My first thread in over a year

[Autumn]

Time goes by quickly, it would seem. I'm reminded of some quote I heard a while ago, possibly from a song, "the years are fast but the days are slow" or something like that.

I randomly visit TFF tonight and find that over a third of the non-stickied threads on the front page of General Chat were started by one person. Is TFF getting less and less active as time goes on? I know I hardly visit the site anymore, nor have I played a Final Fantasy game for a long time. Many of the threads in General Chat don't seem to have a great deal of replies either. How nice it would be to re-live the past few years.

Finally, I'll set a nice problem for anyone who reads this to think about and I promise to hand out a prize if you get the right answer:

I present you with a coin which you have no prior information on - for all you know it could be fair (probability of flipping a heads is 50%) or it might not be fair (e.g. probability of flipping a heads is 60%). I flip the coin once and it comes out to be heads. If I flip the coin again, with what probability would you expect heads to come up?

Spoiler: No one will get this.

[Che]

50%.

[Fate]

50%.

For all we know, the coin s/he has might be rigged. I say it has heads on both sides, so my guess is 100%! Isn't that right?

[Govinda]

Party on Wayne?

[Kilala]

Heh heh...
Logic says's 50%. But from the spoiler it couldn't be. So then maybe 100%? But then that is too obvious and you give the example of 60%.
Sometimes I can be very dumb. But a coin has 2 sides... Unless you count the rim, so then it would be 33.33333333%.
But a chance of 60 %? Does it have more sides or something?

[RagnaToad]

It would be a little over 50% chance to get another heads.

Sure the coin could be forged and give another heads automatically, so it would be 100%. But since you don't know anything about it being forged or not, it could be anything from almost 0% chance to give heads (I say almost because you know there's at least á chance to get heads) to 100% chance to get heads.

Tell me I'm right!
Yeah, that's what I thought.

(If you hadn't flipped it first and seen it gave heads, it would be exactly 50%, but now the chance of it being rigged to give a 0% chance of tails has been eliminated.)

[Volendral]

It should be 56%.

[RagnaToad]

It should be 56%.

Any motivation? I don't think there's any mathematical argument for that figure.

I get Heads 90% of the time, I get tails 9 out of 10 times. I've done it twice. No lie. I rarely see Heads appear when I call it. So when I play Madden I go Tails all the time lol. Actually I always call Tails. [...]

It's not about the actual amount of times a physical coin will give heads or tails. It's a theoretical approach.

[Volendral]

Any motivation? I don't think there's any mathematical argument for that figure.

Eh, I phrased it wrong. I meant to say I think it might be. Nothing mathematical about it, just trying to remember something my junior high teacher said in a discussion about this 9 years ago. I probably have no business in this thread .

[Fate]

I randomly visit TFF tonight and find that over a third of the non-stickied threads on the front page of General Chat were started by one person. Is TFF getting less and less active as time goes on?

Exactly. One person is making over a third of the threads in General Chat because that person is aware of the inactivity that is going on, right? So in all honesty, shouldn't we be thanking her for trying to bring life and activity back to this forum by creating new threads that people might be interested in?

[loaf]

I get Heads 90% of the time, I get tails 9 out of 10 times. I've done it twice. No lie. I rarely see Heads appear when I call it. So when I play Madden I go Tails all the time lol. Actually I always call Tails. I have a

3.141592653589793238462643383279502884197169399375 10582097494459230781640628620899862803482534211706 79821480865132823066470938446095505822317253594081 28481117450284102701938521105559644622948954930381 96442881097566593344612847564823378678316527120190 91456485669234603486104543266482133936072602491412 73724587006606315588174881520920962829254091715364 36789259036001133053054882046652138414695194151160 9 chance of getting Heads.

[Fate]

But theoretical probabilities are never exact! Honestly, nine out of ten people will not get five heads and five tails when flipping a coin. I'd say that experimental probabilities are far more accurate!

[RagnaToad]

But theoretical probabilities are never exact! Honestly, nine out of ten people will not get five heads and five tails when flipping a coin. I'd say that experimental probabilities are far more accurate!

What kind of an argument is that?

If a coin is made so that it is fair and has a 50% chance to give heads, you flip it 1000 times, and you get only 499 heads, it is not a fair coin anymore?

come on...

[Govinda]

Party on Garth!

[Autumn]

1. Wayne's World has a rating of 6.9/10 on IMDb. I think that's too high.

2. I wasn't criticizing Kilala for starting so many threads. I was asking a genuine question about the activity of TFF these days. As an aside comment, I do admire the effort at trying to instill more activity into the boards, especially if it is particuarly challenging to do so.

3. There's nothing "rigged" about this coin as in it has 2 heads, or multiple sides. It's a coin with two sides, one showing heads and the other tails.

Unless you count the rim, so then it would be 33.33333333%.

The chance of a coin landing on the edge after flipping it is almost surely 0.

4. I'm not asking for the probability of having a heads come up if I flip the coin. Since I have no information about this coin I do not know. I can only come up with a probability with which I expect heads to come up in the second flip given I've seen it come up in the first flip.

56% is not the right answer.

RagnaToad is right in saying the expected probability is over 50% and the comment "If you hadn't flipped it first and seen it gave heads, it would be exactly 50%" is also correct. However, you can come up with an exact expected value.

"it could be anything from almost 0% chance to give heads (I say almost because you know there's at least á chance to get heads) to 100% chance to get heads." is not a correct line of reasoning. Yes, the real probability is anything between [0,1] but this is by definition true.

Actually, I don't expect the value to be calculated by anyone (it's not hard once you know the pre-requisite stats knowledge) but anyone who can give an intuitive way of finding the expected probability, especially without knowing much statistics is, in my view, very clever

Edit: Wow, I have 83k+ Gil. I don't even know how I amassed so much.

[RagnaToad]

If you consider the first toss to be a sign of the coin being 50/50 heads/tails to 100% heads, it would be logical to think of the average of all values between 50% and 100% to be the chance one would expect for the coin to be heads again.

It's in human nature to think of the first toss as NOT a coincidence (even though it might just as well be a 1 in a million chance). So, one would think "at least it can give heads like a regular, fair coin". So the chance a person would wrongfully expect it to be heads again would be somewhere between 50% and 100%, thus with an average of 75%.

Though that's not very scientific, since the result of the first toss might be a 1 in an infinity chance just as well as a certainty...

I personally would still say the chance would be 50,000...0001% (comma indicates decimals). But perhaps your question was about what the human mind would make of it, which would probably (though wrongfully) be 75%.

[Autumn]

It's in human nature to think of the first toss as NOT a coincidence (even though it might just as well be a 1 in a million chance). So, one would think "at least it can give heads like a regular, fair coin". So the chance a person would wrongfully expect it to be heads again would be somewhere between 50% and 100%, thus with an average of 75%.

Though that's not very scientific, since the result of the first toss might be a 1 in an infinity chance just as well as a certainty...

I personally would still say the chance would be 50,000...0001% (comma indicates decimals). But perhaps your question was about what the human mind would make of it, which would probably (though wrongfully) be 75%.

No, my use of the word 'expected' was (and is) in the strict mathematical sense. No human subjectivity comes into it. Still, you've made a nice effort and I was going to give all my Gil to you, but I looked around on the Commerce page and I can't see how. I fear this is the start of technology outpacing my old man's brain.

Spoiler: The answer is 2/3

[Polk]

What's the most you ever lost on a coin toss?

[RagnaToad]

Hmm, I thought about that possibility, cause I knew another "riddle" like this one, only not with a coin. I think I saw something in the likes of it on a House M.D. episode. If only I knew what episode. It had something to do with the fact that you already have 1 solid heads, right? But aren't you supposed to mention that you will flip the coin 3 times or something?

Though I recall some argument concerning human paranoia affecting our way of thinking on this one. What's the scientific explanation for 2/3, if any?

And you can't give money to other members anymore.

[Autumn]

This isn't a riddle. It's a statistics question.

You're probably thinking of the Monty Hall problem where contestants were presented with 3 doors and one door had a nice prize behind it. You pick a door at random then Monty, who we all like, would proceed to tell you one door which didn't have the prize behind it. He then gives you the option of switching to another door or sticking with your original choice.

The point of the Monty Hall problem is if presented with 2 doors, and you have to choose one, the chance of winning is 0.5. But since Monty eliminates one door for you, you should take this into consideration when making the choice about whether to switch door or not, i.e. the probability is conditional upon a given situation. The chance of winning if you switch doors is then 2/3.

So in a way there is a tenuous relationship between this question and the Monty Hall question. Both use some given information leading to a conditional probability. Intuitively, it would be something along the lines of: since you don't know the true probability of getting heads, you take as given some probability value p (of getting heads) and flip the coin an infinite number of times. But you know the first outcome is a heads, so it's just like discarding all the results which have tails as the first outcome. For low values of p the probability of getting heads is lower, which means you'll be discarding more results when p is less than 0.5. Clearly, this implies the expected value of getting heads is above 50%.

[RagnaToad]

I don't quite understand the way you explain the coin thing.

But I think I understand the Monty Hall problem.

You have a 1/3 chance to pick a car instead of a goat. Monty then shows you one of the goats BUT what he basically does is making it so that you can't pick that door anymore. So at this point you only have 2 doors left. Because you have a 1/3 chance to have picked the car (cause there were 3 doors in the beginning), you only have a 1/3 chance that if you switch to the remaining door, you switch from car to goat.

OR think of it like this:

You pick a door and you have 2/3 chance that the car is behind the doors you didn't pick, right? But a goat is revealed in one of the two doors you didn't pick. So the doors you didn't pick still have 2/3 chance, but obviously, you won't pick the door that has been revealed (and actually, you can't ). So you have 2/3 chance that it's in "one of the doors" you didn't pick --> 2/3 chance it's in the door you can still switch to.

@Autumn: I'm working on the coin thing in my head. Trying to apply this to the coin...

[Meier Link]

In reality you still have a 49.9/100% chance of getting heads. You honestly don't have a true 50/50 chance seeing there is the third side to the coin which is sides.

So on average you have a 49.9% chance that it will be heads and the same of it being tales with a .2% chance that it will mystically land on its side.

The logical explination of this is the fact that you are flipping the coin so even if you some how weighted either side of the coin to "help" improve apon your statistic the outcome is still the same a 49.9% chance. Angles, deflection, and leveling have nothing and everything to do with the pure luck of the draw. You flip it so by shear volume mass you have statiscly screwed yourself into giving yourself this percentage. Now if you rolled the coin then your percentages would change drastically if the coin was weighted to one side but this is not the case.

Of course if the coin is duel sided the you still have the chance that it would land on its side, which would be .2%. Unless this coin that we have "no prior knowledge of" has a face of .032 and a width (side) of 3 inches. Then statistically it would almost always land on its side.

Limiting your question shows nothing and will also help to proove nothing. By doing this even if someone was to guess the correct responce you could still say "no" and change your secnario to suit your favor.

[RagnaToad]

Now if you rolled the coin then your percentages would change drastically if the coin was weighted to one side but this is not the case.

How is that any different from flipping a coin? The heavier side would still be more plausible to be down when the coin lands... Just like it would when you roll it, as you're stating here.

[Meier Link]

No a rolled coin is more likely to land on a heavier side then a flipped coin. A flipped coin is doing exacty that, flipping side to side as to where a rolled coin is on one side and depending on a heavier side. There is honestly no comparison to the two.

The only simularities would exsist if the coin landed on edge and rolled at that point it would apply to the heavier side hitting downwards in most cases.

Flipping is that the coin is quite literally out of control. There is no balance and there is no ryme or reason to the landing of the coin. That is why it is called chance / luck.

[RagnaToad]

So basically, you are saying that a coin of which the heads side is 1000.000.000 times heavier won't necessarily be heads more likely?

You're saying the heavier side only matters when there's rolling in the process?


Then why does a toast with jam on one side will most likely fall on the jam side?

And why does an axe EDIT: MOST LIKELY land with the iron (read: heavy) part in a tree when you throw it?

[Meier Link]

So basically, you are saying that a coin of which the heads side is 1000.000.000 times heavier won't necessarily be heads more likely?

Show me a coin that weighs that much and I would say you are right, seeing one of that magnatude does not exsist then your theaory is incompreshinsable.

You're saying the heavier side only matters when there's rolling in the process?'

The majority of the time yes.

Then why does a toast with jam on one side will most likely fall on the jam side?

This question is irrelivant to the subject at hand unless you are flipping the toast, which by the way is not a rigid structure like a coin, you could possibly have a point where both sides are touching the ground. But in reality, with toast you are thinking in a unidirectional function out of toaster, you pick it up, jam one side and sit it on edge. Gravity comes into affect here and it pulls the motionless toast to one side. Once again irrelivant.

And why does an axe land with the iron (read: heavy) part in a tree when you throw it?

You are speaking statistics again and makeing a statement that it always hits iron side first, which is an assumption. This is not always the case. And you are talking about where one side is dramatically heavier then the other. With a coin you have to think about size verses volume in a circular shape (which an axe has NOT).

Put some thought behind what you are saying and try to keep it to the subject at hand, none of the examples you tried to proivide are in relevance to the question. Thinking outside the box will only put you further into another one.

Then again for all we know the coin could be tossed into a pile of shite and could easily be ebing touched on more then one side. Like I said "Limiting your question shows nothing and will also help to proove nothing. By doing this even if someone was to guess the correct responce you could still say "no" and change your secnario to suit your favor." There are a million different responces that could be used and all could be correct depending on the scenario. I just picked the more logical one.

[RagnaToad]

All of the examples I mentioned are relevant.

1. It's not because of the fact that the difference between one side of a coin and the other side cannot be 1.000.000.000 that it is impossible to force a coin into falling on a certain side more likely than on the other side... I was just exaggerating. Obviously, you missed the point I was making. You're saying I would be right if a coin like that existed, but then where do you draw the line? It CAN affect the coin when it's 2 times heavier, but it can't when it's 1% heavier?

2. You seem to think there's a major difference between flipping a coin and (whatever) "flipping" a toast. What is the difference? A coin is smaller and most of the time round?

3. An object will by definition fall on its heavier side more likely, no?

4. You contradict yourself. First you're saying that the chances will still be 50% (I'm not gonna count the rim), even if one side were heavier. The next moment you're saying that a rolling coin will "more likeley" fall on its heavier side than a flipped coin would. Meaning that a flipped coin would too, just not as likely, thus proving your first statement to be wrong.

[Meier Link]

All of the examples I mentioned are relevant.

1. It's not because of the fact that the difference between one side of a coin and the other side cannot be 1.000.000.000 that it is impossible to force a coin into falling on a certain side more likely than on the other side... I was just exaggerating. Obviously, you missed the point I was making. You're saying I would be right if a coind like that existed, but then where do you draw the line? It CAn affect the coin when it's 2 times heavier, but it can't when it's 1% heavier?

Like I said show me a coin that is 2 time heavier on one side let alone 1,000,000,000 times. If you take the simple logic that you are using then you also have to think that you are also adding weight that could increase the chances that it will land on its side. The odds are you are FLIPPING A COIN not just sitting it on it's side, so the odds are not so much on the weight but on the facings. It is simple enough.

2. You seem to think there's a major difference between flipping a coin and (whatever) "flipping" a toast. What is the difference? A coin is smaller and most of the time round?

Umm yeah there is a difference. There are about 1000 differences. Here is one, one is soft and pliable while the other is rigid and hard. Here is another one, toast is more likely to bend and fold then a coin. Are you getting a point in the difference yet or should I go on? Square Vs Circle? Wheat Vs metal alloy? Crust Vs no crust? (ok those last 2 where a joke)

3. An object will by definition fall on its heavier side more likely, no?

Once again it depends on the scenario, this is a very undefined one at that. In a controlled situation yes it happens most of the time, but when flipping a coin there is NO contol. None, nota, nein, zilch. And that is the point you are missing here. The possiblity of of setting a coin to the point where on side drastically out weighs the other is slim to none. While Changing the center of graviy and the balance of the coin will not affect an over all outcome of the randomness that is caused by quite literally hurling a coin end over end until it pings the ground and does the same thing again and again until it stops.

Here is something else to put into your head, if the light side hits DOWN then the heavier side will force it down. Your logic of this is very one sided, kind of like the coin you are trying to create.

[RagnaToad]

You make it sound like I was saying that it is possible to make a coin give tails/heads constantly...

I don't see any logic in how you think that it is possible to affect the landing of a toast (let's stick to this one) but not of a coin? How is a coin more uncontrolable than a toast? And what is "flipping" a coin anyway? Isn't that just making it fall from a height?

Basically, you're saying that a coin is the sole object in this universe that cannot be forged to create a (albeit slightly) different outcome? That's kind of... weird.

[Meier Link]

I don't see any logic in how you think that it is possible to affect the landing of a toast (let's stick to this one) but not of a coin? How is a coin more uncontrolable than a toast? And what is "flipping" a coin anyway? Isn't that just making it fall from a height?

Toast has more possible outcomes then flipping a coin. Like I said there are over a 1000 different differences between the two. What is your obcession with toast anyways?

You also have to add in rotation, not just end over end but side over side from all directions. Then again why are you debating with me if you are asking me what flipping a coin is?

Basically, you're saying that a coin is the sole object in this universe that cannot be forged to create a (albeit slightly) different outcome? That's kind of... weird.

Never said that, please don't try to put words in my mouth.