If you’re trying to construct an actual scenario, a casino wouldn’t let that happen. They’d kick the player out because “they believe them to be an advantaged player”, because they don’t like losing money. And eventually you reach a point where it’s simply more likely that there is a bias somewhere in the system that hasn’t been detected yet.

That means it would be a feature of the system (player / table / dice) rather than of the maths - the maths is based on perfectly controlled probabilities.

Practically, you can’t ensure it’s a 100% fair system, so the simple “each outcome is 1/6” breaks down. If you could guarantee that it was perfectly fair, then what I said earlier stands. In a Real-World situation, the assumptions change significantly - you can’t have perfect knowledge of everyone’s intentions, whether it could be a scam etc.

EDIT: however, most gamblers fallacies aren’t based on the idea “I have actual evidence that the system is rigged”. Things like “5 hasn’t come up on the roulette wheel, it must be overdue” aren’t based on an assumption of bias, they’re based on an assumption of fairness, which says that eventually all numbers will come up equally. However, they don’t have to come up equally before the heat death of the universe.

Thanks! A couple more questions for you and anyone else who'd like to chip in:

1.) What sort of deals do publishers get for the games they publish? e.g. a literary publisher will get the right to sell and distribute an individual book, but the author largely retains control of the "franchise", in the sense that the publisher couldn't just override them one morning and commission a sequel to someone else or change the ending to the novel. How does it work for game developers? Do they also retain some form of artistic control, or do they surrender everything related to the game?

2.) In the literary world, it's always the authors who go courting the publishing houses. Is it the same in the gaming world, or do publishers actively seek out smaller game studios? And how do the parties communicate? Is there the equivalent of literary agents doing the intermediation?

3.) I'm having a hard time imagining a large publishing house giving a small developer access to resources like game engines and even employees for a game that evidently doesn't have anything to show for itself yet. How does that process work? Does the developer team need to prove itself first by creating one or two successful games before they can hope for the endorsement of a publisher, or can a pitch be so strong that they get these resources even with little more than a game concept to go on?

Thank you to everyone who has contributed so far for helping lift the veil of my ignorance!

Well, I own it, so it's mine.

Exclusively, you?

Patience is required for two things.

1. You must check repeatedly during the shortest days of the year to find out on which one the shadow of the stick is the the longest at noon.

2. You must keep track day after day for a year until the shortest day returns again. Until the shortest days return, however, all you need to do is to add a day to your tally.

BY THE WAY, everytime you apply for a credit card or loan, your score will go down. Im not adding to explanation i just wanted to add that fun little fact in

In the unholy metric imperial system flb is just a femtopound

Also, when the algae die, they’re eaten by decomposers, which take in a ton of oxygen, causing more things to die, causing more decomposers to thrive…

Aren't micro organisms also made from cells? Wouldn't they also be destroyed during the freezing process?

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." ?

In a universe of infinite time and space, everything is probable.

There's a mound builder site near Saint Louis where they used that exact method. There is a central observation point then posts laid in circles around it. Some of the posts align perfectly with the solstices others with planting times.

Even without the sticks in the ground most people who spend a lot of time outdoors would notice the pattern of the sun shifting across the sky and daylight changes.

It sucks. It's a drag. It doesn't pay well. But it's a right we all have. Anyone can have their life turned upside down in court, and the right to be judged by a jury of your peers is a right granted to everyone, provided that everyone takes turns being in that jury pool as well. It has to be random. It has to be well-mixed. And it has to be a civic duty. If I were to depend on 12 strangers to cast judgement on me, affecting the rest of my life I would want them to be willing and interested. I provide the same level of engagement sitting on a jury as I would hope to expect if the roles were reversed. It's similar to the Shopping Cart theory. Just be a decent person.

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> For the photon, no time would have passed at all.

This is often said but isn't correct. There is no reference frame for the photon. Without one you can't say how much time has passed for it.

That's odd, today ties are so sophisticated. To think that it's intended use was same as a rag is funny.

> it’s way riskier using you card since that’s always emitting the signal

It's not. The card has no power. The power is wirelessly sent to the card when you are tapping it.

If you bring the proper device close to the card it will start talking vs your phone which needs the CC or debit card first opened before it bothers looking for a terminal to talk to.

Using fewer engine worse, more engine better.

> Contactless tap is basically the same as chip, just done over radio waves instead of wires. This makes it easier to eavesdrop, but as we established already, eavesdropping on a chip payment isn't all that helpful to a thief, so we don't really care about that! > > Now, finally, the payment apps. When you install a payment app and register a card to it, what you are essentially doing is turning your phone/watch/whatever into a credit card chip. The credit card company creates a secret program that works like a chip--takes a gibberish question in, gives a gibberish answer back--and installs a copy of it to your device. So when you tap your device to the reader, it gets asked a gibberish question, it creates a gibberish answer, and radios it back to the terminal, just like a chip. This proves that you have the physical device. It doesn't prove you have the physical card, but registering the card in the app in the first place did prove that you must have had it at some point, which is good enough.

Another bit of security for tap purchases is a low limit. If I use my CC's chip I can do a transaction worth the entire limit on the card. However if I tap I can only do idk $100, $250? Somewhere in there.

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It was originally like a napkin/handkerchief. You would use it for cleaning things. Then they started making them fancier, then they got too fancy to use for that.

So they used to serve a purpose, but now they're just for aesthetics.

It's easy to figure out the rough length of the year. You can count, and you know roughly when it gets cold, and roughly when it gets hot. You notice that the Moon goes through phases, about once every 30 days. And hey, after about 12 cycles of the Moon, it goes from hot to cold and then back to hot. So how did they figure out exactly 365 days?

Let's say you build a house. You can walk outside and look at your cool house, and you notice that the sun casts a shadow on the ground. The top of your roof makes a shadow that goes right there. You're an inquisitive kind of guy. So let's say that you kind of keep an eye on how far out that shadow goes into your yard. Some days when it's too hot to do anything, you can just watch the shadow move across the grass.

So then, being the inquisitive kind of guy that you are, you notice that depending on the time of year, the shadow reaches a different part of your yard. It doesn't always go out as far. So one day you go out when the shadow is at its maximum distance, and you go poke a stick in the ground. You mark the farthest point that the shadow reached that day. The next day, the shadow doesn't reach quite as far. Almost, but not exactly.

Keep in mind that if you're lucky, you might not even have to poke a stick in the ground. Maybe on the day of the year when the shadow is at its very longest, it just happens to touch the base of a tree, or your fence line, or your barn.

So anyway, you just start counting the days until it touches that stick again. On the longest shadow day of the year, you find that it's 365 days from when it touches that stick, to the next day the shadow touches the stick. And that repeats, basically every single year.

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.

Stopping distance is determined by your tire grip. Brakes can already lock up all for tires. Modern and even most old cars are over braked. There's nothing gained from engine braking as it all relies on the tires maintaining traction.

To control speed outside of emergency stopping engine braking is very useful.

Since the pull of gravity is pretty much constant on Earth’s surface, a measure of mass implies a weight and vice versa.

You are right, mass is measured in kilograms and slugs, and weight in Newtons and pounds. However, people don’t bother with the difference because we something with 454g of mass has 1 pound of weight (while on Earth).