Is a coin more likely to flip tails if it has already flipped heads a bunch?

Philosophy Forums Science, Technology, and Math
1810

When many flips have been in one direction, you know there is statistical overall pressure to get back to the mean. That is why it is the mean, the AVERAGE over time. This is just a fact.

Flip enough coins and the average of heads and tails will each converge on 0.5. Fact.

That is what I am saying. You can keep looking at only the individual flip, but depending on where that flip occurs is a background of statistical context that cannot be ignored. So you’ve had many heads in a row, and you want to flip one more? Sure, 50/50. Then keep flipping and see what happens. It will converge back to the mean like a force of nature.

1811

statistics doesn’t exert pressure. there’s no force in the universe that makes that happen.

I wrote an experiment a few months ago, maybe longer - back when Pedro was still in the conversation - that went as follows: flip a coin until its historical balance is heavily tails - 1000 more tails than heads, say. Then, after this point – if what you say is correct, the following 1000, maybe 5000 or 10000, flips should be noticably heads-heavy.

But they aren’t. If you’ve flipped a lot more tails than heads, the subsequent flips aren’t any more likely to be heads-heavy. It’s equally split between heads-heavy and tails-heavy. In other words, if you’re +1000 tails, over the next 10000 flips you’re just as likely to end up more tails-heavy than you already were as you are likely to go back to the middle.

That force doesn’t exist. That pressure doesn’t exist. It’s a fiction. Random is random, and coins do not remember their history.

1812

If what you said was true, then it wouldnt be the case that random coin flips converge on an average value. Yet they do.

Flip a coin a million times, and do this sequence a billion trillion different times. Guess what it will converge on every time? 0.5

That is hard statistical reality. In no possible universe will you flip a coin 1 million times and get 1 million heads. Never gonna happen.

1813

Then think about it in terms of dice. A 1-6 six-sided die, if you roll it a million times the result as average will always, ALWAYS converge on 3.5. The exact center.

Why is that? It is because of what you do not understand. The power of statistical pressure, which is a very real thing in the real world.

1814

Explained another way: the odds of disobeying the statistical likely path tend to be less likely more so with each successive iteration. Example: What are the actual odds of flipping 1 million heads in a row with no tails?

Here is an AI explanation you might like: " The odds of flipping 1 million heads with no tails on a fair coin are extremely low, essentially impossible; mathematically, it’s represented as a probability of “1 divided by 2 raised to the power of 1 million” (written as 1 / 2^1,000,000), which is a number so small it’s practically zero."

Now remember we are situating this IN REAL LIFE. No one is going to actually sit around and flip a coin 1 million times and then do it again and again forever until… some weird result obtains. In every possible instance in which someone ACTUALLY did it, it would end up averaging at 0.5. And that is the point here. This is not some theoretical exercise in mere mentalizing. Statistics DOES exert a very real pressure IN REALITY and we are all subject to it. No matter how many fantastical weird fantasy heavens and impossible alternatre universes you want to imagine, none of that stuff is actually going to obtain. Monkeys randomly pounding on keyboards will NEVER produce Hamlet. I do not care however many moneys you want to use.

And if you can’t even follow that much, then pay attention to this: at each progressive step in the iteration, it becomes less likely to continue the deviation from previous iterations. And this “less likely” amount is greater and increasingly greater all the time than the mere numeric increase in raw statistical likelihood. Why? Because we are not taking about mere numbers, we are talking about patterns and meaningful results… If you rolled a thousand heads in a row, the odds of rolling another head are still 1/2. But the odds of rolling a thousand heads in a row AND THEN rolling ANOTHER heads are way way way way way way way less than just 1/2. You see, the odds iterate and accumulate into increasing unlikelihood.

1815

Which part of what I said specifically? You disagree when I say coins don’t have a memory?

I actually agree that they -tend to- converge to be closer to 50/50, I just disagree that there’s a real “pressure” and I disagree with various other things you said, like when you were talking about a region within a region. You also can’t predict some future regions skew towards tails just because some past regions skew towards heads. But I do believe that, over more and more flips, it will most probably get close to 50% if it’s a fair coin.

1816

Think about it like this:

You have a table and on it 2 coins, we’ll call it coin A and coin B.

We do a physical analysis on the 2 coins (without flipping them) and discover that they’re effectively indistinguishable – not entirely indistinguishable, this one has a finger print over here, that one has a different finger print over there, there’s little bits raised on here on this one, a slight indent on that one, but no difference that would lead one to say “A is more likely to flip heads” or anything – all the differences you can find are shallow and cosmetic and wouldn’t affect the physics of the coin flipping in air very much at all. So effectively two equal coins.

Unbeknownst to us, one of these coins (coin A) is pretty close to brand new and hasn’t been flipped at all. The other one (coin B) has been flipped many times and has just flipped 8 heads in a row, and out of the 100 flips it’s had in its lifetime, it’s flipped 60 heads and only 40 tails - so this coin is very heads-heavy and is in the middle of a big heads streak.

My position is basically just saying, if the two coins are effectively physically indistinguishable, there’s no magic in the universe that should lead you to reasonably predict Coin B is due some tails. The coins are physically close to identical, and so what they’re likely to do in the future – which is a physical question – if there were any real difference between the coins, should be physically discoverable by some physical analysis.

The alternative position is that despite the fact that there’s no discernable physical difference that would cause B to flip more tails than A, there’s some non-physical force in the universe that is going to make B flip more tails. Like the universe - or perhaps the coin itself - knows that it’s flipped loads of heads, remembers that, and is somehow affecting the physics of the coin such that it will land more tails in the future.

I don’t believe this ethereal property of the history of the coin could possibly have any affect, if the coin is otherwise effectively identical to coin A. If they’re both fair coins, they’re both fair coins. You can’t make a fair coin become unfair just by flipping it and seeing it flip a bunch of heads.

1817

This question came up on stack overflow recently. A lot of different approaches, many well-worded answers.

1819

I’m not clear on what this claim means. We know that a single fair coin will tend to produce half heads and half tails. But we also know that three fair coins, A B and C, being flipped one after another will also tend to produce half heads and half tails. Suppose coin A has flipped more heads than tails, but the three coins together have flipped more tails than heads. If we are flipping con A, is the pressure towards flipping heads or towards flipping tails?

Maybe you will say that the pressures cancel out. So take this one step further:

Suppose I am flipping a coin, and someone else is flipping the other coins behind a screen. The expected distribution of each coin is 50-50, and the expected distribution of all the coins together is 50-50. Could my observation of the outcome of my coin flips tell me information about the outcome of the other coins’ flips? Because if my coin should be more likely to flip heads after an abundance of tails, and I observe it flipping 50-50, it is evidence that the other coins have been flipping too many heads, and exert a countervailing pressure on my coin to flip tails. It won’t be definitive of course, but over many trials I should be able to guess the other coins’ flips at better than 50-50 based on my coin’s flips.

That would be an empirical test of the claim, assuming I understand the concept of pressure correctly.

1820

This is simply false.
Statistics is effects and consequences. There is no cauality here. It just observations and extrapolations.
To think otherwise is nothing more than childish teleloogy, and mistake in perception often found in people with a religious bent or MAGA

1821

No idea why you are bringing religion or politics into this. It is simply about logic.

Take an endless number of monkey and give them an endless amount of time to pound away on typewriters. They will NEVER, ever, produce Hamlet.

Think about why that is, then get back to me :+1:

1822

The odds of producing Hamlet is just the odds of producing a specific string of length n by randomly selecting characters. I agree the odds are very small for large n, but it’s not zero. And we can calculate it, and we can test the calculations for smaller values of n to empirically verify the techniques.

Do you disagree with any of that?

1823

Ok then, calculate it.

1824

Calculate that shit. I’ll wait.

In the meantime, ain’t no fucking way in hell that a bunch of apes punching on typewriters would ever, EVER, EVER, EVER, I do not care how many infinite infinities of time you want to figure, would ever produce a complete Shakespare’s Hamlet.

Now just sit and think about that. Because “that is why you fail”. In Yoda’s words.

1825

.
:100:% agree… probability is a magicians trick/a ruse, I do not go through life thinking in terms of probabilities, because irl probabilities require countless factors, causing most outcomes to be incalculable or rendered impossible.
.
Not all mathematical functions are applicable to all problems.

1826

I think it’s just \frac{1}{k^n} where k is the number of possible characters on the typewriter (letters, numbers, punctuation) and n is the number of characters in the string.

Again, that’s going to be small: the odds of typing a 2-character string on a keyboard with only the 26 English letters is 1 in 676; for a 3-character string it’s 1 in 17576. Those are pretty unlikely, but small enough that we can test them empirically and verify a normal distribution around those odds.

“Any sufficiently advanced technology is indistinguishable from magic.”

I would be surprised if anyone has ever claimed otherwise. But probability and statistics are applicable to coin flips, and to the outcome of random processes (the proverbial ‘monkeys on typewriters’).

It’s true that many things affect outcomes IRL, but not all effects are of equal magnitude. Technically the gravitational pull of the nearest black hole affects the outcome of a dice role, but 1) the shape of the die and the number of sides have so much greater an effect, and 2) the effect of the black hole isn’t correlated with the number on the die (i.e. it doesn’t consistently 5 more likely than 6). So for practical purposes, we can ignore the tiny amount of noise exerted by the black hole.

That’s also true of whatever influence the previous roll exerts. I’m still not clear on what mechanism @HumAnIze is proposing with his “pressure”, but there is not zero: with each roll the die sheds some small number of atoms, heats and cools, accumulates structural stresses and possibly microfractures in the material that composes it, etc. But the sum of those effects is vanishingly small, and they aren’t correlated with the numbers on the die.

1827

Right, and this is especially true because of a mistaken concept of infinity. Infinity does not absolve infinitesimal possibilities compounded upon each other to astronomical levels, let alone absolve the universe of the fact of MEANING.

Meaning is what pure math / analytical types do not understand. They think in terms of “oh this number is theoretically non-zero, therefore combine with infinity and = reality” yet that is philosophically unjustified.

1828

Think about the idea of “apes pounding on typewriters”. Are those apes pushing individual keys? Are they aware there even are individual keys, or patterns within those? Of course not.

Before you start to write about how that doesn;t matter, think about this. There is a concept in math that is not understood especially by mathematicians, because it has not yet been properly explicated as far as I have ever seen. It can be approached theoretically by thinking about trying to take the derivative of an infinitesimal probability in terms of further iterations over more time. Each new iteration adds MORE unlikeliness than the sum total of what came before, because the precise approximation of MEANING is what is required to continue along the correct path, which must also take into account its own probabilistic history as ever-compounded exponential unlikelihoods, and in fact there is only ONE SINGLE possible next step in the process to keep correctly tracking that path, while every single other possibility not only terminates the effort but completely ruins and invalidates that entire ‘possible universe’ even and especially in terms of all of the super unlikely probabilistic lottery-winning it has already happened to do.

It takes a philosophical mind to comprehend this, but what I am talking about is the fact that as very very very unlikely possibilities keep extending, stretching themselves further and further along a curve of even more infinitesimal possibilities always trying to approximate some end-goal of completed meaning, the chances that the next step iteration in the process will miss becomes more and more likely such that it’s antithesis, namely the correct next step, actually becomes less likely than the entire history of that particular attempt relative to all other possible universes in which the same attempt was also made and the same stage reached before failure.

Maybe I am not explaining this well, that is Ok. But you need to think of probabilities not only in terms of the one single “n%” or “0.X” but as a relation between that term and another second term, this second term being something like the probabilistic ratio between the first term and the net sum of its own alternate possibilities given the entire universe of exhausting efforts tracing along its own meaningful plane curvature approaching the ultimate end goal, whatever that goal might be.

Eventually, it just becomes more and more unlikely that the next step will keep tracking the answer, that the unlikelihood of it even outstrips the totality of all possible universes in which such attempts are even being made. This relates to reality because when we talk about possible universes we are setting this in reality, for example in the world of what “apes pounding on typrwriters” REALLY means in the REAL world.

Anyway, I don’t care if I didnt explain that very well, because I know what I mean and I know it is correct. Infinity is a theoretical construct, not a reality manifested; in terms of this fact, I don’t care how many supposed eons and eons and eons of situations of apes trying to replicate Hamlet, it simply would not ever happen. You don’t need to assign it a numercal value = pure zero in order to realize that the accumulating exponentially-building impossibilities eventually outstrip the entire universe of all possible worlds.

Sort of like, a single chess game has more possible moves than there are atoms in the universe. That seems insane, and it is insane to think about. But it is also true. It means chess moves would never be exhausted in terms of the physical universe, just like the fact that apes on typewriters would never exhaust Hamlet.

1829

They shall. But there will be a spelling mistake on page five and two indent and formatting errors that philopshers will pend the rest of eternity trying to explain.

1830

I thought about it and your example re-inforces my opinion that stats is all about results. They do not impose pressure as you first suggested.
You can throw a dice a milion times and never get a ONE, but on the very next throw the chance of getting a ONE is still 1 in six. The dice does not “know” there is no pressure on the dice to perform. The ONE is not “DUE”.
There is always and forever a 1 in 6 chance.

In the case of the monkeys. They have to produce Hamlet, and the Bible and also any and all works of literature, since they are infinite in number. They will also produce an infinite amount of badly finished reems of gibberish.
That’s what infinity is like. boundless.