johrnjohrn t1_jdpvcg1 wrote

I worked for a website that had hundreds of employees. The development department probably had two dozen. Some were database devs, some were user interface devs, some were "full stack" devs, which I understand to mean they can do it all. There were people working on strictly search engine optimization. There were folks working strictly on improving the search function. That was only the dev team. The IT team was in charge of the company infrastructure like internet, servers, computers, networking, security, etc. The finance team had probably 15 people max during my time there. This company sold physical merchandise internationally from three fulfillment centers. There was a logistics team and all the fulfillment centers had dozens of employees. There was a customer service department with a couple dozen employees. There was a creative department that made content for the website. So, sound guy, film guys, editors. There was a legal department, an HR department, a product development team, a marketing team, a graphic design team, content writers, data analysts, so on.

That company was doing about $120 million per year and roughly about 300 total employees during my time there. So you can just scale those numbers up or down depending on the revenue of the company to get some idea of how personnel can grow and shrink.


johrnjohrn t1_ja9vmsv wrote

I'm not trying to construct an actual scenario. I am constructing a hypothetical scenario that says there is no chance that the system is rigged, and there are a quintillion throws that are all identical, which is entirely possible, but highly improbable. In real life we can say, "that would never happen", but the math says you are incorrect and it 100% could happen. Now, this situation, which is mathematically possible, plays out (hypothetically). Which bet are you going to make after the one quintillionth throw? And are you a fool if you use past information to say the next throw will remain the same as the past quintillion?


johrnjohrn t1_ja9s99d wrote

Would you not sit up at a story on the news where someone rolled 7's at a craps table for a year straight, only stopping to eat and sleep? If you paid any attention to that story would you be a fool? They bring officials in and claim the game is still fair and allow it to continue. Are you a fool if you claim it is rigged? Now that same roller rolls for multiple decades. Do you still calmly say, "we are foolish to assume this person will roll 7's one more time just because of the past 50 years they have continued to roll 7's. Each roll is a new roll." ?


johrnjohrn t1_ja9qjlw wrote

I never offered that the die has memory. I only offered a hypothetical in which a fair die rolled one quintillion times on the same number by what a mathematician would say is pure chance. And your suggestion that I believe that implies that you have some inherent belief that the math "breaks down" at some undefined, seemingly ridiculous point. Regardless of the number of rolls I pick, you will say it doesn't matter and I say at some point it does. That is the rub. You have absolute confidence that any limitless number I can think of wouldn't sway you into reconsidering which number would be most "rational" to pick next if this all occurred in front of your eyes.

I think what I'm really saying is that normally we'd expect, on average, a die that may roll the same number that can be explained with mathematical probabilities. And those probabilistic averages play out the same, all day every day in casinos everywhere, because we observe them, and the laws of physics appear fixed. Any gambler who thinks those laws of physics and probabilities will change based on their crude observations of a small number of rolls is, in fact, a fool.

Now, you suddenly have an outlier that outlies averages so far that the whole casino industry topples because of it. Although my scenario is absurdly unlikely, your math shows that it is equally possible, albeit unequally probable. Is the gambler who watches the seemingly supernatural phenomenon unfold in real time all that foolish if they were to bet on the next outcome to be the same as the prior quintillion?

I suppose this might be a question of philosophy and not math. And I'm not arguing with the defined math, but I firmly stand beside the point that eventually it is not irrational to assume the same number might be rolled one more time after observing it a quintillion times.


johrnjohrn t1_ja9oihv wrote

You have done a good job of explaining the math. And thank you.

Now, you're sitting at that gambling table and someone gives you the opportunity to choose one number that will appear on the die for the next roll after one quintillion. Are you going to choose some number other than the one that came up one quintillion times or some other number? I imagine you would choose the same number instead of picking some other number at random.


johrnjohrn t1_ja9fnnh wrote

To add to this, maybe what I'm touching on without knowing it is similar to the problems Einstein was trying to solve when euclidian geometry failed. Yes, space bends as does time when you get off the paper and into the real universe. Probablities that explain away the gamblers fallacy as a fallacy maybe break in the real world when pushed to the same brink as Einstein pushed things when he invented relativity. Maybe??


johrnjohrn t1_ja9eo35 wrote

What does it being absurdly unlikely have to do with anything? And at what point do you consider it "absurdly unlikely"? 100 throws? 1000 throws? 1 million throws?

By even pointing out the absurdity seems to indicate that you have an inherent understanding that it does at some point begin to matter.


johrnjohrn t1_ja9cn4k wrote

Would you personally brush off the one quintillion consecutive throws if the die was determined to be fair by a team of scientists? Then another quintillion? And if someone now gave you the chance to bet on the next outcome, which would you choose? I argue that if you are rational you would bet that the streak continues. But mathematically you shouldn't change your bet, and you should ignore the two quintillion consecutive throws up until this point, right? Do you see the problem here?


johrnjohrn t1_ja9a36l wrote

Thanks for validating. I empathize with the math. When it comes to casinos or whatever, there are likely strings that will come out of any number of dice throws, but you bet your ass that at some point the pit bosses will start watching closely, never dismissing the lead up to this point. At some point the manager is called in from off duty. At some point the game is shut down. The gambler can't just get away with saying, "But each roll has an independent probability!" No, the casino crew has now "fallen victim to the gamblers fallacy". But inherently, we understand they haven't. They have made a reasonable decision that they can't afford that person throwing the dice one more time. But what was the point of shutting it down if the dice were fair and any number of gamblers could start doing the same thing on any other number of tables? Do all casinos just shut down forever, therefore falling victim to some version of the fallacy?


johrnjohrn t1_ja92xlc wrote

Indeed, you have repeated the part I already understand, but it feels like saying that, "The probability that I could transform into a duck are the same in this moment that they were 10 seconds ago according to quantum physics". At some point it seems that a certain number of throws in a row would force us to consider things differently. If I did indeed turn into a duck, folks would not shrug that off as a quantum possibility, even if highly improbable. Hypothetically, if you had one quintillion throws in a row, you would have a team of scientists on the scene and it would make international news. Nobody would ever shrug that off and say "ah well, the probability of the next roll doesn't change." At that point, all involved scientists and statisticians and any interested parties would effectively be falling victim to the gamblers fallacy, but it still seems to make sense that they would, right?


johrnjohrn t1_ja8wxcq wrote

I've understood the math on this for a long time, but can someone here help me understand....... if you rolled a 6 on 1,000 rolls simultaneously, aren't you forced at some point to grapple that the odds of that streak are incredibly, incredibly low, and the likelihood that it will be broken is a fair bet to take on that information alone?

Like, if someone said before the rolls "here, I'll give you a billion dollars if that dice rolls 6 1000 times", you inherently know that that is highly unlikely to happen.

I get it, each roll is independent, but the "gamblers fallacy" doesn't seem like complete fallacy in this scenario. Someone please help me close the gap on my understanding.

I'm guessing someone is going to answer, "You have the same chance regardless of 1,000 rolls". I know. But in a way you're betting now with historic information that 1,001 rolls in a row is likely enough to bet on it.

If 1,000 isn't enough to get us past the "independent roll" answer, let's go with one trillion. One quintillion rolls. I don't care. At some point you would question the validity of probabilites and all that, right?


johrnjohrn t1_ja48h8l wrote

Haha! I think often about the fact that farming was "invented" at some point, albeit by multiple civilizations simultaneously. But I think, "man what a bunch of morons to not have thought of it before." Yet here I am, completely incapable of making my pea plant produce peas. I def would have been culled from the herd early.