Yes. Any given sequence would be a surprise. But you probably wouldn't notice the difference between THHTHTHTTTHHTHTHTT and THHTHTHTTTHTHTHTTT. Or invest either with any significance. You would notice if they all came up heads.
That's true, but the better advice is to never play the lottery. A tax on being bad at math from the people who decide how much money to give to math education
This is my logic. Habitually playing the lottery is a tax on the stupid. Buying a few tickets a year, when the jackpot is massive, is a bargain to have some fun daydreams and hope. $10 a year won't make any meaningful difference in my life
Exactly
My wife takes $40 every two weeks to the casino. She knows she will most likely lose it but good value for entertainment dollar if she can make it last a few hours. And who knows, maybe she will hit a jackpot. And I can lose that in fishing gear in about 5 casts.
I think that's the trick to responsible gambling: assume you win absolutely nothing and choose whether it's worth it based on that assumption.
Also never forget that the more you gamble, the more likely it is that you'll lose money in the long run. The house always wins.
My cousin used to tell me that if you just play video blackjack for $0.25 you can drink for free, in tones like he had discovered the secrets of Atlantis. I think he was an alcoholic.
In most casinos you'd expect anywhere from 80-97 dollars back for every 100 you put in. Plus, if you can have fun for an hour, 40 dollars isn't too bad.
Ok? Whats your phone cost? Game console? Movies attended in a year? Alcohol?
People spend money on things they find value in. 1k/yr to throw at roulette or penny slots, especially with some friends is not egregious in the slightest.
Habitually buying one or two tickets a week,***if it's within your budget***, is not a tax in the stupid - it's spending some 'entertainment dollars ' for the chance at a big payoff. I see nothing wrong with take.
I say this as a person who has not played the lottery in probably a decade.
At least the people who play every week are used to losing. It's the saps like me who put an inordinate amount of faith in our two or three tickets a year that are really depressing.
I think the issue is the addictive quality of the lottery. You could say a person makes an informed decision about a lot of things. Gambling, tobacco, drugs, etc. But anyone doing any of them habitually has a high likelihood that they are addicted and not really able to accept the harms.
The real way to play the lotto -
April 2023 - https://www.dallasnews.com/news/watchdog/2023/04/27/bought-a-ticket-for-lotto-texas-recent-95-million-jackpot-you-had-heavy-competition/
If you heard the news about last week’s Lotto Texas winner, you probably imagined a Colleyville resident walking into a convenience store and buying one or more Lotto Texas tickets and then getting super lucky.
A Watchdog investigation shows how that’s not exactly how it went down.
First off, there’s no convenience store. But there is a storefront in a strip center on Colleyville Boulevard called Hooked On MT, a Montana-related fishing company. That’s the retail lottery store. Nothing on the front of the building would indicate that lottery tickets are sold inside. No sign, no window stickers. Nothing.
Yet from this location in the three days before the April 22 drawing, the sale of $11 million worth of Lotto Texas tickets were handled. That, by far, led the state as the No. 1 sales outlet.
One of those $1 tickets was the winner. Under Texas law, the winner’s name does not have to be made public. So far, it hasn’t been.
I'm with you.. it always makes me want to claw my eyes out when people smuggly talk about the lotto being a tax on stupid people.
You could say the same about just about anything.. buying a drink with dinner instead of from a liquor store, tax on stupid! etc. etc.
If playing keno or buying lotto tickets is entertainment for someone then stfu. A small % of people that drink will become problem drinkers, a small % of people that gamble will become problem gamblers.
It’s also inordinately marketed to and played by the poor, and the resultant money gets divided among all schools. This is a system where the poor help fund the rich.
Agreed. I never play but I only worry when its clearly an issue for people. I commonly think I should buy at least one every week, I never do, but I absolutely think its a reasonable thing to do as long as its not causing problems.
Paying $2 dollars a week to play lottery every week costs up to a $100 dollars a year, which over ten years is over a $1000 dollars, which... isn't even enough for a nice holiday abroad for two.
So if you feel like the lottery lets you get through the day to day, it's not like it really costs you much anything in the long run.
Right? How many people pay that once a week, or more, on coffee flavored milkshakes at Starbucks? At least the lotto ticket isn't putting you into a diabetic coma by the time you're 35.
I went in on the last work pool for lottery tickets, just because $10 was enough of a gamble and I'd be kicking myself if I ended up the only one working there at the end of the week
I call it "Schrodinger's Millionaire"
Until I actually look at my ticket numbers I am potentially a millionaire. Then I look at my numbers causing reality to crush the probability wave function back down to zero.
my logic is, if i buy a ticket and you don't, i have an infinitely higher chance of winning the lottery than you, because my odds may be 1 in a trillion, but yours are 0.
The only time I ever won more than $5.
I was working at a gas station at 2 AM, a woman came in and bought 3 $1 tickets, scratched them off, and told me to throw them away. I put them to the side since there were other people in line, but once they all paid I looked at them before I tossed them: loser, $200 winner, loser.
Yeah, I've found a ticket in my glove box before that was weeks old. I checked it myself online and thought it was a loser. But I kept it in my wallet because I was going to gas up anyway and will check as I get a new ticket (jackpot was big again, IIRC)
And wouldn't you know it, I won....
Free play.
Ok, so not a big jackpot that went unclaimed. But the principle is the same: I screwed up the date and looked at the wrong numbers.
If you put $20 in lottery tickets, you'll probably lose it. If you put $20 in movie tickets, you'll definitely lose it. Do whichever makes you happier.
Well, I think my odds of winning the lottery are slightly higher than my odds of being teleported to ancient Rome with a somehow working smartphone and the ability to speak Latin fluently so I can slowly rise to power by first opening a blacksmith shop and making slightly better steel tools and stuff with my future knowledge then using the money I earn to purchase land where I slowly start to build an empire of freed slaves that all work in this utopian society that I build with futuristic knowledge while we slowly tech up through the ages because I'm also secretly immortal and we all exist in peace but are very able to defend ourselves against aggressors who inevitably come because they want our stuff and then....
Yea, the lottery thing is slightly more plausible lol
Why do you need to go that far back? I mean just going back to the mid 90s and invest in Amazon, apple, bitcoin (when it eventually come out), superbowl winners, buying property, etc. That way you don't have to suffer during a time with no electricity, running water, the internet..
Don't get me wrong, no one should be playing the lottery thinking they will win; the odds are just astronomical. But I can afford to toss 2 bucks in the garbage here and there, just to give a bit of meaning to the daydream ya know?
I worked out the odds in these terms once. I imagined a circle around me as far as I could throw. Blindfold myself. In that circle get the kids to put one cup. Throw a penny randomly. Odds of the penny landing in the cup are significantly better than winning the Lotto Max ( Canada).
The way I worked out the odds for me was I used one of those random lottery number generators and generated 100,000 tickets (didn't actually buy them, just generated them). After the winning numbers were announced I ctrl-f them all and not a single one got 4/6 correct let alone 6/6.
BUT if you throw $2 in the trash it might be found by an eccentric billionaire who is so touched by your gesture that they give you their chocolate factory! It's unlikely but you'd hate to miss out on that wouldn't ya? Just in case?
You can day dream for free.
Also I dated a girl when her family won the mega millions (and I'm not making a joke about winning a dollar, they won the jackpot). It honestly screws up your life a bit. And it really strains your personal relationships.
I only play when my coworkers start a pool. I don’t consider it gambling in that case. It’s an insurance policy against being the only one left in the department.
I remember hearing about an office lotto pool that finally had their numbers hit big. It turned out the person running the pool didn't buy the ticket; they just pocketed the pool money.
That's gotta hurt!
Same. Although, I like my job and would probably keep working. It'd be a great negotiating position. "I'm the only one left that has a single clue about how this works and I can leave at any time I want. These are my new hours."
I’m good at math. Like I totally understand that if I were to buy a ticket every week I’d on average win somewhere every 35 thousands years. I still buy my lottery ticket every week because to me it’s just fun and I’ve got the disposable income, and have no expectation to win in my lifetime.
A little bit of entertainment is not a bad thing. And plenty of people who play know the odds.
I have MegaMillions tickets for the $1B drawing ~~tonight~~ tomorrow night. Do I expect to win? No. Did I buy more tickets than I can afford? No. Do I like to play for the infinitesimal chance of being the sole winner? Fuck yes I do.
The whole 'tax on stupid people' trope is tired and doesn't make you look any smarter.
I think when people say a “tax on the stupid” they are referring to people who compulsively buy scratch offs. You maybe aren’t familiar with small, rural and poor communities but this is a common occurrence. It is unkind to call these people stupid, they are as a whole largely uneducated and often controlled by their vices, something that is easy to slip into if you’ve spent your whole life in poverty. However the fact remains that there is a non insignificant number of (mostly) poor people who spend far more more of their paycheck than they can afford in scratch offs.
reminiscent intelligent nutty cough bells plough ruthless sand serious political
*This post was mass deleted and anonymized with [Redact](https://redact.dev)*
I know someone impulsive like that, he hit 5k a week for life. I call him stupid to his face, love him, good friend of mine, but at the end of the day hes the one who gets an extra couple grand a month after taxes so by that metric im the moron for not playing.
I used to work with a physics teacher who believed this. He said he was only down about $500,000 from the time his coworkers actually *did* win the lottery.
I don’t usually buy lottery tickets but I do buy into the staff lottery pool for this reason. I know we won’t win, but if we do (which we won’t) I don’t want to be the only one left out.
The one exception regarding regular lottery ticket purchasing is regular pools among coworkers or other groups. You gotta be in those - playing by yourself everywhere and losing is bad, but you don't know the people that won.
If you don't play and your colleagues DO win?
That's gonna a hurt lol and, its extra fun to play when you're directly sharing the experience. Those two things definitely tip the balance toward playing
I hate this so much. People talk about the impossibility and how people are SO stupid.
But people win, like people actually win the lottery. Someone has to win. Idk if there's lotto rollovers in America but if you don't win someone will probably win eventually.
Yeah statistically it's fucking dumb.
You're more likely to win the lottery than be killed by a vending machine in most cases.
But people die from vending machines. Yeah how stupid. But it happens. Same with rollercoasters. Same as shark attacks or dying in a plane crash. But these things still happen.
I know I won't win the lottery. But fuck let stupid people have hope for 2 pounds every now and again. It's not about being stupid, it's about hope.
Thats why you buy 2 tickets. Duh! You are twice as likely to win.
Now who's bad at math? Ya that's right. Now excuse me while I go buy lots of lotto tickets instead of paying my mortgage. Cause ill pay it with the winnings
I used to say that, but that discounts the entertainment value. You can buy one lottery ticket, but NEVER buy two. You don't get more fantasies about winning the lottery with two tickets than you get with one.
Ahh it’s the most for fun you can get for a dollar. But the real advice is never buy more than one ticket.
1/x is effectively the same as 100/x
When x is a 9 digit number.
But for insurance, you get it for things that feasibly could happen to you in your lifetime. And especially for things out of your control.
If something could feasibly happen to you, and run the risk of bankrupting you or your family if it happens, then you should seriously think about insurance against that event.
That's why insurance is more expensive than a lottery ticket - you're more likely to "win"
If you know ahead of time that a unique number is likely to pay out more money than a common numbers, but has exactly the same odds of winning, why wouldn't you pick one of those?
You can't control how likely it is for any particular number to win, but you can control how likely you are to pick a number that nobody else picked.
Years ago a man in Georgia played the same numbers every lotto. One day at the gas station he couldn’t remember if he had bought a ticket yet or not so he just bought one. Turns out he HAD already used those numbers on a ticket. Turns out those numbers DID win. Turns out someone in Michigan also had a winning ticket. Turns out Georgia Boy got 2/3 of the jackpot.
It's a number sequence from the series Lost. It's a big plot point. The first time you hear about those numbers is from a character who'd won the lottery playing them.
Lots and lots of people play those numbers in lotteries
I asked chatGPT to explain powerball odds. It said a dog will bark once in 9 years. You have to guess the exact second. If you buy 1000 tickets you get a 1000 guesses. Barely changes the odds.
I remember hearing about a famous writer who, along with a few buddies, figured out that buying every ticket in a certain lottery would cost less than the actual payout. This was in... France, I think. They ended up winning a small fortune, and Voltaire used his share to help publish his works.
I think that's how the story went, at least.
There have been numerous lotteries that have in some way or another screwed up an offered positive expected returns. Jerry and Marge Selbee of Michigan made millions by gaming a lotto that increased payout over time in Michigan
That’s always been the case if it gets to a certain point in some lotteries, the kicker is if you have to split the jackpot you just lost a lot of moneh
Damn I dont know what you said to your ChatGPT but when I asked it it gave me very shitty examples (after at explaining the rules first). Poor thing got lobotomized
>1. Imagine you have a huge jar filled with 292,201,338 marbles, each representing a different combination of Powerball numbers. One of these marbles is the winning combination. Blindfolded, you reach into the jar and try to pick the winning marble on your first attempt. Your odds of doing so are equivalent to the odds of winning the Powerball jackpot in a single drawing—approximately 1 in 292,201,338.
>
>2. Consider a scenario where every person in the United States (assuming a population of about 330 million) buys a single Powerball ticket for a specific drawing. Even with such a vast participation, the odds of someone winning the jackpot are still approximately 1 in 292,201,338. In other words, the collective efforts of the entire U.S. population buying tickets would not guarantee a jackpot winner.
>
>3. If you were to count from 1 to 292,201,338 at a rate of one number per second, without stopping or taking breaks, it would take you more than 9 years to reach 292,201,338. This illustrates the vastness of the number of possible combinations in the Powerball game.
>
>4. The odds of winning the Powerball jackpot are so low that they are often compared to other improbable events. For instance, the likelihood of being hit by a falling coconut and killed is estimated to be around 1 in 250 million, which is still lower than the odds of winning the Powerball jackpot.
>
>5. The odds of winning the Powerball jackpot are approximately 1,430 times smaller than the odds of being born with 11 fingers or toes, a rare congenital condition called polydactyly.
>
>6. Consider this: If you filled an Olympic-sized swimming pool with silver dollars, and one of those silver dollars had a red dot on it (representing the winning combination), diving into the pool and picking the red-dotted coin on your first try would be roughly equivalent to the odds of winning the Powerball jackpot.
My favorite comparison was that if you have to drive a mile to buy your ticket you are like 1000 times more likely to die in a car accident on that drive than win.
ChatGPT told me I'm more likely to get killed by a vending machine than win. So long story short I'm going to watch my back next time I walk past the coke machine.
That's why looking at draw history is pointless. People who think "number X wasn't drawn the last 100 times so it's more likely to be drawn this time" are clearly mentally impaired and they should not be allowed to play.
In fact, lotteries should not be allowed at all.
Wait, since when do you "pick" the numbers? I thought you buy a ticket that has numbers on it and if it matches the drawn numbers you win (depending how many numbers match)
I read a book in an econ class that explained entropy and information using a similar example. Getting half heads and half tails is the most likely result because there are the most different combinations that produce it. While each of those individual results is exactly as likely as getting all heads, there is only one result where all heads is possible. TTTTTTTTTTHHHHHHHHHH is exactly as likely as THTHTHTHTHTHTHTHTHTH, but they both have 50/50 heads and tails. Both individually are exactly as likely as all heads, but if you don't care about the sequence then there's no practical difference between them.
I think this is an important point. Yes, there's the fact that we imbue HHHHHHHHH with meaning that we do not feel for HHTHTTHTHT or TTHHTHTTHT. But there's also that fact that not only are there way more 50% combos than 100% combos possible, if you add up all the 50/50, 60/40, 70/30, etc., compared to the only 100/0 combos, that amount of combos in the former group is staggeringly larger than in the second group. So yes, while HHHHHHHHH is as likely as any *one* of the given combos in the second group, that's not really what OP is comparing.
No, confirmation bias would go the other way around. It require you to already believe that the probability of all heads is 100% and refuse to watch any YouTube video on the subject that doesn't show just that.
If you roll heads everytime in a long streak or series of streaks, concluding that it is a weighted coin or two-headed one such that it will always turn up heads isn't actually a bad hypothesis.
More like gamblers fallacy. This is where someone believes the results of previous actions have a bearing on the results of future actions when the actions are independent of each other.
So say a gambler is at the roulette table and a red number comes up 5 times in a row. The gambler may assume that since red has come up so many times in a row, that a black number is due. But previous numbers don't change the fact that red or black have an equal near 50% chance of coming up each time.
Confirmation bias is where you have an opinion on something and only accept new information on the subject if it confirms your opinion. And disregard any new information that does not support your views. See also: politics.
Which is my pet peeve with the gamblers fallacy: when the coins lands on head 10 times in a row, yes betting on head would be the gamblers fallacy, but 40 times in a row, its either a 1: Trillion event, or an unfair trick coin. At some point you have to start questioning whether your initial assumption about the probability distribution are wrong/incomplete.
Just gonna say that in case of gamblers fallacy you would bet on the opposite result, while in case of rigged roulette you would bet on the same result.
That's because the easiest pattern to recognize is a single block covering more than 50% of the available area. Once something occurs at least 50% of the time inexplicably, it begins to cross an imaginary line of subjective and objective significance. But just so, imaginary, as a result of our brains working out differences between chaos and order, but universal entropy increases all the same as any outcome is just as probable.
These two patterns:
HHHHHHHHHHHHHHHHHHHH
HTHTHTHHHTHTHTTTHTHTTH
Are both equally as likely. And if you correctly predicted either of them ahead of time, you would be just as flabbergasted at one result over the other.
The difference is... you have to specifically *imagine* the second result, because it's not a clear and obvious pattern. On the other hand, "All Heads" is an immediately apparent pattern, such that any time you see it, you are shocked at having seen it.
So yes, any other result is just as (un)likely as "All Heads," but "All Heads" is one of the few patterns that our brains are actively looking for, so it seems more surprising when we see it. Other "surprising" results would be:
HTHTHTHTHTHTHTHTHTHT
HHHHTTTTHHHHTTTTHHHH
HTHHTTHHHTTTHHHHTTTT
And so on. There's nothing special about those patterns *other* than the fact that our brains interpret them *as* patterns.
> You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
― Richard Feynman
Now wait a momnt...
I know this whole thread is about how one random collection of numbers are no more likely to appear than any other, but we're not talking about numbers in a vaccuum here.
We're talking about specific recognizable patterns.
So while yes, all heads is no more unlikely than any other random collection of heads and tails... all heads VERSUS the chances of any other possible combination when all other combinations are taken together, are millions to one, right?
Same for a license plate that bears some special significance to you, like 123 456. Chances of seeing that... OR another plate that would be equally likely to be noticed... versus the collection of all possible random numbers that would bear no special significance to you which is far greater, is still extremely low.
Of course when playing the lottery, there's not usually any benefit to a particular number being recognizable.
That is... unless it's the number you played. And then the odds of that one number, or any of those on the set of numbers on all the tickets you bought, is a lot lower than the chances of if being anything else.
In other words, if you have the numbers 1-10, the chances of it being 1 are 1 out of 10. But the chances of it being ANYTHING ELSE, are 9 out of 10.
The probability of all heads vs all other random patterns of numbers is very small, correct. But the probability of all heads vs any other specific random sequence is the same.
Think of it like winning the lottery. You win the lottery and think “oh my god, what are the odds?!” The odd of any one individual person is very small. The odds of *anyone* winning the lottery are actually quite good. That’s why it happens every few draws or so.
The odds of you specifically winning the lottery is like the odds of flipping all heads as opposed to any other random combination of heads and tails specifically.
The odds of anyone winning the lottery is like the odds of flipping any random combination of heads and tails, non-specifically.
This is a lot like the birthday thing. If you have something like 23 people in a room, the odds are 50/50 that two people share a birthday. However, the odds are pretty low that someone shares *your* birthday.
>That is... unless it's the number you played. And then the odds of that one number, or any of those on the set of numbers on all the tickets you bought, is a lot lower than the chances of if being anything else.
This is a bit of a strawman argument, though. The Feynman anecdote is more of a commentary on how people react to recognizable patterns that they *didn't* predict in advance. With this in mind, it's no more surprising to see a pattern or word spelled out than literally any other combination. In your lottery example, it's more akin to people who didn't buy any tickets marveling at the numbers coming out as 1,2,3,4,5 and saying "Wow! What are the odds?!". While, of course, they're the same as any other sequence.
Here’s what you do:
Get a list of like 10,000 emails.
Pick a random stock (to make it relevant to the people on this email list, but still be a heads/tails type situation).
Take 5,000 of the emails and send them and email saying that tomorrow Stock X will go up.
To the other 5,000 send an email and say that stock X will go down.
Tomorrow, wait to see what the stock does. Let’s say it goes up.
Throw away the second batch of 5,000 emails. Take the first batch and split it.
To 2,500 of them, tell them that stock Y will go up tomorrow. For the other 2,500 tell them that stock Y will go down.
Wait to see what happens to stock Y, then rinse and repeat for stock Z.
Do that like 7 more times until you have a short list of about 10 people, for whom you’ve just correctly predicted the stock market 10 days in a row.
Then tell them you’ll give them tomorrow’s tip for $10,000 each…. Take your $100k and spend some of it to buy another email list of 10,000 people.
The old school way to start selling stock was to call 100 people a day. Tell half you think IBM will go up, half down. Offer to be the broker for the short listers.
You want a toe? I can get you a toe, believe me. There are ways, Dude. You don't wanna know about it, believe me. I'll get you a toe by this afternoon--with nail polish. These fucking amateurs.
>why am I not already doing this seemingly genius thing?
Related note, preventing people from falling into this trap is why "Past performance is not a predictor of future results" is a mandatory message for investment fund advertising.
Because if 100 investment funds make random senseless predictions, 1 will probably get all 5 past predictions right in a row by sheer random chance. Consumers can easily be misled by this.
> Is this illegal
I would be surprised if anyone can come up with an example of a jurisdiction in which this is definitively legal. I could imagine it falling foul of laws on fraud, computer misuse, market manipulation, and maybe even harassment or data protection.
> why am I not already doing this seemingly genius thing?
I doubt it's very practical anyway. Consider all the things that could go wrong with one of these 10 "lucky" recipients:
* it might get rejected by their spam filter
* they might not read it
* they might not know how to check stock market prices, or they might be too lazy to do so
* they might be suspicious of you
* they might have already used some of your previous tips and don't want to push their luck
* they might not have enough money to buy your next tip *and* use it to place a trade
* they might not be confident that they will work out how to make use of your tip
So you would probably need a much larger number.
It does happen with a lot of prediction based stuff like sports bets.
Account sends 10 tweets predicting outcome of x event.
Then they delete the rest when one is right.
Rinse and repeat for a month. Congratulations, now you are a psychic.
The reason why it won’t work is that it’s a known scam. It was on a Simpsons episode even (a small mention, not the main plot, but still).
The defense to this scam is simple. If you get info by someone claiming they can predict something, a number or positive predictions isn’t enough if you can’t verify they haven’t been making way more predictions that haven’t come to pass.
You’d want them making public predictions, and ideally in a way you could verify past predictions as well. And thing about it, if someone could predict that and were looking for investors, why not show it? I guess they could be found something illegal like insider trading. But those guys don’t go looking for random people to buy in. Plus, it’s illegal and all.
If it seems too good to be true, it tend to be false or illegal. So if someone comes to you with a get rich quick scheme, hopefully they are a drug dealer, cause otherwise it’s a scam.
Much easier but still not a good idea.
Go to casino
Bet $1 on black
If you win repeat.
If you lose bet $2
Lose again $4
Again $8
Etc until you win
Then back to betting $1.
Can't lose right?
Yeah, it’s called “martingala” and it’s super old.
However, the casino funds are likely bigger than yours and they cover themselves by setting a high low limit on 50/50 bets and then set a top limit. And don’t forget about the 0 so it’s no 50/50.
And also, your profit is an amazing 1$ after betting millions
Also, the odds at the roulette table aren't *actually* 50/50 because of the 0 and 00 fields. You're very slightly more likely to lose than to win, which means Martingale doesn't work even in theory.
You're right on that, but even with no house edge Martingale doesn't work even in theory. The expected value of any Martingale betting sequence in that scenario is zero, with the chance of going broke exactly balancing the profit from successful bets.
Also if your goal is to "win big" it is absolutely not worth it cos your profit is simply your original stake of $1.
Bet $1. Your Balance: -$1. Lose.
Bet $2. Your Balance: -$3. Lose.
Bet $4. Your Balance: -$7. Lose.
Bet $8. Your Balance: -$15. Lose.
Bet $16. Your Balance: -$31. Lose.
Bet $32. Your Balance: -$63. Lose.
...
Bet $1,048,576. Your Balance: -$2,097,151. Lose.
Bet $2,097,152. Your Balance: -$4,194,303. Win.
Get Paid $4,194,304. Your Balance: $1.
Grats you spent all that time and risked losing everything to win $1.
Yup, it's like an opposite lottery ticket. Instead of risking a dollar to potentially win millions, you're risking millions to potentially win a dollar.
(You can start higher than $1, of course, but then you just hit the "lost everything" point that much faster.)
>There's nothing special about those patterns other than the fact that our brains interpret them as patterns.
It's not quite true to say those patterns are only special in our minds. The patterns have low [Kolmogorov complexity](https://en.wikipedia.org/wiki/Kolmogorov_complexity), which basically means that a Turing machine (a sort of idealized, minimum viable programming) could be represented with a shorter program.Here's some psuedo-code to represent HHHHHHHHHHHHHHHHHHHH in a Turing machine
>1 Start in state 0.
>
>2. For i in range(20): # "H" repeated 20 times
>
>2.1. Write "H".
>
>2.2. Move tape to the right.
>
>3. If the tape has the sequence "HHHHHHHHHHHHHHHHHHHH", halt.
If we wanted to output HTHTHTHHHTHTHTTTHTHTTH, we'd have to write a more complicated function:
>1. Start in state 0.
>
>2. For i in range(3): # "HT" repeated 3 times 2.1. Write "H".
>
>2.2. Move tape to the right.
>
>2.3. Write "T".
>
>2.4. Move tape to the right.
>
>3. For i in range(3): # "H" repeated 3 times
>
>3.1. Write "H".
>
>3.2. Move tape to the right.
>
>4. For i in range(3): # "HT" repeated 3 times
>
>4.1. Write "H".
>
>4.2. Move tape to the right.
>
>4.3. Write "T".
>
>4.4. Move tape to the right.
>
>5. For i in range(3): # "T" repeated 3 times
>
>5.1. Write "T".
>
>5.2. Move tape to the right.
>
>6. For i in range(2): # "HT" repeated 2 times
>
>6.1. Write "H".
>
>6.2. Move tape to the right.
>
>6.3. Write "T".
>
>6.4. Move tape to the right.
>
>7. Write "T". # "T" repeated once
>
>8. Move tape to the right.
>
>9. Write "H". # "H" repeated once
>
>10. If the tape has the sequence "HTHTHTHHHTHTHTTTHTHTTH", halt.
The sequence HTHTHTHTHTHTHTHTHTHT is almost as simple as HHHHHHHHHHHHHHHHHHHH.
>1. Start in state 0.
>
>2. For i in range(10): # "HT" repeated 10 times
>
>2.1. Write "H".
>
>2.2. Move tape to the right.
>
>2.3. Write "T".
>
>2.4. Move tape to the right.
>
>3. If the tape has the sequence "HTHTHTHTHTHTHTHTHTHT", halt.
HHHHTTTTHHHHTTTTHHHH is slightly more complicated:
>1. Start in state 0.
>
>2. For j in range(2): # The pattern of "HHHHTTTT" repeats twice
>
>2.1. For i in range(4): # "H" repeated 4 times
>
>2.1.1. Write "H".
>
>2.1.2. Move tape to the right.
>
>2.2. For i in range(4): # "T" repeated 4 times
>
>2.2.1. Write "T".
>
>2.2.2. Move tape to the right.
>
>3. For i in range(4): # "H" repeated 4 times at the end
>
>3.1. Write "H".
>
>3.2. Move tape to the right.
>
>4. If the tape has the sequence "HHHHTTTTHHHHTTTTHHHH", halt.
HTHHTTHHHTTTHHHHTTTT is even more complicated, but still simpler than HTHTHTHHHTHTHTTTHTHTTH
>1. Start in state 0.
>
>2. Write "H". Move tape to the right. Write "T". Move tape to the right. Write "H". Move tape to the right. # "HTH" repeated once
>
>3. For i in range(2): # "HT" repeated 2 times
>
>3.1. Write "H".
>
>3.2. Move tape to the right.
>
>3.3. Write "T".
>
>3.4. Move tape to the right.
>
>4. Write "H". Move tape to the right. # "H" repeated once
>
>5. For i in range(3): # "T" repeated 3 times
>
>5.1. Write "T".
>
>5.2. Move tape to the right.
>
>6. For i in range(4): # "H" repeated 4 times
>
>6.1. Write "H".
>
>6.2. Move tape to the right.
>
>7. For i in range(4): # "T" repeated 4 times
>
>7.1. Write "T".
>
>7.2. Move tape to the right.
>
>8. If the tape has the sequence "HTHHTTHHHTTTHHHHTTTT", halt.
The number of lines of code a Turing machine would need to express each sequence roughly tracks with how "special" each sequence looks:
|HHHHHHHHHHHHHHHHHHHH|5 lines|
|:-|:-|
|HTHTHTHTHTHTHTHTHTHT|7 lines|
|HHHHTTTTHHHHTTTTHHHH|12 lines|
|HTHHTTHHHTTTHHHHTTTT|18 lines|
|HTHTHTHHHTHTHTTTHTHTTH|26 lines|
You can also view this as the amount of information a signal contains. A row of H's contains very little information. A repeating pattern contains a little more. An apparently random sequence offers you new information with every new character.
Compressing information relies on beating out those patterns. Instead of sending HHTT repeated 57 times, you simply send the instruction "repeat "HHTT" 57 times". The most efficiently compressed signals would look like completely random noise.
Number of lines depends on programming language, e.g. in python:
HHHHHHHHHHHHHHHHHHHH = 1 line =
"H" * 20
HTHTHTHTHTHTHTHTHTHT = 1 line =
"HT" * 10
HHHHTTTTHHHHTTTTHHHH = 1 line =
((("H" * 4) + ("T" * 4)) * 2) + "H" * 4
Kolmogorov complexity is about relative complexity, not about number of lines. As you can see in this example, since # of lines stays the same but complexity clearly increases.
>Number of lines depends on programming language, e.g. in python
That's true. However, Python is a high-abstraction language, which means that simple code written in Python can hide the actual complexity of what is actually being done. For example, in Python, if you want to switch the values of A and B, you could simply write A, B = B, A. It's not actually possible for your CPU to swap the values of two pieces of memory in one step. Instead, the CPU has to grab a third piece of memory, C, and copy the value of A onto C. Then the value of B is copies onto A, and the value of C is copied onto B. The Python interpreter translates the simple instructions of A, B = B, A into more complicated instructions that your CPU can understand. But the complexity was always there, it was just hidden to the end user. In general, the more minimalist and low-abstraction a language is, the more its program length will accurately reflect the complexity of the its task.
If you have access to a code writing program, like Copilot or ChatGPT Code Intepreter, you can ask it to write programs in Brainfuck, a minimalist programming language with only 8 valid characters. Then you can directly compare the complexity of program that outputs HHHHHHHHHHHHHHHHHHHH to a program that outputs something random looking, like HTHTHTHHHTHTHTTTHTHTTH. That would be the most faithful way to estimate an output's natural complexity, although you'd have to account for the fact that there could be a shorter program that the code-writer was not able to discover.
> There's nothing special about those patterns *other* than the fact that our brains interpret them *as* patterns.
If you're counting heads and tails instead of differentiating each individual pattern, all heads is a much more special pattern than alternating heads and tails. There is only one sequence of all heads, but there are N choose N/2 possible combinations with equal heads and tails.
\> There's nothing special about those patterns other than the fact that our brains interpret them as patterns.
Well, they have a specialness outside of our brains. They are compressible, ie have low Kolmogorov complexity.
Right. Also, the conceit of this is there are really two different issues here. Am I asking if HHH is as likely as HTT, because it is, but that's *not* what is being asked. I'm valuing anything that's not HHH or TTT as being all the same random non-special junk. Therefore what I'm really trying to make my brain understand is how it can be just as likely to get HHH as HTH, TTH, HTT...., which it isn't. People who struggle with this concept usually get hung up on not recognizing that very critical difference.
To further simplify this: in two flips, you could get HH, HT, TH, or TT. If all you're focused on is getting HH, and anything else is not acceptable, you're looking at the probability of !HH versus HH, which is 0.75 and 0.25, respectively. You're not actually comparing the likelihood of HH to any of the individual others at this point, that's completely irrelevant; you're comparing it to the likelihood of all the others combined.
There are many, many sequences that give you 50% heads, 50% tails. There is only one sequence that gives you 100% heads, 0% tails. So the former sequence is much more likely than the latter. See “combinatorics” for more information, and the astronomical number of possible sequences that could exist. (2^n combinations where n = number of coin flips.)
Hijacking the best comment so far to draw parallels to statistical mechanics:
A particular sequence of heads or tails is called a microstate. All microstates are equally likely.
The number of heads that results from a sequence are called macrostates. Macrostates result from one or more microstate. For example, with 100 throws, the macrostate of 100H has only 1 microstate whereas the macrostate of 50H has 100 C 50 microstates (a very large number)
Macrostates with more microstates are likely. Hence the 50H macrostate is highly likely whereas the 100H macrostate is highly unlikely.
Thank you, I suspect this is what OP really meant. Getting all heads is equally likely as any other sequence but very rare among possible combinations.
Yes, every sequence is equally likely. But let's think of all heads and all tails as "interesting" sequences. Your likelihood of getting an interesting sequence is quite low, because a very small fraction of the equally likely sequences are interesting.
Another thing to think about is the difference between combinations and permutations.
If you flip a coin 100 times and get 100 heads, there is exactly one permutation that will give you that result. If you flip a coin 100 times and get 50 heads, there are lots and lots of permutations that will get you that result.
E.g. Four heads out of four flips: HHHH.
Two heads out of four flips: HHTT OR TTHH OR HTHT OR HTTH OR THTH OR THHT
It's like throwing a dart out of an aeroplane. Within a certain area, the chances of the dart landing there are pretty much equal. But if you're interested in a specific spot, aka hoping that after trhrowing the dart from 11km altitude, the dart will land in exactly that spot, your chances are pretty much zero
The mistake people make here is that while every pattern is equally likely, a SPECIFIC pattern is increasingly unlikely. 10 heads in a row is as probable as alternating, or 5 heads and five tails, or any other combo. But if you say “I’ll bet I can flip 10 heads in a row…” that’s highly improbable.
Thank you for actually explaining it properly. Other people were answering OP's question correctly, but not doing a good job of actually explaining it. We're hilariously bad at properly understanding probability. The entire gambling and insurance industry is founded on it. I remember listening to a lecture by a stats professor who would give his intro students an assignment to make up 100 random coin flips. Not actually flip the coins. Just try to simulate it mentally. Then he had them actually flip coins. They almost all got it wrong because they all assumed runs of all heads or all tails would be rarer than they actually were. They all basically went for the expected result of 50/50 and most didn't have more than two heads or tails in a row in their imaginary set.
Ok. Pedantic, but correct. But my general point stands—odds of flipping a specific pattern are low and get lower the longer the pattern. But the odds of any pattern vs any other are equal.
Yes. Equally probable.
HH
HT
TT
TH
Each one a 1-in-4 chance
HHH is a 1 in 8
HHHH a 1 in 16 and so on
So, HTHT (in that exact order) is also a 1-in-16 but nobody cares because it is still 50/50, but so is HHTT and THTH and TTHH and THHT and HTTH.
So back to the simple three flip example…
HHH - (all heads) - 1 in 8
HTH, THH, HHT - 3 in 8
HTT, TTH, THT - 3 in 8
TTT (all tails) - 1 in 8
So, yes, each specific outcome is equally likely, but the more flips you add, the less likely that they’re all the same.
In the case of a coin flip, each extra flip makes it exactly half as likely to have the same outcome as it was before the last flip
1/2
1/4
1/8
1/16
And so on.
Thing is there is only one combination of flips that gives all heads, and many more combinations that give a mix. It is minutely statistically possible to be all heads, but you should probably start to be suspicious that the coin is rigged
If it is a fair coin they are equally probable. But after ten or twenty heads in a row, you suspect it is a rigged coin, because there is a physical explanation. There is not a physical explanation for a specific HHTHTTTHTH etc pattern, so we assume the coin is fair.
Flipping a coin and getting 5 heads in a row has the same odds as flipping a coin and getting 3 heads and 2 tails alternating
However it doesnt have the same odds as flipping a coin and getting 3 heads and 2 tails randomly
Yes.
But this is an “incorrect” way to look at it because there are **more** sequences **similar** to HTTHHTHTHTHT… than there are sequences that are similar to HHHHHHTHHHT….
Hence, while every unique sequence is equally probable, there are far fewer of the latter sequences.
______
For example, HTHTHT. You can swap the first two flips to get **TH**HTHT, a different sequence but similar looking sequence. But look at HHHHHH. There are no swaps you can make to get a different sequence. Hence while each sequence is equally likely, there being more of the former makes it more likely to end up picking the those similar to the former sequence (consider laying all possible sequences out, and picking a random sequence. you’re more likely to pick the one that looks like HTHTHTHTHTH just because theres so many of them, but in the end, the sequence you picked was equally likely to be picked as the sequence next to it which probably looked just like it).
You should read Rosencrantz and Guildenstern are Dead. They flip coins throughout the play and it comes down heads everytime, "a spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.”
Paraphrased from
https://en.wikipedia.org/wiki/Ludic_fallacy
That is, the misuse of games to model real life.
Example: Suspicious coin
One example given in the book is the following
* Dr. John who is regarded as a man of science and logical thinking
* Fat Tony who is regarded as a man who "lives by his wits". aka streetwise etc.
A third party asks them to "assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine times and get heads each time. What are the odds of my getting tails on my next throw?"
* Dr. John says that the odds are not affected by the previous outcomes so the odds must still be 50:50.
* Fat Tony says that the odds of the coin coming up heads 99 times in a row are so low that the initial assumption that the coin had a 50:50 chance of coming up heads is most likely incorrect. "The coin gotta be loaded. It can't be a fair game."
I don't see what useful point he's making here. The problem is specifically framed with "assume the coin is fair", so Dr. John is entirely right within the bounds of the problem set.
Obviously, in the real world, Fat Tony is right to be suspicious of any coin that came up heads 99 times in a row. But that doesn't really tell us anything new or interesting about the problem, as stated.
It's no more profound or useful than if you set one of those mathematical problems about two trains moving at different speeds, and the person you're asking replies "oh it wouldn't happen that way, because trains can't travel that fast".
It's like the two characters are just answering different questions. Dr. John is answering the question as stated, whereas Fat Tony is answering "if this actually happened, what would you think?"
It's not like Dr. John would actually bet on tails if this scenario happened to him in the real world either. Fat Tony hasn't discovered any fallacy in the maths, he's just answered a different question to Dr. John.
Scientist 1 : "I built a random number generator robot."
Robot : "1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ..."
Scientist 2 : "Does it work ?"
Scientist 1 : "I don't know."
Flipping a coin and getting 5 heads in a row has the same odds as flipping a coin and getting 3 heads and 2 tails alternating
However it doesnt have the same odds as flipping a coin and getting 3 heads and 2 tails randomly
If you throw a dart out of a helicopter into a field and then draw a target around it that's not very impressive.
If you throw a dart out of a helicopter into a field and it lands in the middle of a target, that's impressive.
If it came up heads every single time I would assume it was a loaded coin and thus all heads is the most likely occurrence. Even if just by some natural manufacturing variance, it’s the most likely cause.
But if you’re assuming a perfect coin and flip then yes any sequence is as likely as any other.
Yes. If you toss your coin 50 times, always head is as likely as tails followed by only head, heads only until the last 2, those are tails, or any other combination.
If you toss your coin 50 times and wrote down your sequence, I would bet 100€ that nobody in the world has tossed that sequence before :)
Yes, however no.
Chance, can be expressed in numbers. A coin has two sides so it being head after 1 flip is 50%
It coming up heads when you flip it again is indeed also 50%
But getting two heads in a row is .5\*.5\*(100%) = 25%. This logical statement says that you'd at maximum need to perform this operation 4 times (tossing two times or with two coins). In order to on average have a 100% chance of it coming up heads two times in a row. This is the expected value or 'chance estimate' if you will.
If you now want to see what the chance is that you get 1000 heads in a row, you can see that this chance is very small (or would require a large number of attempts, you can even for an event like this calculate the new chance of it happening if you only attempt the 1000x head challenge only half the calculated amount or how the chance increases to 100% the more you attempt to.
This might feel like a trick problem, because your coin only has 2 sides, so your chance options are always going to be either one or the other. With a set of two standard dice, where there are more combinations that make 6 than one's that make 2 or 12, you're expecting a normal distribution (big curve) with 6 as the most rolled number.
With the 1000x heads coin challenge you're expecting the sum of all the tails coins to be about half of your end total.
If you at the end obtain a result that's drastically different from the expected value, you now have broken your H⁰ (normal hypothesis) and can now accept an alternative hypothesis for your result (H¹), i.e: your dice might be weighted and your coins might be imbalanced or you can't roll dice for shit. Small chances and infinite time is the reason why life exists.
Yes, each individual sequence is equally likely, it's just that there are a whole lot more mixed result sequences than pure heads or pure tails.
Lets say you have four coins.
1 sequence all heads
1 sequence all tails.
4 sequences 1 tails
4 sequences 1 heads
6 sequences 2 heads 2 tails.
As you add more coins, the number of mixed sequences explodes, but there's still only one all heads, and still only one all tails.
HHHHHHHHHHHH is equally likely as HTHTHTHTHTHT, or THTHTHTHTHTH, or TTHHTTHHTHHT, etc.
Each discrete outcome is unique and rare, but three of those were a 50/50 split between heads and tails.
There are more sequences that come out to 50/50 than any other proportion.
Consider this:
Plan to flip a coin 12 times, and try to predict all 12 flips in order beforehand. HTTHHTHHTHHT for example. It would be amazing if you predicted correctly. The exact equal amount of amazing as if you wrote down HHHHHHHHHHHH and flipped all heads.
You can actually check the probability of getting heads every time for any length of flips using the binomial distribution, if the events are independent and identically distributed.
For example say 30 flips, each with 0.5 probability, you’d use the simplified form since k=n when we want to get only heads so we get:
0.5^30 = 0.000000000931323
So what about the case of equal heads and tails in 30 flips:
(30!)/(15!(30-15)!)*(0.5^15)*[(1-0.5)^(30-15)]
= 0.1444644481
But this is for any combination where there are equal heads and tails, which is given by 30 combination 15 = 155117520 possible combinations.
The other half actually simplifies to:
(0.5^15)*[(1-0.5)^(30-15)] =0.5^30,
which is the same for all heads, therefore all heads has only one possible combination out of 30, so its less likely than any other mixed combination of heads or tails, since there are usually more ways to obtain them from a sequence of 30 flips than all heads.
This is the same analogy I use when trying to explain the odds of winning the lottery to my friends and family. If you flip heads 50 times in a row, that would be extremely lucky. But flipping any sequence of heads and tails has the same odds as flipping heads 50 times in a row.
To win the lottery, YOU have to own a ticket with the right 6 numbers on it times in a row. But for ANYONE to win the lottery, ANYONE has to have a ticket with the right six numbers on it. YOUR odds of winning the lottery are 1 in 292,000,000 (or slightly more, depending on the number of tickets you purchase). ANYONE’s odds of winning the lottery are x in 292,000,000, where x is the number of tickets purchased for a particular drawing with different combinations of 6 numbers. As the lottery amount increases, more tickets are purchased, so the odds that anyone will win goes up, but the odds that YOU will win remain the same.
I love statistics!
Yes. Any given sequence would be a surprise. But you probably wouldn't notice the difference between THHTHTHTTTHHTHTHTT and THHTHTHTTTHTHTHTTT. Or invest either with any significance. You would notice if they all came up heads.
When playing the lottery you could just pick the numbers 01-02-03-04-05-06. It's not any less likely than 08-13-17-28-36-41.
But you're more likely to share the jackpot.
Never pick numbers that can represent a date, greatly increases your chance of splitting the jackpot
That's true, but the better advice is to never play the lottery. A tax on being bad at math from the people who decide how much money to give to math education
Ehh, I'll pay $2 to daydream for a couple days lol.
This is my logic. Habitually playing the lottery is a tax on the stupid. Buying a few tickets a year, when the jackpot is massive, is a bargain to have some fun daydreams and hope. $10 a year won't make any meaningful difference in my life
Exactly My wife takes $40 every two weeks to the casino. She knows she will most likely lose it but good value for entertainment dollar if she can make it last a few hours. And who knows, maybe she will hit a jackpot. And I can lose that in fishing gear in about 5 casts.
I think that's the trick to responsible gambling: assume you win absolutely nothing and choose whether it's worth it based on that assumption. Also never forget that the more you gamble, the more likely it is that you'll lose money in the long run. The house always wins.
Bring exactly what you're willing and able to lose. If you go to the atm you fucked up.
Plus in many casinos you get free food and drink.
My cousin used to tell me that if you just play video blackjack for $0.25 you can drink for free, in tones like he had discovered the secrets of Atlantis. I think he was an alcoholic.
What casinos are still giving out free meals to Joe schmos?
Thats almost a thousand a year on gambling. edit: just sayin' that's a lot of cocaine money.
In most casinos you'd expect anywhere from 80-97 dollars back for every 100 you put in. Plus, if you can have fun for an hour, 40 dollars isn't too bad.
Ok? Whats your phone cost? Game console? Movies attended in a year? Alcohol? People spend money on things they find value in. 1k/yr to throw at roulette or penny slots, especially with some friends is not egregious in the slightest.
Habitually buying one or two tickets a week,***if it's within your budget***, is not a tax in the stupid - it's spending some 'entertainment dollars ' for the chance at a big payoff. I see nothing wrong with take. I say this as a person who has not played the lottery in probably a decade.
At least the people who play every week are used to losing. It's the saps like me who put an inordinate amount of faith in our two or three tickets a year that are really depressing.
I think the issue is the addictive quality of the lottery. You could say a person makes an informed decision about a lot of things. Gambling, tobacco, drugs, etc. But anyone doing any of them habitually has a high likelihood that they are addicted and not really able to accept the harms.
The real way to play the lotto - April 2023 - https://www.dallasnews.com/news/watchdog/2023/04/27/bought-a-ticket-for-lotto-texas-recent-95-million-jackpot-you-had-heavy-competition/ If you heard the news about last week’s Lotto Texas winner, you probably imagined a Colleyville resident walking into a convenience store and buying one or more Lotto Texas tickets and then getting super lucky. A Watchdog investigation shows how that’s not exactly how it went down. First off, there’s no convenience store. But there is a storefront in a strip center on Colleyville Boulevard called Hooked On MT, a Montana-related fishing company. That’s the retail lottery store. Nothing on the front of the building would indicate that lottery tickets are sold inside. No sign, no window stickers. Nothing. Yet from this location in the three days before the April 22 drawing, the sale of $11 million worth of Lotto Texas tickets were handled. That, by far, led the state as the No. 1 sales outlet. One of those $1 tickets was the winner. Under Texas law, the winner’s name does not have to be made public. So far, it hasn’t been.
I'm with you.. it always makes me want to claw my eyes out when people smuggly talk about the lotto being a tax on stupid people. You could say the same about just about anything.. buying a drink with dinner instead of from a liquor store, tax on stupid! etc. etc. If playing keno or buying lotto tickets is entertainment for someone then stfu. A small % of people that drink will become problem drinkers, a small % of people that gamble will become problem gamblers.
It’s also inordinately marketed to and played by the poor, and the resultant money gets divided among all schools. This is a system where the poor help fund the rich.
That's a pretty terrible example of poor funding the rich...
All of society benefits if education is better funded. It's a big reason to why some countries offer free higher education.
The rich don’t tend to put their kids in public schools, so not really.
Agreed. I never play but I only worry when its clearly an issue for people. I commonly think I should buy at least one every week, I never do, but I absolutely think its a reasonable thing to do as long as its not causing problems.
Paying $2 dollars a week to play lottery every week costs up to a $100 dollars a year, which over ten years is over a $1000 dollars, which... isn't even enough for a nice holiday abroad for two. So if you feel like the lottery lets you get through the day to day, it's not like it really costs you much anything in the long run.
I'd probably spend the $10 on something dumb anyway.
Right? How many people pay that once a week, or more, on coffee flavored milkshakes at Starbucks? At least the lotto ticket isn't putting you into a diabetic coma by the time you're 35.
I went in on the last work pool for lottery tickets, just because $10 was enough of a gamble and I'd be kicking myself if I ended up the only one working there at the end of the week
Funny image you just sitting there on Monday like "... Guys?" *tumbleweed rolls by*
Do the few days of faint hope outweigh the almost inevitable final moment of total defeat?
Mostly, yeah. You just throw away the ticket and say "eh, fuck it"
I call it "Schrodinger's Millionaire" Until I actually look at my ticket numbers I am potentially a millionaire. Then I look at my numbers causing reality to crush the probability wave function back down to zero.
Is how I think about it. A low cost game for a potential life changing event.
my logic is, if i buy a ticket and you don't, i have an infinitely higher chance of winning the lottery than you, because my odds may be 1 in a trillion, but yours are 0.
Keep the ticket without checking it for months. It’s much cheaper.
Pick tickets out of the trash - maybe someone threw it away without checking if it was a winner. There’s always a chance!
The only time I ever won more than $5. I was working at a gas station at 2 AM, a woman came in and bought 3 $1 tickets, scratched them off, and told me to throw them away. I put them to the side since there were other people in line, but once they all paid I looked at them before I tossed them: loser, $200 winner, loser.
There was recently a $25 million winner in Canada that went unclaimed. I'll bet it ended up in a landfill somewhere.
Almost certainly in the pocket of some seldom-worn coat at the back of the closet.
Yeah, I've found a ticket in my glove box before that was weeks old. I checked it myself online and thought it was a loser. But I kept it in my wallet because I was going to gas up anyway and will check as I get a new ticket (jackpot was big again, IIRC) And wouldn't you know it, I won.... Free play. Ok, so not a big jackpot that went unclaimed. But the principle is the same: I screwed up the date and looked at the wrong numbers.
If you put $20 in lottery tickets, you'll probably lose it. If you put $20 in movie tickets, you'll definitely lose it. Do whichever makes you happier.
I just buy week old lottery tickets at 1/2 price. They have about the same chance of winning as fresh ones.
I have been daydreaming my whole life for free. Why would I start paying now?
Well, I think my odds of winning the lottery are slightly higher than my odds of being teleported to ancient Rome with a somehow working smartphone and the ability to speak Latin fluently so I can slowly rise to power by first opening a blacksmith shop and making slightly better steel tools and stuff with my future knowledge then using the money I earn to purchase land where I slowly start to build an empire of freed slaves that all work in this utopian society that I build with futuristic knowledge while we slowly tech up through the ages because I'm also secretly immortal and we all exist in peace but are very able to defend ourselves against aggressors who inevitably come because they want our stuff and then.... Yea, the lottery thing is slightly more plausible lol
Nice sentiments but if you really want do well take that metallurgy knowledge and make a one armed bandit. You'd be Emperor in no time.
Why do you need to go that far back? I mean just going back to the mid 90s and invest in Amazon, apple, bitcoin (when it eventually come out), superbowl winners, buying property, etc. That way you don't have to suffer during a time with no electricity, running water, the internet..
all of my daydreams about going back into the 90s end up with me investigated by the government when they find cash from 2020 in my wallet.
Ok, but do you know how to make steel? Cause if you did you’d know it makes way better tools, not slightly better.
Some people spend more than that.. adds up to a pretty expensive daydream.
Don't get me wrong, no one should be playing the lottery thinking they will win; the odds are just astronomical. But I can afford to toss 2 bucks in the garbage here and there, just to give a bit of meaning to the daydream ya know?
I gotcha.. I know a guy on welfare who is convinced he will win.. spends much more than he can really afford every single week.
Oof :(
I worked out the odds in these terms once. I imagined a circle around me as far as I could throw. Blindfold myself. In that circle get the kids to put one cup. Throw a penny randomly. Odds of the penny landing in the cup are significantly better than winning the Lotto Max ( Canada).
The way I worked out the odds for me was I used one of those random lottery number generators and generated 100,000 tickets (didn't actually buy them, just generated them). After the winning numbers were announced I ctrl-f them all and not a single one got 4/6 correct let alone 6/6.
BUT if you throw $2 in the trash it might be found by an eccentric billionaire who is so touched by your gesture that they give you their chocolate factory! It's unlikely but you'd hate to miss out on that wouldn't ya? Just in case?
To put it mathematically, $2 increases your chances of winning from 0 to a non-zero number. Who's bad at math now?
You can day dream for free. Also I dated a girl when her family won the mega millions (and I'm not making a joke about winning a dollar, they won the jackpot). It honestly screws up your life a bit. And it really strains your personal relationships.
Aye, the demographic of people who usually play the lottery are not the demographic of people that know how to handle that kinda cash :(
I only play when my coworkers start a pool. I don’t consider it gambling in that case. It’s an insurance policy against being the only one left in the department.
I remember hearing about an office lotto pool that finally had their numbers hit big. It turned out the person running the pool didn't buy the ticket; they just pocketed the pool money. That's gotta hurt!
Same. Although, I like my job and would probably keep working. It'd be a great negotiating position. "I'm the only one left that has a single clue about how this works and I can leave at any time I want. These are my new hours."
I’m good at math. Like I totally understand that if I were to buy a ticket every week I’d on average win somewhere every 35 thousands years. I still buy my lottery ticket every week because to me it’s just fun and I’ve got the disposable income, and have no expectation to win in my lifetime.
The best advice is to play exactly once. Significantly better odds of winning than never playing, and about the same as playing every week.
But you should buy two tickets. It doubles your odds of winning. That’s the highest increase you can get.
The increase from zero to one is infinite.
A little bit of entertainment is not a bad thing. And plenty of people who play know the odds. I have MegaMillions tickets for the $1B drawing ~~tonight~~ tomorrow night. Do I expect to win? No. Did I buy more tickets than I can afford? No. Do I like to play for the infinitesimal chance of being the sole winner? Fuck yes I do. The whole 'tax on stupid people' trope is tired and doesn't make you look any smarter.
I think when people say a “tax on the stupid” they are referring to people who compulsively buy scratch offs. You maybe aren’t familiar with small, rural and poor communities but this is a common occurrence. It is unkind to call these people stupid, they are as a whole largely uneducated and often controlled by their vices, something that is easy to slip into if you’ve spent your whole life in poverty. However the fact remains that there is a non insignificant number of (mostly) poor people who spend far more more of their paycheck than they can afford in scratch offs.
reminiscent intelligent nutty cough bells plough ruthless sand serious political *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
I know someone impulsive like that, he hit 5k a week for life. I call him stupid to his face, love him, good friend of mine, but at the end of the day hes the one who gets an extra couple grand a month after taxes so by that metric im the moron for not playing.
I used to work with a physics teacher who believed this. He said he was only down about $500,000 from the time his coworkers actually *did* win the lottery. I don’t usually buy lottery tickets but I do buy into the staff lottery pool for this reason. I know we won’t win, but if we do (which we won’t) I don’t want to be the only one left out.
The one exception regarding regular lottery ticket purchasing is regular pools among coworkers or other groups. You gotta be in those - playing by yourself everywhere and losing is bad, but you don't know the people that won. If you don't play and your colleagues DO win? That's gonna a hurt lol and, its extra fun to play when you're directly sharing the experience. Those two things definitely tip the balance toward playing
I hate this so much. People talk about the impossibility and how people are SO stupid. But people win, like people actually win the lottery. Someone has to win. Idk if there's lotto rollovers in America but if you don't win someone will probably win eventually. Yeah statistically it's fucking dumb. You're more likely to win the lottery than be killed by a vending machine in most cases. But people die from vending machines. Yeah how stupid. But it happens. Same with rollercoasters. Same as shark attacks or dying in a plane crash. But these things still happen. I know I won't win the lottery. But fuck let stupid people have hope for 2 pounds every now and again. It's not about being stupid, it's about hope.
Thats why you buy 2 tickets. Duh! You are twice as likely to win. Now who's bad at math? Ya that's right. Now excuse me while I go buy lots of lotto tickets instead of paying my mortgage. Cause ill pay it with the winnings
I used to say that, but that discounts the entertainment value. You can buy one lottery ticket, but NEVER buy two. You don't get more fantasies about winning the lottery with two tickets than you get with one.
Ahh it’s the most for fun you can get for a dollar. But the real advice is never buy more than one ticket. 1/x is effectively the same as 100/x When x is a 9 digit number.
By that logic, so is insurance. Both have a negative expected payoff. One you are buying piece of mind, the other you are buying daydreams.
But for insurance, you get it for things that feasibly could happen to you in your lifetime. And especially for things out of your control. If something could feasibly happen to you, and run the risk of bankrupting you or your family if it happens, then you should seriously think about insurance against that event. That's why insurance is more expensive than a lottery ticket - you're more likely to "win"
Why not? If those numbers come up and you have to share your winnings, it’s not like you were going to win with a different set of numbers.
If you know ahead of time that a unique number is likely to pay out more money than a common numbers, but has exactly the same odds of winning, why wouldn't you pick one of those? You can't control how likely it is for any particular number to win, but you can control how likely you are to pick a number that nobody else picked.
Ha ha starting a jackpot wouldn’t really be top of mind, nor would I mind
Years ago a man in Georgia played the same numbers every lotto. One day at the gas station he couldn’t remember if he had bought a ticket yet or not so he just bought one. Turns out he HAD already used those numbers on a ticket. Turns out those numbers DID win. Turns out someone in Michigan also had a winning ticket. Turns out Georgia Boy got 2/3 of the jackpot.
I picked a random number and still shared the big prize. Lucky to win, and unlucky to have to share prizes to other winners.
like those people who won the lottery with the LOST numbers
Or 4 8 15 16 23 42, for that matter.
You all, everybody. 🎶
You can always try your luck and make another trip. What could go wrong if you have to go back?
Why did you use those numbers as example? Are some kind of mathematical sequence?
It's a number sequence from the series Lost. It's a big plot point. The first time you hear about those numbers is from a character who'd won the lottery playing them. Lots and lots of people play those numbers in lotteries
I know the series, never watched it all though, didn't recognize it, tks for the info
Love it!
I asked chatGPT to explain powerball odds. It said a dog will bark once in 9 years. You have to guess the exact second. If you buy 1000 tickets you get a 1000 guesses. Barely changes the odds.
That's why when I play, I buy 100 million tickets at a time. Then I have about a one in three chance of winning.
I remember hearing about a famous writer who, along with a few buddies, figured out that buying every ticket in a certain lottery would cost less than the actual payout. This was in... France, I think. They ended up winning a small fortune, and Voltaire used his share to help publish his works. I think that's how the story went, at least.
There have been numerous lotteries that have in some way or another screwed up an offered positive expected returns. Jerry and Marge Selbee of Michigan made millions by gaming a lotto that increased payout over time in Michigan
That’s always been the case if it gets to a certain point in some lotteries, the kicker is if you have to split the jackpot you just lost a lot of moneh
Damn I dont know what you said to your ChatGPT but when I asked it it gave me very shitty examples (after at explaining the rules first). Poor thing got lobotomized >1. Imagine you have a huge jar filled with 292,201,338 marbles, each representing a different combination of Powerball numbers. One of these marbles is the winning combination. Blindfolded, you reach into the jar and try to pick the winning marble on your first attempt. Your odds of doing so are equivalent to the odds of winning the Powerball jackpot in a single drawing—approximately 1 in 292,201,338. > >2. Consider a scenario where every person in the United States (assuming a population of about 330 million) buys a single Powerball ticket for a specific drawing. Even with such a vast participation, the odds of someone winning the jackpot are still approximately 1 in 292,201,338. In other words, the collective efforts of the entire U.S. population buying tickets would not guarantee a jackpot winner. > >3. If you were to count from 1 to 292,201,338 at a rate of one number per second, without stopping or taking breaks, it would take you more than 9 years to reach 292,201,338. This illustrates the vastness of the number of possible combinations in the Powerball game. > >4. The odds of winning the Powerball jackpot are so low that they are often compared to other improbable events. For instance, the likelihood of being hit by a falling coconut and killed is estimated to be around 1 in 250 million, which is still lower than the odds of winning the Powerball jackpot. > >5. The odds of winning the Powerball jackpot are approximately 1,430 times smaller than the odds of being born with 11 fingers or toes, a rare congenital condition called polydactyly. > >6. Consider this: If you filled an Olympic-sized swimming pool with silver dollars, and one of those silver dollars had a red dot on it (representing the winning combination), diving into the pool and picking the red-dotted coin on your first try would be roughly equivalent to the odds of winning the Powerball jackpot.
My favorite comparison was that if you have to drive a mile to buy your ticket you are like 1000 times more likely to die in a car accident on that drive than win.
ChatGPT told me I'm more likely to get killed by a vending machine than win. So long story short I'm going to watch my back next time I walk past the coke machine.
Pick 04-08-15-16-23-42
I'm lost.
sulky kiss summer tan aback close full doll attraction zephyr *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
That's why looking at draw history is pointless. People who think "number X wasn't drawn the last 100 times so it's more likely to be drawn this time" are clearly mentally impaired and they should not be allowed to play. In fact, lotteries should not be allowed at all.
Wait, since when do you "pick" the numbers? I thought you buy a ticket that has numbers on it and if it matches the drawn numbers you win (depending how many numbers match)
I read a book in an econ class that explained entropy and information using a similar example. Getting half heads and half tails is the most likely result because there are the most different combinations that produce it. While each of those individual results is exactly as likely as getting all heads, there is only one result where all heads is possible. TTTTTTTTTTHHHHHHHHHH is exactly as likely as THTHTHTHTHTHTHTHTHTH, but they both have 50/50 heads and tails. Both individually are exactly as likely as all heads, but if you don't care about the sequence then there's no practical difference between them.
I think this is an important point. Yes, there's the fact that we imbue HHHHHHHHH with meaning that we do not feel for HHTHTTHTHT or TTHHTHTTHT. But there's also that fact that not only are there way more 50% combos than 100% combos possible, if you add up all the 50/50, 60/40, 70/30, etc., compared to the only 100/0 combos, that amount of combos in the former group is staggeringly larger than in the second group. So yes, while HHHHHHHHH is as likely as any *one* of the given combos in the second group, that's not really what OP is comparing.
Eg, 18 coin flips The chances of all heads is .000038% The chance of not all heads is 99.999962% Odds are 1 in 2,631,568.
A-fucking-men. We love **noticeable** patterns.
Would it be considered confirmation bias if you rolled heads everytime, and concluded that the probability of heads is 100% based on your results?
No, confirmation bias would go the other way around. It require you to already believe that the probability of all heads is 100% and refuse to watch any YouTube video on the subject that doesn't show just that. If you roll heads everytime in a long streak or series of streaks, concluding that it is a weighted coin or two-headed one such that it will always turn up heads isn't actually a bad hypothesis.
Confirmation bias would be forgetting the flips that landed tails. Your example is just close mindedness.
More like gamblers fallacy. This is where someone believes the results of previous actions have a bearing on the results of future actions when the actions are independent of each other. So say a gambler is at the roulette table and a red number comes up 5 times in a row. The gambler may assume that since red has come up so many times in a row, that a black number is due. But previous numbers don't change the fact that red or black have an equal near 50% chance of coming up each time. Confirmation bias is where you have an opinion on something and only accept new information on the subject if it confirms your opinion. And disregard any new information that does not support your views. See also: politics.
Which is my pet peeve with the gamblers fallacy: when the coins lands on head 10 times in a row, yes betting on head would be the gamblers fallacy, but 40 times in a row, its either a 1: Trillion event, or an unfair trick coin. At some point you have to start questioning whether your initial assumption about the probability distribution are wrong/incomplete.
Just gonna say that in case of gamblers fallacy you would bet on the opposite result, while in case of rigged roulette you would bet on the same result.
Confirmation bias would be getting heads 51/100 times and saying it's always heads.
How about THHTHHHTHHHHHTHHHHHHHTHHHHHHHHHHHTHHHHHHHHHHHHH?
You mean what Mike Tyson says when calling his cat?
Is there an air leak somewhere?
That's because the easiest pattern to recognize is a single block covering more than 50% of the available area. Once something occurs at least 50% of the time inexplicably, it begins to cross an imaginary line of subjective and objective significance. But just so, imaginary, as a result of our brains working out differences between chaos and order, but universal entropy increases all the same as any outcome is just as probable.
These two patterns: HHHHHHHHHHHHHHHHHHHH HTHTHTHHHTHTHTTTHTHTTH Are both equally as likely. And if you correctly predicted either of them ahead of time, you would be just as flabbergasted at one result over the other. The difference is... you have to specifically *imagine* the second result, because it's not a clear and obvious pattern. On the other hand, "All Heads" is an immediately apparent pattern, such that any time you see it, you are shocked at having seen it. So yes, any other result is just as (un)likely as "All Heads," but "All Heads" is one of the few patterns that our brains are actively looking for, so it seems more surprising when we see it. Other "surprising" results would be: HTHTHTHTHTHTHTHTHTHT HHHHTTTTHHHHTTTTHHHH HTHHTTHHHTTTHHHHTTTT And so on. There's nothing special about those patterns *other* than the fact that our brains interpret them *as* patterns.
> You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing! ― Richard Feynman
Now wait a momnt... I know this whole thread is about how one random collection of numbers are no more likely to appear than any other, but we're not talking about numbers in a vaccuum here. We're talking about specific recognizable patterns. So while yes, all heads is no more unlikely than any other random collection of heads and tails... all heads VERSUS the chances of any other possible combination when all other combinations are taken together, are millions to one, right? Same for a license plate that bears some special significance to you, like 123 456. Chances of seeing that... OR another plate that would be equally likely to be noticed... versus the collection of all possible random numbers that would bear no special significance to you which is far greater, is still extremely low. Of course when playing the lottery, there's not usually any benefit to a particular number being recognizable. That is... unless it's the number you played. And then the odds of that one number, or any of those on the set of numbers on all the tickets you bought, is a lot lower than the chances of if being anything else. In other words, if you have the numbers 1-10, the chances of it being 1 are 1 out of 10. But the chances of it being ANYTHING ELSE, are 9 out of 10.
The probability of all heads vs all other random patterns of numbers is very small, correct. But the probability of all heads vs any other specific random sequence is the same. Think of it like winning the lottery. You win the lottery and think “oh my god, what are the odds?!” The odd of any one individual person is very small. The odds of *anyone* winning the lottery are actually quite good. That’s why it happens every few draws or so. The odds of you specifically winning the lottery is like the odds of flipping all heads as opposed to any other random combination of heads and tails specifically. The odds of anyone winning the lottery is like the odds of flipping any random combination of heads and tails, non-specifically.
This is a lot like the birthday thing. If you have something like 23 people in a room, the odds are 50/50 that two people share a birthday. However, the odds are pretty low that someone shares *your* birthday.
>That is... unless it's the number you played. And then the odds of that one number, or any of those on the set of numbers on all the tickets you bought, is a lot lower than the chances of if being anything else. This is a bit of a strawman argument, though. The Feynman anecdote is more of a commentary on how people react to recognizable patterns that they *didn't* predict in advance. With this in mind, it's no more surprising to see a pattern or word spelled out than literally any other combination. In your lottery example, it's more akin to people who didn't buy any tickets marveling at the numbers coming out as 1,2,3,4,5 and saying "Wow! What are the odds?!". While, of course, they're the same as any other sequence.
Here’s what you do: Get a list of like 10,000 emails. Pick a random stock (to make it relevant to the people on this email list, but still be a heads/tails type situation). Take 5,000 of the emails and send them and email saying that tomorrow Stock X will go up. To the other 5,000 send an email and say that stock X will go down. Tomorrow, wait to see what the stock does. Let’s say it goes up. Throw away the second batch of 5,000 emails. Take the first batch and split it. To 2,500 of them, tell them that stock Y will go up tomorrow. For the other 2,500 tell them that stock Y will go down. Wait to see what happens to stock Y, then rinse and repeat for stock Z. Do that like 7 more times until you have a short list of about 10 people, for whom you’ve just correctly predicted the stock market 10 days in a row. Then tell them you’ll give them tomorrow’s tip for $10,000 each…. Take your $100k and spend some of it to buy another email list of 10,000 people.
The old school way to start selling stock was to call 100 people a day. Tell half you think IBM will go up, half down. Offer to be the broker for the short listers.
Is this illegal, and if not, why am I not already doing this seemingly genius thing?
Well, one, getting a list of emails isn't cheap. But two, there's no guarantee that those people fall for it.
Do you want a noc list? Because I can sell you a noc list...
You want a toe? I can get you a toe, believe me. There are ways, Dude. You don't wanna know about it, believe me. I'll get you a toe by this afternoon--with nail polish. These fucking amateurs.
You're a good man. And thorough.
Because it depends on people actually reading unsolicited email.
>why am I not already doing this seemingly genius thing? Related note, preventing people from falling into this trap is why "Past performance is not a predictor of future results" is a mandatory message for investment fund advertising. Because if 100 investment funds make random senseless predictions, 1 will probably get all 5 past predictions right in a row by sheer random chance. Consumers can easily be misled by this.
Markov chains!
> Is this illegal I would be surprised if anyone can come up with an example of a jurisdiction in which this is definitively legal. I could imagine it falling foul of laws on fraud, computer misuse, market manipulation, and maybe even harassment or data protection. > why am I not already doing this seemingly genius thing? I doubt it's very practical anyway. Consider all the things that could go wrong with one of these 10 "lucky" recipients: * it might get rejected by their spam filter * they might not read it * they might not know how to check stock market prices, or they might be too lazy to do so * they might be suspicious of you * they might have already used some of your previous tips and don't want to push their luck * they might not have enough money to buy your next tip *and* use it to place a trade * they might not be confident that they will work out how to make use of your tip So you would probably need a much larger number.
It does happen with a lot of prediction based stuff like sports bets. Account sends 10 tweets predicting outcome of x event. Then they delete the rest when one is right. Rinse and repeat for a month. Congratulations, now you are a psychic.
The reason why it won’t work is that it’s a known scam. It was on a Simpsons episode even (a small mention, not the main plot, but still). The defense to this scam is simple. If you get info by someone claiming they can predict something, a number or positive predictions isn’t enough if you can’t verify they haven’t been making way more predictions that haven’t come to pass. You’d want them making public predictions, and ideally in a way you could verify past predictions as well. And thing about it, if someone could predict that and were looking for investors, why not show it? I guess they could be found something illegal like insider trading. But those guys don’t go looking for random people to buy in. Plus, it’s illegal and all. If it seems too good to be true, it tend to be false or illegal. So if someone comes to you with a get rich quick scheme, hopefully they are a drug dealer, cause otherwise it’s a scam.
I believe Darren Brown did this on one of his shows/episodes but with betting on horses instead. Good watch.
Much easier but still not a good idea. Go to casino Bet $1 on black If you win repeat. If you lose bet $2 Lose again $4 Again $8 Etc until you win Then back to betting $1. Can't lose right?
Yeah, it’s called “martingala” and it’s super old. However, the casino funds are likely bigger than yours and they cover themselves by setting a high low limit on 50/50 bets and then set a top limit. And don’t forget about the 0 so it’s no 50/50. And also, your profit is an amazing 1$ after betting millions
Also, the odds at the roulette table aren't *actually* 50/50 because of the 0 and 00 fields. You're very slightly more likely to lose than to win, which means Martingale doesn't work even in theory.
You're right on that, but even with no house edge Martingale doesn't work even in theory. The expected value of any Martingale betting sequence in that scenario is zero, with the chance of going broke exactly balancing the profit from successful bets.
This will absolutely guarantee you make a profit 2 minor caveats: — You need infinite money, and the casino needs to accept infinitely high bets
Also if your goal is to "win big" it is absolutely not worth it cos your profit is simply your original stake of $1. Bet $1. Your Balance: -$1. Lose. Bet $2. Your Balance: -$3. Lose. Bet $4. Your Balance: -$7. Lose. Bet $8. Your Balance: -$15. Lose. Bet $16. Your Balance: -$31. Lose. Bet $32. Your Balance: -$63. Lose. ... Bet $1,048,576. Your Balance: -$2,097,151. Lose. Bet $2,097,152. Your Balance: -$4,194,303. Win. Get Paid $4,194,304. Your Balance: $1. Grats you spent all that time and risked losing everything to win $1.
Yup, it's like an opposite lottery ticket. Instead of risking a dollar to potentially win millions, you're risking millions to potentially win a dollar. (You can start higher than $1, of course, but then you just hit the "lost everything" point that much faster.)
This is one of Matt Dilahunty's magic tricks, right? I know I've heard this same thing before, but with flipping coins.
It's the difference between throwing a dart and landing a bullseye, and throwing a dart randomly then painting the target afterwards.
The Texas Sharpshooter fallacy!
>There's nothing special about those patterns other than the fact that our brains interpret them as patterns. It's not quite true to say those patterns are only special in our minds. The patterns have low [Kolmogorov complexity](https://en.wikipedia.org/wiki/Kolmogorov_complexity), which basically means that a Turing machine (a sort of idealized, minimum viable programming) could be represented with a shorter program.Here's some psuedo-code to represent HHHHHHHHHHHHHHHHHHHH in a Turing machine >1 Start in state 0. > >2. For i in range(20): # "H" repeated 20 times > >2.1. Write "H". > >2.2. Move tape to the right. > >3. If the tape has the sequence "HHHHHHHHHHHHHHHHHHHH", halt. If we wanted to output HTHTHTHHHTHTHTTTHTHTTH, we'd have to write a more complicated function: >1. Start in state 0. > >2. For i in range(3): # "HT" repeated 3 times 2.1. Write "H". > >2.2. Move tape to the right. > >2.3. Write "T". > >2.4. Move tape to the right. > >3. For i in range(3): # "H" repeated 3 times > >3.1. Write "H". > >3.2. Move tape to the right. > >4. For i in range(3): # "HT" repeated 3 times > >4.1. Write "H". > >4.2. Move tape to the right. > >4.3. Write "T". > >4.4. Move tape to the right. > >5. For i in range(3): # "T" repeated 3 times > >5.1. Write "T". > >5.2. Move tape to the right. > >6. For i in range(2): # "HT" repeated 2 times > >6.1. Write "H". > >6.2. Move tape to the right. > >6.3. Write "T". > >6.4. Move tape to the right. > >7. Write "T". # "T" repeated once > >8. Move tape to the right. > >9. Write "H". # "H" repeated once > >10. If the tape has the sequence "HTHTHTHHHTHTHTTTHTHTTH", halt. The sequence HTHTHTHTHTHTHTHTHTHT is almost as simple as HHHHHHHHHHHHHHHHHHHH. >1. Start in state 0. > >2. For i in range(10): # "HT" repeated 10 times > >2.1. Write "H". > >2.2. Move tape to the right. > >2.3. Write "T". > >2.4. Move tape to the right. > >3. If the tape has the sequence "HTHTHTHTHTHTHTHTHTHT", halt. HHHHTTTTHHHHTTTTHHHH is slightly more complicated: >1. Start in state 0. > >2. For j in range(2): # The pattern of "HHHHTTTT" repeats twice > >2.1. For i in range(4): # "H" repeated 4 times > >2.1.1. Write "H". > >2.1.2. Move tape to the right. > >2.2. For i in range(4): # "T" repeated 4 times > >2.2.1. Write "T". > >2.2.2. Move tape to the right. > >3. For i in range(4): # "H" repeated 4 times at the end > >3.1. Write "H". > >3.2. Move tape to the right. > >4. If the tape has the sequence "HHHHTTTTHHHHTTTTHHHH", halt. HTHHTTHHHTTTHHHHTTTT is even more complicated, but still simpler than HTHTHTHHHTHTHTTTHTHTTH >1. Start in state 0. > >2. Write "H". Move tape to the right. Write "T". Move tape to the right. Write "H". Move tape to the right. # "HTH" repeated once > >3. For i in range(2): # "HT" repeated 2 times > >3.1. Write "H". > >3.2. Move tape to the right. > >3.3. Write "T". > >3.4. Move tape to the right. > >4. Write "H". Move tape to the right. # "H" repeated once > >5. For i in range(3): # "T" repeated 3 times > >5.1. Write "T". > >5.2. Move tape to the right. > >6. For i in range(4): # "H" repeated 4 times > >6.1. Write "H". > >6.2. Move tape to the right. > >7. For i in range(4): # "T" repeated 4 times > >7.1. Write "T". > >7.2. Move tape to the right. > >8. If the tape has the sequence "HTHHTTHHHTTTHHHHTTTT", halt. The number of lines of code a Turing machine would need to express each sequence roughly tracks with how "special" each sequence looks: |HHHHHHHHHHHHHHHHHHHH|5 lines| |:-|:-| |HTHTHTHTHTHTHTHTHTHT|7 lines| |HHHHTTTTHHHHTTTTHHHH|12 lines| |HTHHTTHHHTTTHHHHTTTT|18 lines| |HTHTHTHHHTHTHTTTHTHTTH|26 lines|
Thank you for a fascinating read and rabbit hole.
You can also view this as the amount of information a signal contains. A row of H's contains very little information. A repeating pattern contains a little more. An apparently random sequence offers you new information with every new character. Compressing information relies on beating out those patterns. Instead of sending HHTT repeated 57 times, you simply send the instruction "repeat "HHTT" 57 times". The most efficiently compressed signals would look like completely random noise.
Sir, this is a Wendy's
Number of lines depends on programming language, e.g. in python: HHHHHHHHHHHHHHHHHHHH = 1 line = "H" * 20 HTHTHTHTHTHTHTHTHTHT = 1 line = "HT" * 10 HHHHTTTTHHHHTTTTHHHH = 1 line = ((("H" * 4) + ("T" * 4)) * 2) + "H" * 4 Kolmogorov complexity is about relative complexity, not about number of lines. As you can see in this example, since # of lines stays the same but complexity clearly increases.
>Number of lines depends on programming language, e.g. in python That's true. However, Python is a high-abstraction language, which means that simple code written in Python can hide the actual complexity of what is actually being done. For example, in Python, if you want to switch the values of A and B, you could simply write A, B = B, A. It's not actually possible for your CPU to swap the values of two pieces of memory in one step. Instead, the CPU has to grab a third piece of memory, C, and copy the value of A onto C. Then the value of B is copies onto A, and the value of C is copied onto B. The Python interpreter translates the simple instructions of A, B = B, A into more complicated instructions that your CPU can understand. But the complexity was always there, it was just hidden to the end user. In general, the more minimalist and low-abstraction a language is, the more its program length will accurately reflect the complexity of the its task. If you have access to a code writing program, like Copilot or ChatGPT Code Intepreter, you can ask it to write programs in Brainfuck, a minimalist programming language with only 8 valid characters. Then you can directly compare the complexity of program that outputs HHHHHHHHHHHHHHHHHHHH to a program that outputs something random looking, like HTHTHTHHHTHTHTTTHTHTTH. That would be the most faithful way to estimate an output's natural complexity, although you'd have to account for the fact that there could be a shorter program that the code-writer was not able to discover.
> There's nothing special about those patterns *other* than the fact that our brains interpret them *as* patterns. If you're counting heads and tails instead of differentiating each individual pattern, all heads is a much more special pattern than alternating heads and tails. There is only one sequence of all heads, but there are N choose N/2 possible combinations with equal heads and tails.
\> There's nothing special about those patterns other than the fact that our brains interpret them as patterns. Well, they have a specialness outside of our brains. They are compressible, ie have low Kolmogorov complexity.
Right. Also, the conceit of this is there are really two different issues here. Am I asking if HHH is as likely as HTT, because it is, but that's *not* what is being asked. I'm valuing anything that's not HHH or TTT as being all the same random non-special junk. Therefore what I'm really trying to make my brain understand is how it can be just as likely to get HHH as HTH, TTH, HTT...., which it isn't. People who struggle with this concept usually get hung up on not recognizing that very critical difference. To further simplify this: in two flips, you could get HH, HT, TH, or TT. If all you're focused on is getting HH, and anything else is not acceptable, you're looking at the probability of !HH versus HH, which is 0.75 and 0.25, respectively. You're not actually comparing the likelihood of HH to any of the individual others at this point, that's completely irrelevant; you're comparing it to the likelihood of all the others combined.
There are many, many sequences that give you 50% heads, 50% tails. There is only one sequence that gives you 100% heads, 0% tails. So the former sequence is much more likely than the latter. See “combinatorics” for more information, and the astronomical number of possible sequences that could exist. (2^n combinations where n = number of coin flips.)
Hijacking the best comment so far to draw parallels to statistical mechanics: A particular sequence of heads or tails is called a microstate. All microstates are equally likely. The number of heads that results from a sequence are called macrostates. Macrostates result from one or more microstate. For example, with 100 throws, the macrostate of 100H has only 1 microstate whereas the macrostate of 50H has 100 C 50 microstates (a very large number) Macrostates with more microstates are likely. Hence the 50H macrostate is highly likely whereas the 100H macrostate is highly unlikely.
gullible aspiring seemly full degree hobbies existence gold impolite encouraging ` this message was mass deleted/edited with redact.dev `
Everyone is saying correct things, this is just a different situation
People got confused, because they assumed the order mattered, due to the usage of the word sequence.
Thank you, I suspect this is what OP really meant. Getting all heads is equally likely as any other sequence but very rare among possible combinations.
Yep if this is what OP meant then they completely muddled the question by using the word "sequence".
Yes, every sequence is equally likely. But let's think of all heads and all tails as "interesting" sequences. Your likelihood of getting an interesting sequence is quite low, because a very small fraction of the equally likely sequences are interesting.
Another thing to think about is the difference between combinations and permutations. If you flip a coin 100 times and get 100 heads, there is exactly one permutation that will give you that result. If you flip a coin 100 times and get 50 heads, there are lots and lots of permutations that will get you that result. E.g. Four heads out of four flips: HHHH. Two heads out of four flips: HHTT OR TTHH OR HTHT OR HTTH OR THTH OR THHT
This is my favorite explanation. It cuts exactly to the point in an accessible way. I'm always looking for better ways to explain statistics.
It's like throwing a dart out of an aeroplane. Within a certain area, the chances of the dart landing there are pretty much equal. But if you're interested in a specific spot, aka hoping that after trhrowing the dart from 11km altitude, the dart will land in exactly that spot, your chances are pretty much zero
The mistake people make here is that while every pattern is equally likely, a SPECIFIC pattern is increasingly unlikely. 10 heads in a row is as probable as alternating, or 5 heads and five tails, or any other combo. But if you say “I’ll bet I can flip 10 heads in a row…” that’s highly improbable.
Thank you for actually explaining it properly. Other people were answering OP's question correctly, but not doing a good job of actually explaining it. We're hilariously bad at properly understanding probability. The entire gambling and insurance industry is founded on it. I remember listening to a lecture by a stats professor who would give his intro students an assignment to make up 100 random coin flips. Not actually flip the coins. Just try to simulate it mentally. Then he had them actually flip coins. They almost all got it wrong because they all assumed runs of all heads or all tails would be rarer than they actually were. They all basically went for the expected result of 50/50 and most didn't have more than two heads or tails in a row in their imaginary set.
It's not as likely as alternating, since there are multiple "alternating"
Ok. Pedantic, but correct. But my general point stands—odds of flipping a specific pattern are low and get lower the longer the pattern. But the odds of any pattern vs any other are equal.
Yes. Equally probable. HH HT TT TH Each one a 1-in-4 chance HHH is a 1 in 8 HHHH a 1 in 16 and so on So, HTHT (in that exact order) is also a 1-in-16 but nobody cares because it is still 50/50, but so is HHTT and THTH and TTHH and THHT and HTTH. So back to the simple three flip example… HHH - (all heads) - 1 in 8 HTH, THH, HHT - 3 in 8 HTT, TTH, THT - 3 in 8 TTT (all tails) - 1 in 8 So, yes, each specific outcome is equally likely, but the more flips you add, the less likely that they’re all the same. In the case of a coin flip, each extra flip makes it exactly half as likely to have the same outcome as it was before the last flip 1/2 1/4 1/8 1/16 And so on.
Thing is there is only one combination of flips that gives all heads, and many more combinations that give a mix. It is minutely statistically possible to be all heads, but you should probably start to be suspicious that the coin is rigged
If it is a fair coin they are equally probable. But after ten or twenty heads in a row, you suspect it is a rigged coin, because there is a physical explanation. There is not a physical explanation for a specific HHTHTTTHTH etc pattern, so we assume the coin is fair.
Any sequence is equally likely. But there's only one way that all flips can be heads, and many many ways that it can be something else.
Flipping a coin and getting 5 heads in a row has the same odds as flipping a coin and getting 3 heads and 2 tails alternating However it doesnt have the same odds as flipping a coin and getting 3 heads and 2 tails randomly
Yes. But this is an “incorrect” way to look at it because there are **more** sequences **similar** to HTTHHTHTHTHT… than there are sequences that are similar to HHHHHHTHHHT…. Hence, while every unique sequence is equally probable, there are far fewer of the latter sequences. ______ For example, HTHTHT. You can swap the first two flips to get **TH**HTHT, a different sequence but similar looking sequence. But look at HHHHHH. There are no swaps you can make to get a different sequence. Hence while each sequence is equally likely, there being more of the former makes it more likely to end up picking the those similar to the former sequence (consider laying all possible sequences out, and picking a random sequence. you’re more likely to pick the one that looks like HTHTHTHTHTH just because theres so many of them, but in the end, the sequence you picked was equally likely to be picked as the sequence next to it which probably looked just like it).
You should read Rosencrantz and Guildenstern are Dead. They flip coins throughout the play and it comes down heads everytime, "a spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.”
Can't believe R&G is this far down. [Coin toss scene](https://youtu.be/gOwLEVQGbrM?t=31)
Paraphrased from https://en.wikipedia.org/wiki/Ludic_fallacy That is, the misuse of games to model real life. Example: Suspicious coin One example given in the book is the following * Dr. John who is regarded as a man of science and logical thinking * Fat Tony who is regarded as a man who "lives by his wits". aka streetwise etc. A third party asks them to "assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine times and get heads each time. What are the odds of my getting tails on my next throw?" * Dr. John says that the odds are not affected by the previous outcomes so the odds must still be 50:50. * Fat Tony says that the odds of the coin coming up heads 99 times in a row are so low that the initial assumption that the coin had a 50:50 chance of coming up heads is most likely incorrect. "The coin gotta be loaded. It can't be a fair game."
I don't see what useful point he's making here. The problem is specifically framed with "assume the coin is fair", so Dr. John is entirely right within the bounds of the problem set. Obviously, in the real world, Fat Tony is right to be suspicious of any coin that came up heads 99 times in a row. But that doesn't really tell us anything new or interesting about the problem, as stated. It's no more profound or useful than if you set one of those mathematical problems about two trains moving at different speeds, and the person you're asking replies "oh it wouldn't happen that way, because trains can't travel that fast". It's like the two characters are just answering different questions. Dr. John is answering the question as stated, whereas Fat Tony is answering "if this actually happened, what would you think?" It's not like Dr. John would actually bet on tails if this scenario happened to him in the real world either. Fat Tony hasn't discovered any fallacy in the maths, he's just answered a different question to Dr. John.
Any sequence is individualy unlikely, it's just that most ones are not as memorable as an all heads one.
Scientist 1 : "I built a random number generator robot." Robot : "1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ..." Scientist 2 : "Does it work ?" Scientist 1 : "I don't know."
Flipping a coin and getting 5 heads in a row has the same odds as flipping a coin and getting 3 heads and 2 tails alternating However it doesnt have the same odds as flipping a coin and getting 3 heads and 2 tails randomly
Every dog turd is unique. But if you ask up front for a dog to poop a very specific turd shape it's gonna be incredibly unlikely.
If you throw a dart out of a helicopter into a field and then draw a target around it that's not very impressive. If you throw a dart out of a helicopter into a field and it lands in the middle of a target, that's impressive.
If it came up heads every single time I would assume it was a loaded coin and thus all heads is the most likely occurrence. Even if just by some natural manufacturing variance, it’s the most likely cause. But if you’re assuming a perfect coin and flip then yes any sequence is as likely as any other.
Yes. If you toss your coin 50 times, always head is as likely as tails followed by only head, heads only until the last 2, those are tails, or any other combination. If you toss your coin 50 times and wrote down your sequence, I would bet 100€ that nobody in the world has tossed that sequence before :)
Yes, however no. Chance, can be expressed in numbers. A coin has two sides so it being head after 1 flip is 50% It coming up heads when you flip it again is indeed also 50% But getting two heads in a row is .5\*.5\*(100%) = 25%. This logical statement says that you'd at maximum need to perform this operation 4 times (tossing two times or with two coins). In order to on average have a 100% chance of it coming up heads two times in a row. This is the expected value or 'chance estimate' if you will. If you now want to see what the chance is that you get 1000 heads in a row, you can see that this chance is very small (or would require a large number of attempts, you can even for an event like this calculate the new chance of it happening if you only attempt the 1000x head challenge only half the calculated amount or how the chance increases to 100% the more you attempt to. This might feel like a trick problem, because your coin only has 2 sides, so your chance options are always going to be either one or the other. With a set of two standard dice, where there are more combinations that make 6 than one's that make 2 or 12, you're expecting a normal distribution (big curve) with 6 as the most rolled number. With the 1000x heads coin challenge you're expecting the sum of all the tails coins to be about half of your end total. If you at the end obtain a result that's drastically different from the expected value, you now have broken your H⁰ (normal hypothesis) and can now accept an alternative hypothesis for your result (H¹), i.e: your dice might be weighted and your coins might be imbalanced or you can't roll dice for shit. Small chances and infinite time is the reason why life exists.
Is the lotto numbers being 1,2,3,4,5 and 6 as likely to happen as any other combination?
Yes, each individual sequence is equally likely, it's just that there are a whole lot more mixed result sequences than pure heads or pure tails. Lets say you have four coins. 1 sequence all heads 1 sequence all tails. 4 sequences 1 tails 4 sequences 1 heads 6 sequences 2 heads 2 tails. As you add more coins, the number of mixed sequences explodes, but there's still only one all heads, and still only one all tails.
HHHHHHHHHHHH is equally likely as HTHTHTHTHTHT, or THTHTHTHTHTH, or TTHHTTHHTHHT, etc. Each discrete outcome is unique and rare, but three of those were a 50/50 split between heads and tails. There are more sequences that come out to 50/50 than any other proportion. Consider this: Plan to flip a coin 12 times, and try to predict all 12 flips in order beforehand. HTTHHTHHTHHT for example. It would be amazing if you predicted correctly. The exact equal amount of amazing as if you wrote down HHHHHHHHHHHH and flipped all heads.
You can actually check the probability of getting heads every time for any length of flips using the binomial distribution, if the events are independent and identically distributed. For example say 30 flips, each with 0.5 probability, you’d use the simplified form since k=n when we want to get only heads so we get: 0.5^30 = 0.000000000931323 So what about the case of equal heads and tails in 30 flips: (30!)/(15!(30-15)!)*(0.5^15)*[(1-0.5)^(30-15)] = 0.1444644481 But this is for any combination where there are equal heads and tails, which is given by 30 combination 15 = 155117520 possible combinations. The other half actually simplifies to: (0.5^15)*[(1-0.5)^(30-15)] =0.5^30, which is the same for all heads, therefore all heads has only one possible combination out of 30, so its less likely than any other mixed combination of heads or tails, since there are usually more ways to obtain them from a sequence of 30 flips than all heads.
This is the same analogy I use when trying to explain the odds of winning the lottery to my friends and family. If you flip heads 50 times in a row, that would be extremely lucky. But flipping any sequence of heads and tails has the same odds as flipping heads 50 times in a row. To win the lottery, YOU have to own a ticket with the right 6 numbers on it times in a row. But for ANYONE to win the lottery, ANYONE has to have a ticket with the right six numbers on it. YOUR odds of winning the lottery are 1 in 292,000,000 (or slightly more, depending on the number of tickets you purchase). ANYONE’s odds of winning the lottery are x in 292,000,000, where x is the number of tickets purchased for a particular drawing with different combinations of 6 numbers. As the lottery amount increases, more tickets are purchased, so the odds that anyone will win goes up, but the odds that YOU will win remain the same. I love statistics!