to secure it beforehand, the contrast is at a maximum, and the choice should be easy.
Geez Louise.
>Most Trump supporters are just ignorant
A little under 50% of the population supports Trump. All of them are ignorant? Uh huh.
> but Scott Adams is no isolated fool, so unfortunately his continued support for Trump is, yes, willfully seditious.
Geez Louise.
>but when you have someone openly attempting to retroactively cancel an election after he lost,
Let me fix that for you to add some context: "but when you have someone OPENLY AND LEGALLY attempting to retroactively cancel an election after he lost".
Trump is going through the court system. He has a right to do that. Do you want to live in a country where candidates are not allowed to challenge election results in court?? Really really? So far outcomes of the lawsuits resulted in some votes that were missed to be counted (like the flash cards in Georgia), some re-counts that resulted in Biden getting a bigger voter-share, and a number of lawsuits being thrown out. Seems like the system is working as intended. WHAT'S THE PROBLEM?
https://news.ycombinator.com/newsguidelines.html
https://twitter.com/ScottAdamsSays/status/133412978500655923...
As best I can tell, everyone on that train is 99.9% full of shit and acting in a pretty dangerous manner. I’m no history buff, but I have never heard of any previous presidential election where utterly depraved lies and the filthiest of propaganda were so prevalent, especially coming from people in the highest positions of power.
https://news.ycombinator.com/newsguidelines.html
On this site, let's try to avoid the online shaming culture. One of its properties is to link everything anybody ever said or did to the worst thing about them. If all we do is rush along the edges of that directed graph, discussion soon implodes into a high-activation-low-information state. That may be the game on much of the internet, but it's obviously not consistent with curious conversation, which is the mandate of this site, so please let's play a different game here.
https://hn.algolia.com/?query=online%20shaming%20by%3Adang&s...
(We detached this subthread from https://news.ycombinator.com/item?id=25279168 and marked it off topic.)
Except, that they are welcome. Y Combinator has fostered a community with a lot of anti-democratic sentiments.
It's sick, and history will look upon you all with pity and contempt. You should resign and get out.
So let say, a set of:
- sequential numbers.
- sequential primes.
- sequential even or odd.
- a commonly memorized multiplication table 3,6,9,12...
- squares 2,4,8,16,32...
- other famous sequences - eg fibonacci
- famous numbers - eg 4,8,15,16,23,42
- the same numbers being picked multiple days in a row
As a bonus, I like to think of the number of lotteries important enough to warrant making the news. Then you can calculate how frequently you can expect to see a 'crazy lottery winning combination' story.
The list of squares looks more like powers of two btw ;)
Let’s assume that there are on average 2 lottery drawings per week per country, which means c400 lotteries.
So 400/150000 = 1/375 chance per week, so it’s going to happen every 10 or so years.
The U.K. has 7 draws per week, and I assume the USA has draws in every state, so it could add up fast. I’m assuming most lotteries are weekly, but they could be much more infrequent.
I assume there are other funky possibilities like the crazy thought that someone could get their own phone number as a result, or the sequence 10,20,30,40,50,60 etc so I suspect there are a few other notable sequences hidden in there.
EDIT: Oh, the best part: we have this "lottery for the impatient" that has draws every 4 minutes :)
In any case, there's probably a few people out there who picked "1 2 3 4 5" that are kicking themselves extra hard.
I’d be more worried about lack of transparency and poor controls on the part of the game administration. The secretive organization that runs one of the big lotteries requires NDAs for everything and is super secretive, but lacked internal controls to prevent an insider from rigging the game.
[0]: https://en.wikipedia.org/wiki/Interesting_number_paradox
(Note that Kolmogorov complexity is not generally computable, because you could solve the halting problem if you can compute it for all sequences).
In general the probability that some unlikely events occur is high.
(Code here: <https://gist.github.com/wolfgang42/2df001b05065488620700f0fd...>)
Also, if the numbers have to be picked from a grid, the layout of the form may drive what people pick (similar to why 2580 is a relatively popular security pin. See https://www.datagenetics.com/blog/september32012/)
And interesting squares you picked there :-)
[Edit] We had a lot of funny stories dealing with obsessed players. One of them accused us of cheating because he found the winning numbers in the newspapers of the last week, in the section of financial news. He also sent us copies of the newspapers, filled with encirceld numbers. It remembered me of one scene in the movie A beautiful mind where John Nash does the same with words.
aka sad stories of the mentally ill people your company was exploiting.
Or, rather, kindly take your clickbaity comments and shove them 'you know where'
- Ambrose Bierce, The Unabridged Devil's Dictionary
If I was completely rational I'd bet my house on it when it tips into my favour. I am not completely rational.
It would be rational to bet your house on it if you could repeat the draw an infinity of times, so that the outcome would converge to the expected value.
I could came up easily with a bunch of well know companies/industries breaking all these rules at once, but that's an other topic.
Let's say we've got k of these different kinds of interestingnesses, and an average sequence can start at like a quarter of the numbers. Then the number of draws that we would consider interesting are no more than 0.25 * k * M. So the probability of an interesting draw is 0.25 * k * M / (M choose 5). If M = 69 (apparently the PowerBall rules), then it's 0.25 * k * 69 / 11238513 = k / 651508.
The probability of drawing one of these in c draws is 1 - (1 - k / 651508)^c. For a draw to be at least 50-50 (where it becomes more surprising to not have seen one, that's at least -log(2)/log(1 - k/651508) draws.
For 5 interesting sequences, that's about 90k draws. For 10 interesting sequences, that's about 45k draws. For 100 interesting sequences, it's about 4.5k draws. By 100 sequences, I think the number of numbers the sequence is eligible to start at will drop by a ton. Even having a quarter of numbers be eligible start positions with 10 really interesting sequences seems like a tall order.
So I'd guess the number of draws for a "real" answer is between 5k and 100k draws.
Looks like about 50 U.S. states and territories do it 2x / week. I don't know internationally, but let's double that number to 100 places, 2x per week: 200 draws per week.
5k/200-100k/200 = 25 - 500 weeks = 6mo to a decade before this isn't surprising. I'm leaning more toward the decade end.
Not enough people noticing the part where it says "The organisers say the sequence is often picked."
Often?
This seems to indicate that if you are going to enter, you should choose high numbers that aren't, for example, part of memorable sequences, dates, etc. So all numbers > 31. Avoid all even or all odd, progressions, etc.
On a more serious note, if the EV of a lottery is positive, a winning strategy must be to only play unlikely numbers.
A trivially constructed strategy with higher expected value: A surprising number of people choose 1, 2, 3, 4, 5, 6 as their numbers. So, instead of a strategy of using Quick Pick, you could use a strategy of starting with Quick Pick and discarding the result until it's something other than 1, 2, 3, 4, 5, 6, which you then use. That has a higher expected value than Quick Pick by itself. The number of people using this strategy is dwarfed by the number of people using the "1, 2, 3, 4, 5, 6" strategy.
This could be expanded to avoiding months, birthdays, etc.
> you could use a strategy of starting with Quick Pick and discarding the result until it's something other than 1, 2, 3, 4, 5, 6, which you then use
https://www.bbc.co.uk/news/world-africa-55154525
Would be just a lovely Easter egg if someone intervened and updated it to be "world-africa-5678910"
You are no less likely to win, but you are more likely to split any winnings with another player who also bought that number, lowering the expected value of the ticket.
For instance, when flipping a coin 100 times, the odds of the outcome being describable by a 40-bit program in a predetermined language are only 1 in 2^60.
[1] https://en.wikipedia.org/wiki/Algorithmic_information_theory
[2] https://en.wikipedia.org/wiki/Algorithmically_random_sequenc...
However that does change the problem statement; we do still expect "123456" to occur equally as often as any other sequence, interesting or not.
https://www.youtube.com/watch?v=QjaB1JBfJLQ
Why on earth would you pick numbers that were certain to draw attention?
edit: wait for morse code S-O-S :)
There’s a paradox related to this train of thought: the “unexpected hanging paradox.”[0]
[0]: https://en.wikipedia.org/wiki/Unexpected_hanging_paradox
[1] https://en.wikipedia.org/wiki/Reverse_psychology
Not only that, but sequences like this are significantly more likely to have many winners (assuming the lottery allows ticket purchasers to select their own numbers).
Shortly after the 9/11 terror attacks on New York, the Pick 3 came up with 9-1-1. Math happens.
4, 15, 23, 24, 35, 42 were drawn back to back weeks live on TV. They also had a probe but nothing malicious have been found. RNG being RNG.
http://news.bbc.co.uk/2/hi/8259801.stm
I can say that with something like 99.99999% confidence. Which doesn't mean "See it could happen!". It means "No its never gonna happen"
> The lottery organisers described it as a freak coincidence and pointed out that the numbers were drawn in a different order.
So, not the same broadcast.
If the probability was something like 1/2^512, and it happened, i think its safe to say that something is fixed.
Take the Bulgaria example. How many lotteries are run around the world, such that we'd hear about a rare coincidence like this? Probably about a 1000 a week. So now the one-in-a-million chance is a one-in-a-thousand chance on a weekly basis, or put differently, we should expect to see it happen about every 20 years.
Follow one lottery, and then watch it this weekend. If the same numbers come up this weekend as last - it is probably fixed.
Now follow every lottery, and watch them all over a few years. If the same numbers come up one week as last, it could be fix (maybe higher probability than normal) but it's most likely a fluke.
We need to consider all the "interesting" things that can happen. It can be sequential numbers like in the article, or anything that strikes you when it happens but didn't think about before.
There is still a chance for a mistake. Fraud is unlikely: why would a fraudster do that? It is extremely noticeable and is likely to make the earnings shared.
https://www.youtube.com/watch?v=UIUIO1ImtJo
It's a very simple argument: the draw from the week before is the ticket. The next draw, which is completely independent, either matches the ticket, or it doesn't.
But I can assure you this is not fraud, because our fraudsters aren't dumb enough to pick sequential numbers and draw even more attention to themselves.
0: https://youtu.be/a6iW-8xPw3k
> our fraudsters aren't dumb enough to pick...
Maybe they are bored of getting away with it? I think the main other necessary data point is that this was an "electronic" lottery. There was a video somewhere (can't find it) where the National Lottery supposedly explains why "this isn't unusual".
In the video they must have mentioned the phrase "random number generator" at least 5 times and never explained why the numbers aren't unusual.
Brings to mind the people in the 2000s that built dice throwing machines and then piped the results to online random number services. Whatever was wrong with our classic lottery ball machine?
PJvZ
That is quite a claim you make there!
http://www.ruralhome.org/storage/documents/ts2010/ts-report/...
Suburbs are significantly more people than small towns, and large metro areas in general hold vast majority of population.
It allowed myself and many of my peers to graduate with significantly less debt than if we had to pay for college ourselves.
However OPs point about mostly lower socioeconomic groups funding the lottery is still relevant as it raises questions about whether this pseudo-regressive “tax” is a fair way to fund a public good like education.
My state recently made certain slot machine games legal. I found myself overlooking the parking lot of one of the casinos at 8am while waiting for my grocery pickup. The addicts were already arriving. Somehow every car seemed to have been in an accident and not been repaired. The parking lot was covered in oil stains.
When the casinos opened I imagined people going out occasionally for a fun night gambling. This was far from that.
A specific, new, fully funded program like a scholarship is actually possibly a better form of this than just general funding for the school system.
Well sure, you're allocating the new dollars to education, then moving the old allocations over to your pet project...
My father and I once debated the merits of this, and he made a point that stuck with me: the overall funding for education didn't change. It's just that the money that used to come from the government now comes from lotteries instead.
Meaning the burden of that cost has shifted from the collected taxes, which is more proportionally paid by the rich, to the lottery system which is more proportionally paid by the poor.
I am 100% going to bring that up with the old man the next time we're allowed in the same room[0]. I think he'll like it.
[0] Covid risks...
It also makes the state university (UGA) much, much harder to gain admission to, since demand for a free college education is high. Applications (and thus necessary GPA/SAT scores) are through the roof... Ivy-qualified students (again, often from wealthy families) are often encouraged to go to UGA for free instead.
HOPE already vastly exceeded its budget once, leading to cutbacks and reforms about a decade ago, with many students losing scholarships or suddenly not qualifiying. A more recent report says it is likely to run out of funds again in 2028. https://www.11alive.com/article/news/local/new-analysis-show...
First to market isn't just luck. It's often the result of work harder and faster and taking more risk than others. It's not as if Bill Gates just sat around and told people to make software.
It's rational to play the lottery if you believe that it's the only way to make a significant economic change to your life.
That's a bigger problem than just education provision.
But that belief is irrational. There are a ton of better ways to make a significant economic change to your life with $1 each week than through playing the lottery. $1 each week is $52 a year, you can buy classes, learn skills, etc. with that money and the time you spend watching numbers get called out.
Last year the HN consensus was that daily fantasy sports betting was some sort of civil liberty.
Governments shouldn't regulate gambling just because people will illegally gamble if they can't legally gamble. Governments should always weigh the morality of what they promote with the profit it will generate.
Fortunately, we can always rely on crime syndicates to provide unrestricted access to vices (either gambling, sex, booze, or drugs) for as long as people will want it, no matter what Rulers and other "pezzonovante" think of such a vices.
Said otherwise, you can not change, and will not change, human nature.
Finance professionals have access to this kind of bet outside the lottery via leverage and complex derivatives and they place bets all the time. Earlier this year Bill Ackman made 2.6B on a really wacky bet against corporate debt [0].
The lottery is absolutely a waste of money for most people, but if you're rational about it you can see it as an opportunity that has no replacement.
0: https://www.cbsnews.com/news/bill-ackman-billionaire-made-2-...
Or maybe it's just fun to play, and people can make their own choices?
Frankly, I think governments should not be in the business of attempting to engineer "desirable" outcomes through coercion. Invest the money that would have been spent on coercion/crackdowns on education and then let people live with the consequences of their actions.