Moderated Coin Flipper

[Leumas]

Never claimed it was flat. Look at that tight oscillation right at the 50% line though. Exactly as predicted. Q.E.D.

QED!!!

YOU GO IT ... By Jove you got it finally...

Thanks for proving yourself wrong with your own data and graph and now finally with your own words.

Never claimed it was flat....

Yes you did...

Over the series, the oscillations damp down, staying closer and closer to the 50/50 line. The oscillations converge on 50/50. Q.E.D.

...What starts out as a very swingy oscillation damps down over time, as each successive flip becomes less influential to the overall trend towards a 50/50 split.

[IMGW=800]http://godisadeadbeatdad.com/CoinFlipperImages/graph.png[/IMGW]​

And here is what I said that you now are repeating and have proven yourself with your own data and your own graph.

...
All you have to do is zoom in a little on the part you call convergent and you can see the erratic oscillations that clearly never settle down as any definition of convergent means...

...
But moreover... I don't think you know the difference between converge and oscillate.

..
And I think you need to check out the meaning of the word "converge"...

Hint:... converge does not mean oscillate.

...
It will forever oscillate like this although you are correct it is closer to the 50%... BUT NEVER CONVERGES on it.

And if you look at the averages of each run you will not fail to notice the wild OSCILLATIONS... observe runs #88 and #89.... and runs #95, #96, #97.

No... it oscillates above and below and sometimes 50% and it is sometimes in favor Tails others in favor of Heads and it gets lower difference the more tosses but sometimes gets higher... there is just no rhyme or reason... it is just indeterministically random.

..
Now let's have a look again at something that illustrates the randomness of the process preventing any asymptotic approach to 50-50 and it will constantly oscillate in favor of heads one time or tails the other and will continue to do so because... it is a random process....

 

[Leumas]

To avoid confusion it might be as well to point out that this convergence is only demonstrated for the relative results. That is, the proportion of results being heads converges to 50% as the number of tosses increases.

However, in terms of absolute numbers, the opposite occurs. The results actually diverge. The more often you toss a coin, the greater the likely difference between the number of heads and half the tosses is going to be.

What does convergence mean?

It does not mean oscillations... tight or otherwise...

And as proven by theprestige... it oscillates.

What does oscillate mean... it does not mean ONE VALUE.

FLUCTUATING around a value for ever and with UNPREDICTABLE magnitudes (tight or otherwise)... is called oscillating.

Just like this....

[IMGW=800]http://godisadeadbeatdad.com/CoinFlipperImages/graph.png[/IMGW]​

 

[Leumas]

I predict that that will actually increase confusion, for Leumas anyway.

In many regards, it is willful.

The above two posts are ironically a perfect illustration of this post ... and a vivid demonstration of this post.

 

[jt512]

What does convergence mean?

Jsfisher and I have both given you the definition of convergence. You have repeatedly proved that you can't comprehend it. I don't know why you are so invested in publicly proving how little you know. Iterative algorithms depend on convergence. How can someone who claims to be a competent programmer not understand what convergence is? For that matter, didn't you say you had a masters degree in engineering? Last time I checked, engineers had to take elementary calculus. You should have learned what convergence is in class.

 

[psionl0]

What does convergence mean?

In the context of Bernoulli trials, it means that the result gets closer to the mean value as the number of trials increases. In fact, you can make your result arbitrarily close* to the mean value by having enough trials.

* To be clear, it is the confidence interval of the expected results (expressed as a probability) that gets arbitrarily close to the mean value. An individual trial run could still have results well outside of the confidence interval (but with a very small probability).

It does not mean oscillations... tight or otherwise...

No it doesn't. However, the results do fluctuate about the mean value in a random manner. There is nothing about a limiting value that says a function can't cross it from time to time. For example, sin(x) / x converges to 0 as x goes towards infinity. Yet sin(x) / x crosses the x axis whenever x is a multiple of pi (and x =/= 0).

 

[Leumas]

Jsfisher and I have both given you the definition of convergence. You have repeatedly proved that you can't comprehend it. I don't know why you are so invested in publicly proving how little you know. Iterative algorithms depend on convergence. How can someone who claims to be a competent programmer not understand what convergence is? For that matter, didn't you say you had a masters degree in engineering? Last time I checked, engineers had to take elementary calculus. You should have learned what convergence is in class.

The above is a complete proof of the words in this post ... ... and ironically and risibly enough of this post too.

 

[Leumas]

* To be clear, it is the confidence interval of the expected results (expressed as a probability) that gets arbitrarily close to the mean value. An individual trial run could still have results well outside of the confidence interval (but with a very small probability).

No it doesn't. However, the results do fluctuate about the mean value in a random manner. ....

Exactly... fluctuates ... i.e. oscillates randomly.... although the GUESSING of this random oscillation's magnitude can get less CHANCE of being wrong... it still remains a guess and is still random AND INDETERMINISTIC.

Thanks for explaining that ... I agree fully... which is what I have been saying... oscillates although closer to 50%... and that does not make it less random or les indeterministic.

So it does not become less random or less oscillating by approaching infinity of tosses and although the guessing becomes less erroneous for the outcome of the infinite amount of tosses the whole thing is still indeterministic and random.

Ah... "infinity"... ironically and risibly... the very apologists who keep harping on how infinity is nonsense in order to "prove" their gods... turn around and start brandishing infinity when it comes to denying indeterminism in order to keep their gods in the game

[IMGW=800]http://godisadeadbeatdad.com/CoinFlipperImages/graph.png[/IMGW]​

.

 

[Dr.Sid]

Yep, he doesn't have a slightest idea .. QED!

 

[jt512]

In the context of Bernoulli trials, it means that the result gets closer to the mean value as the number of trials increases. In fact, you can make your result arbitrarily close* to the mean value by having enough trials.

* To be clear, it is the confidence interval of the expected results (expressed as a probability) that gets arbitrarily close to the mean value. An individual trial run could still have results well outside of the confidence interval (but with a very small probability).

Here is a run of 10,000 flips along with the 90% confidence band (the shaded area).

[imgw=600]http://jt512.dyndns.org/documents/leumas/flips.png[/imgw]

Notice that during this run, there was very little fluctuation about the mean. The cumulative proportion of heads remained less than 0.5 most of the time, although we can see it approaching 0.5 toward the end of the run.

 

[Leumas]

...

[imgw=600]http://jt512.dyndns.org/documents/leumas/flips.png[/imgw]

Notice that during this run, there was very little fluctuation about the mean. The cumulative proportion of heads remained less than 0.5 most of the time, although we can see it approaching 0.5 toward the end of the run.

I suggest you look again at your own graph... infinitely repeating things that are incorrect does not make them converge to the truth.

But hey... I am pleased with how much concerned effort you have put in order to diss on the app that you decreed is worthless and pointless.

All that indefatigably concerned effort... wow... QED!!!

 

[jt512]

I suggest you look again at your own graph... infinitely repeating things that are incorrect does not make them converge to the truth.

I would suggest you try thinking for a change. You can start by looking at the wikipedia article on the Law of Large Numbers, which I've referred you to multiple times. Either that or crack open any elementary statistics text book.

You might also take the hint that when every single person in the thread disagrees with you, you might actually consider the possibility that it is you who is wrong, and not everybody else in the thread.

 

[jsfisher]

Indeed... I wish you would listen to your own admonishment then and stop denying FACTS of reality ... and repeatedly and incessantly slandering me for trying to point out the facts of reality you are vehemently denying.

Present some facts, and see how we make out. Your sweeping unsupported statements and graphs with no context whatsoever don't cut it.

Start with something simple. What is your definition of the word, converge, as it applies to this thread?

 

[zooterkin]

A reminder to all to address the topic of the thread (as far as that can be determined) and to avoid personalising the discussion. Some clean up may be needed on previous posts.

Please refrain from insults and discussing other members in this thread, thank you.

Replying to this modbox in thread will be off topic  Posted By: zooterkin

 

[Leumas]

Present some facts, and see how we make out. Your sweeping unsupported statements and graphs with no context whatsoever don't cut it.

(1) They are not my graphs... they are those of theprestige
(2) the context is right here

And here is another graph that is not mine that is claimed to support convergence when it ironically supports erratic oscillation... which is what is to be expected from a RANDOM process.

The deceptive zoomed out scale might give the impression to the uninformed that it is converging.... but all the discerning have to do is actually ZOOM IN on the DETAILS and see for themselves how it is a random process.

Notice the 3 peaks that touch the 50% line but yet with more flips there is DIVERGENCE and more erratic oscillations... not convergence.

If it were convergent there would not be erratic divergence and oscillations and more divergence.

[IMGW=700]http://godisadeadbeatdad.com/CoinFlipperImages/NotConverge3.png[/IMGW]​

And here is that of theprestige again

[IMGW=800]http://godisadeadbeatdad.com/CoinFlipperImages/graph.png[/IMGW]​

Present some facts, ...

In addition to the ones provided above by theprestige and jt512 proving their errors... here are some more facts from running Coin Flipper 4 that you did not bother to look at

[IMGW=800]http://godisadeadbeatdad.com/CoinFlipperImages/NotConvergent.png[/IMGW]​

 

[theprestige]

Ah... "infinity"... ironically and risibly... the very apologists who keep harping on how infinity is nonsense in order to "prove" their gods... turn around and start brandishing infinity when it comes to denying indeterminism in order to keep their gods in the game

Well that took a turn.

I'm out, guys.

 

[Myriad]

The convergence of the expected results in this context means something like this:

Given a probability p<1.0 (but arbitrarily close to 1.0) and a real number ε>0 (but arbitrarily close to 0), there is some number of unbiased random coin flips n such the the probability that (|count (heads) - count (tails)| / n < ε) is greater than p.

Of course it's a proven theorem in probability theory.

 

[Leumas]

The convergence of the expected results in this context means something like this:

Given a probability p<1.0 (but arbitrarily close to 1.0) and a real number ε>0 (but arbitrarily close to 0), there is some number of unbiased random coin flips n such the the probability that (|count (heads) - count (tails)| / n < ε) is greater than p.

Of course it's a proven theorem in probability theory.

Yes... what is this "n"... infinity?

And what is this arbitrary probability? 1?

And what does "close to" mean... evidently does not mean EXATLY.

And clearly arbitrarily close to... means... by CHANCE it might get to be close but not exactly the same.

arbitrarily

• in a way that is based on chance rather than being planned or based on reason

If it does not get close but keeps arbitrarily getting close then far then close then further then closer then even closer then further and further and then close then further... as can be seen in the two graphs and the data given in this post.

Then this means it is arbitrary and random and indeterministic.



.

 

[theprestige]

The convergence of the expected results in this context means something like this:

Given a probability p<1.0 (but arbitrarily close to 1.0) and a real number ε>0 (but arbitrarily close to 0), there is some number of unbiased random coin flips n such the the probability that (|count (heads) - count (tails)| / n < ε) is greater than p.

Of course it's a proven theorem in probability theory.

And easily demonstrated by every coin flipper posted here. Q.E.D.

(Sorry, I know I said I was out, but I can't resist a good Q.E.D.!)

 

[Leumas]

And easily demonstrated by every coin flipper posted here. Q.E.D.

(Sorry, I know I said I was out, but I can't resist a good Q.E.D.!)

It is arrantly demonstrated that you are wrong by your very own words here in this post... and by your data here in this post and its graph zoomed in to remove the deceptive aspect of its scale... here in this post.... not to mention the data and graphs in this post.

 

[Myriad]

Yes... what is this "n"... infinity?

It's an integer.

And what is this arbitrary probability? 1?

It is not 1, hence the use of the symbols "<1.0"

And what does "close to" mean... evidently does not mean EXATLY.

And clearly arbitrarily close to... means... by CHANCE it might get to be close but not exactly the same.

No chance involved. "Arbitrary" means you get to choose it. You might for example choose p= .99 or .9999 or .99999999, as long as the number of 9's is finite, because as you said we don't like infinite quantities 'round these parts. And you might choose ε= .01 or .00001 or .000000071, as long as the number of lead zeros is finite, because as you said we don't like infinite quantities 'round these parts.

The point is that for any possible choice of p<1.0 and ε>0, there is some number of throws n that meets the stated condition. There is no probability so close to 1.0 and/or epsilon so close to 0 that the corresponding n becomes anything other than a finite integer. That's what it means mathematically when we say a sequence of fair tosses converges on exactly 50% heads.

The calculation of n for any given p and ε is completely deterministic, and no infinite quantities are involved either.