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

Philosophy Forums Science, Technology, and Math
1067

I think I will just take this and run the fuck off with it.

On a serious note:

There are many things that can be discussed on the programming side. Many permutations (of the program lol if I never hear that retarded word uttered in the context of coin flips again I will die happy) are possible. I, in fact, went through several.

There are also many things on the theoretical side of probabilities that can be uttered and fenced on, considered, discussed.

But all of that is the essence of pointless if, as is the case now, you have at no point gone to any pains to address any particular thing or set of things. As soon as you saw “unintuitive paradox,” your mind went into “correction action,” and it ceased being able to hear anything else.

Of course there is a lot to talk about, and I would love to. I do already, in fact, actually, with myself. But not until you pick up the very simple, very straight forward challenges that would show you are willing to engage with points, rather than scurry for protection from the magic coin in a panicky manner.

A manner which I can only respect. But which, nonetheless, is only taking you further from reality.

As a final thought, why the extasis from generating that program?

In a world and situation so harshly, relentlessly, even ruthlesslly attached to a 50 50 on all levels accross all phenomenon, to not only catch a consistent imbalance, but one that fits a prediction based on sound statistical science dogma (even though you seem to think it is some kind of off field opinion) feels better than playing a beautiful game of chess. It is elegance itself. Even now, I am still licking the plate.

And I am wondering, if somebody has even designed anything like it before.

They must have, it is right there staring you in the face.

But I’m wondering.

1068

This is preposterous. Please tell me anything about your program or what little you’ve said about how you think it works or what it shows that I haven’t written 500 words and 50 lines of code about.

I was surprised by your program, and I explored the question in a dozen different ways that I’ve described at length in this thread. That’s not “corrective action” that’s “curiosity”.

The funniest thing about you accusing others of “ceas[ing] to be able to hear anything else” is that you didn’t even look at the programs I posted, while @Flannel_Jesus clicked through and looked at it critically enough to notice that I made a mistake in one of them: The second program has the same boundary effect problem as your program, just watered down by putting the line at 100 instead of zero. I had previously noted that this would produce the same result, but I didn’t notice that’s what I was doing:

FJ points out that his version fixes this by terminating the permutation after the 100-flip tally completes. That way you never go back across the boundary and trigger the boundary effect.

On that idea, here’s another program that I think will do the same thing (FJ will let us know if I’ve bollocksed this one up as well). Instead of ending after finding a specific tail-heavy imbalance, this one only counts th-flips when the permutation will end before the th-sequence, i.e. when the imbalance exceeds the number of flips remaining in the permutation. Again, we’re only counting sequences that won’t hit the boundary, so it should avoid the boundary effect:

This program, too, shows 50-50 thHeads to thTails. Again I ask:

I don’t expect you to answer, but you should at least ask yourself.

Seriously, you should be proud of this. It’s an interesting statistical fluke, and one I will be adding to my nerd-sniping repertoire. It’s like you stumbled on a new Monty Hall problem.

But you’re interpreting it incorrectly, and that’s sad. The actual thing you discovered is cool and you really detract from that when you don’t even try to understand it.

Someday someone will try to nerd-snipe you with it and you’ll say, “Ha, I invented that nerd-snipe!” and get a ton of admiration from your fellow nerds, but then you’ll try to explain it and everyone will get all awkward and quiet and drift away. I really don’t want that for you.

1069

Yes, I guess it’s unfair, even though it wasn’t intended, to imply somehow that you have not put thought or effort into this, or that you have no interest in the subject.

What I am saying is different. What I am saying is that that thought and effort and the reflection of that interest has gone into avoiding points at all costs, rather than addressing them.

Ok Carleas, let’s do this with you. I start reading the first lines of a program or proposal or critique of a program, and I go wait I went through all this shit with these guys al- ah, fuck, I fell for it again.

And the thing I fall for is the notion that I am proposing something, you are studying it, and you are proposing something back, and so forth. At some point, it became I propose something, it rings wrong somehow, and from then on it’s “first let me find stable ground and then maybe, maybe I’ll read what you actually write.”

I find you as hilarious as I find you honest and that is why I am going all this way to explain myself, which I seriously never do.

Consider this. If what I fell on was so quirky and unusual, why did it take you all of half a day to go “ah boundary effect solved.”

Read the rest of what I wrote above before you answer that in your head.

1070

Here is another thing of interest about this missguided “permutational” probabilistics:

Let’s say you have 64 end flips, I guess that’s 6 steps. Of those 64 paths, 25% have X proportion of Hs, 25% Y proportion, etc. For 10 steps, 10 flips, you have 1024 paths, many more options, but the same X proportion of Hs for the first 25%, etc. Therefore, this method of study gives no reason to expect a decreasing margin of deviation. Deviation from what, to begin with.

This can be illustrated with the fractional flip idea. If you have a 6 flip set, each flip is a 0.1667 flip, or 1/6 flip.

So for 2 flips, each flip is 0.5 flips. You expect 50 50, but each flip is already half, so more ways to go wrong, to betray the overall 50 50. For 6 flips, you now have three 0.1667 or 1/6 flips that can make up one half of the 50 50, less ways to go wrong, less chances to deviate. It has to get it wrong three times in a row. And so on. for 10 million flips, we are looking at 50.0001% being a normal expected percentage of Hs. Of course, 0.0000001 flips have 5,000,000 chances to get it right. It will, overall, be more likely to conform to 0.5 H and 0.5 T.

A 0.0000001 flip is more likely to be T if 0.3422342 are T and 0.3443323 are H, because we know there will be a tendency for 0.5 H and 0.5 T. At the 10 million flip magnification, this tendency will have an exceedingly small deviation margin, often as little as 1000 flips or 0.0001%. Think about that, only 2,000 flips that went wrong. 2,000 flips that did not fit a perfect overall 50 50 composition. Out of 10,000,000. This is not random, not even close.

And spare me the “your definition of random my definition of random” bullshit.

This is because a coin, or a coin equivalent, will be evenly weighed and symmetrical and be expected to give as much of one result as the other. For 1 flip, for 6 flips, for 100,000,000,000,000 flips.

This is only the very base, the very tippity tip of phenomena to study re probabilities. From here, thousands of properties and events can be noted and studied. There is almost no end. But none of it is possible if this very basic thing, this concept of a trend, is not understood. This is the backbone of statistics.

1071

Seems to me that the only way to avoid having a boundary effect when counting tails-heavy is something like this:

Flip coins until you’re at some sufficiently tails heavy number, like +1000 tails.

Then, flip the next thousand or two thousand flips and count those as your tails heavy flips.

Then stop counting.

It seems really weird but I think you actually need that last step haha - you have to stop counting, because if you keep looking for the condition and keep counting, well, then there’s a boundary

I think you did that with some of your more recent examples. That seems like it should be considered completely fair. I don’t see why anybody would disagree that going to -1000 (or -100) and then counting the next 1000 (100) flips is a fair selection of tails heavy flips.

When I run that, sometimes tails heavy flips are more heads. Sometimes they’re more tails. It varies. It’s random.

1072

By the way, a 2,000 flip deviation in a 10,000,000 set, a 0.0001% deviation margin, means that the instances of imbalance within the set will be so very few, so far in between, and so small, of necessity, that to nail it at any particular point of imbalance, and to have that same imbalance instance spontaneously repeat itself within the set so that you can note statistical incidences of that case of imbalance, is almost impossible.

To write a program that could do it, one would have to be some kind of genius.

1073

And, when you do do this, two things you will see:

Again, sometimes more tails, sometimes more heads, rarely perfectly balanced.

But tails heavy heads will still fairly often have a percent that’s higher heads than overall heads percent. But it’s not surprising, it’s what you’d expect anyway. To get to that point, you had to get to +1000 tails, so you’re already inherently in a data set that’s light on heads, and you’re counting a new data set that isn’t necessarily going to be light on heads.

1074

If each flip was 50 50, you would expect at least 50% of instances of 10 mill flips where the state just stays heavy forever. It has no reason to go back. If you predict a “boundary,” it’s because, necessarily, you predict the tail heavy flips will be heads heavy, because it would have to to get back to the “boundary.” If each flip is a perfect 50 50, there is no need for any trend to exist, it could just go tails heavy forever, exponentially, just as easily as go back to the boundary.

But, miracle of miracles, it always goes back. And, God himself must be doing this, it goes does about the same on the other side at about the same rate so that, somebody must have forged this, each individual flip probability will have shifted to give every single 10 mill sample an almost perfect 50 50 composition.

1075

I was hoping you guys would eventually formulate this yourselves, so that I wouldn’t have to make you look foolish. But:

Each individual flip cannot be 50 50 and at the same time overall flip composition be 50 50. If a break from overall 50 50 happens, and individual flips remain 50 50, there is no reason it would trend back to balance. In f act, it might be likelier to just stay on the twisted path it entered. Of course, even this wouldn’t hold, what would hold is a kind of unpredictable perfect variance with no possible predictable overall composition.

So, there you go. Sorry to be the guy.

1076

Sure, let’s test it. I have a test in mind.

1077

Wait, I’m way ahead of you.

1078

Fool.

1079

Not Flannel Jesus. Someone else.

1080

You really don’t need to say stuff like that. Official warning, again.

1081

In any case, the test is this:

Flip until you reach +1000 tails. Then flip another million - record if you end up more or less than +1000 tails after that million.

Do that loads of times, get statistics on how often we go from -1000 to more negative, Vs less negative

1082

Sorry, unable to keep reading any responses, if responses anybody wrote.

1083

Real tests are scary, but that’s the test of fire for ideas. That’s why I like doing them.

1084

Yes, I’m still unable to respond, sorry.

1085

There’s something exciting about this.

Like being tied to a chair while your woman makes love to another man.

1086

Do I have the discipline not to tug the rope.