Moderated Coin Flipper

[Leumas]

I think the convergence mentioned is not across multiple runs but over the number of trials in any one run.

10 runs of 1,000 coin flips each is the same as 1 run of 10,000 coin flips.

The more trials you have, the closer you get (converge on) to an even 50/50 split.

Nope... the more trials you get the more it becomes like a probability distribution.... bell curve... not a vertical single line.

In this case converge is being used as converge toward something, in this a 50% average. You can converge toward something without ever reaching it, i.e. approach asymptotically.

Yes... you can... but not in this case... and oscillating UNPREDICTABLY over and above as can be seen by jut looking at the results in the post above.

I tried 100 goes at 10,000,000 flips a go and the running averages were

Running Average H = 50.0009%
Running Average T = 49.9991%

At first glance that looks like pretty darned close to 50-50... no?

But it actually means that out of a 1 billion coin tosses there were still 9,000 more Heads than there were tails.

Now one might think that this will asymptoticly keep getting lesser and finally reach 50-50... but of course not... the next billion flips might shift the balance and have 5000 more tails than heads... and the next billion might make it go 50-50 but the next billion will shift it again and so on and on.

Why??? Because its is random... that is what random means.

The whole point of the app was to play with the coin flip without having to actually spend the rest of one's life doing so in order to see how random coin tosses never really asymptotically approach a deterministic 50-50 result if only one approaches an infinite number of tosses.

Which illustrates that a random process is indeterministic despite the fact that we can have a stochastic algorithm for predicting a spread for the results around an average (e.g. normal distribution).

My app allows a person to PLAY and EXPERIMENT with numbers of tosses that would take years to do otherwise.

...
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.

 

[jsfisher]

Along with slander, concern, and red-herring, we can add converge to the list of concepts Leumas seems to not understand.


Maybe this will help:

In Mathematics, the sequence S_i is said to converge to L if and only if for all d > 0 there exists an N such that |S_j - L| < d for all j > N. "The further out you go, the closer it gets", sorta.

For this thread, the meaning needs to be softened to accommodate statistical properties over absolute inequalities. Probability densities and all that. Easier to imagine than precisely define, so I will leave it at that.

 

[jsfisher]

...
That is 10⁹ flips
...

That, my friend, is getting into the territory of "inappropriate". A sequence of say 10 million random numbers, yeah ok. But one billion, that may be pushing it.

 

[Leumas]

That, my friend, is getting into the territory of "inappropriate". A sequence of say 10 million random numbers, yeah ok. But one billion, that may be pushing it.

What is 100x10,000,000?

When you do 100 times of 10,000,000 flips you have done 10⁹ flips.... and Coin Flipper 4 lets you do that with the click of a mouse.

Or with a tap on a touch screen... or on any of the WIDE RANGE of machines and OSs of today.





.

 

[theprestige]

You never ran mine... and I doubt very much your ran jsfisher's.

Why would I have to run yours? You ran it and posted the results. Should I not believe your results? Should I expect your app to work differently for me than it does for you?

The results you posted, from your app, show exactly what acbytesla predicted. Q.E.D.

But here have a look at this sample run of 95E+7 and 1E+9

That is 10⁹ flips

Now observe how it rives your assertion asunder.... all one has to do is LOOK... and your bare assertion is definitively and irrefragably proven wrong.

Look what happens to the running average between run #95 and #100.

At run #95 the running average is 50.0001 and 49.9999

If your assertions had any validity whatsoever... the next run of 50,000,000 coin flips ought to have made it even closer to 50%... no.

But as can be seen by just looking...

At 950,000,000 flips the running average was 50.0001% to 49.9999%
At 1,000,000,000 flips the running average is 50.0010% and 49.9990%

That is a factor of 10 jump IN THE WRONG direction.

At run #95 there was 950 more heads than tails. At run #100 there was 10,000 more heads than tails.
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.

So no... the FACTS rive to smithereens your BARE ASSERTIONS.... no matter how many times you insist on repeating the error it will not ever converge onto truth.

[IMGW=550]http://godisadeadbeatdad.com/CoinFlipperImages/NotConvergent.png[/IMGW]
​

I don't think you understand how probability works, or what converges means. Q.N.E.D., but still a valid finding, I think.

 

[Leumas]

I did use the app. With 10,000 flips per trial, no "edge case", using the base generator I got:

Do you know how to do screen capture and then crop the image?

Your table means nothing.

Noisy, as I said, but it does appear to be narrowing in on 50% after 1,000 X 10,000 flips.

Here is a screen shot from the actual app not the one you made up...

Show me where the convergence is please

You never ran mine... and I doubt very much your ran jsfisher's.

But here have a look at this sample run of 95E+7 and 1E+9

That is 10⁹ flips

Now observe how it rives your assertion asunder.... all one has to do is LOOK... and your bare assertion is definitively and irrefragably proven wrong.

Look what happens to the running average between run #95 and #100.

At run #95 the running average is 50.0001 and 49.9999

If your assertions had any validity whatsoever... the next run of 50,000,000 coin flips ought to have made it even closer to 50%... no.

But as can be seen by just looking...

At 950,000,000 flips the running average was 50.0001% to 49.9999%
At 1,000,000,000 flips the running average is 50.0010% and 49.9990%

That is a factor of 10 jump IN THE WRONG direction.

At run #95 there was 950 more heads than tails. At run #100 there was 10,000 more heads than tails.
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.

So no... the FACTS rive to smithereens your BARE ASSERTIONS.... no matter how many times you insist on repeating the error it will not ever converge onto truth.

[IMGW=550]http://godisadeadbeatdad.com/CoinFlipperImages/NotConvergent.png[/IMGW]
​

 

[JimOfAllTrades]

10 runs of 1,000 coin flips each is the same as 1 run of 10,000 coin flips.

Only if you add the data together and recalculate the average based on all ten runs.

Run 01 - 490 heads, 510 tails, average for heads .490
Run 02 - 510 heads, 490 tails, average for heads .510
Run 03 - 490 heads, 510 tails, average for heads .490
Run 04 - 510 heads, 490 tails, average for heads .510
Run 05 - 490 heads, 510 tails, average for heads .490
Run 06 - 510 heads, 490 tails, average for heads .510
Run 07 - 490 heads, 510 tails, average for heads .490
Run 08 - 510 heads, 490 tails, average for heads .510
Run 09 - 490 heads, 510 tails, average for heads .490
Run 10 - 510 heads, 490 tails, average for heads .510


In doing this you never get any closer to 50%. As you say it could oscillate forever and never get any closer.

But add those 10 runs together and recalculate and you get exactly 50%. (Not that you'd expect that exactly in the real world.)

Now do one more run of 1000:
Run 11 - 490 heads, 510 tails, average for heads .490

Again, you're no closer on that one run. But add that run to the previous totals and recalculate and you get 5490 heads, 5510 tails, and your overall average is .499 heads, much closer to 50/50.

So with a binary selection chosen at random, the more selections you do the closer it should converge on 50/50.

 

[Leumas]

...

....

Can you please answer the questions below which I will never get an answer for from the people I asked the questions to originally.

I would love to see your answers.

Let's say that one picks the 20th card from the right side of a shuffled and spread out deck of cards every time.

That is not just deterministic... it is not even random

But the deck is shuffled before one picks the 20th card from the right.

Now the deck is not even random numbers... it is the same deck of cards... no?

Do you think anyone can determine whether a red (diamonds/hearts) or black (clubs/spades) card will be drawn??


So

• We have the same deck of cards... no random numbers or changing at all.
• We have the same card position picked every single time... not random or not even unknown... fully determined
• But the cards deck is shuffled before every pick... from the same deck... from the same position

Is the resulting pick (red or black) random?

Is it deterministic? If you say yes... then by whom or what?

 

[JimOfAllTrades]

Can you please answer the questions below which I will never get an answer for from the people I asked the questions to originally.

I would love to see your answers.

I'm not sure I'm versed enough to make a good answer. But let me think about it some and see what I can come up with.

 

[Leumas]

Only if you add the data together and recalculate the average based on all ten runs.

That is what the running average is there for.

In doing this you never get any closer to 50%. As you say it could oscillate forever and never get any closer.

And so does the running average too... look at this post.

As can be seen by just looking...

At 950,000,000 flips the running average was 50.0001% to 49.9999%
At 1,000,000,000 flips the running average is 50.0010% and 49.9990%

That is a factor of 10 jump IN THE WRONG direction.

At run #95 there was 950 more heads than tails. At run #100 there was 10,000 more heads than tails.
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.

[IMGW=550]http://godisadeadbeatdad.com/CoinFlipperImages/NotConvergent.png[/IMGW]
​

 

[jsfisher]

Do you know how to do screen capture and then crop the image?

You know, if your app displayed the running averages after each trial rather than the individual trial result, it would be easily possible to screen capture just one image with the full set of evolving running averages for the last ten or so runs.

That aside, when I have a result you don't like, you accuse me of just making it up....

Your table means nothing.

Case in point.

Here is a screen shot from the actual app not the one you made up...

And again.

 

[jsfisher]

What is 100x10,000,000?

When you do 100 times of 10,000,000 flips you have done 10⁹ flips.... and Coin Flipper 4 lets you do that with the click of a mouse.

Yeah, we know what numbers can be entered and what happens when buttons are pushed.

The point I was raising was the usability of the pseudorandom number generator for a sequence of one billion or more values. Yes, it will provide that many values, but at what point do the values no longer have the required properties?

 

[Leumas]

You know, if your app displayed the running averages after each trial rather than the individual trial result,

You evidently have not looked at the screen at all... it does exactly that... I suggest you look better next time.

That aside, when I have a result you don't like, you accuse me of just making it up....

I did not say you made the results up... you made up a table that is meaningless.... and the results in it mean nothing since they have no reference to anything.

Here have a look at this sample run of 95E+7 and 1E+9

That is 10⁹ flips

Now observe how it rives your assertion asunder.... all one has to do is LOOK... and your bare assertion is definitively and irrefragably proven wrong.

Look what happens to the running average between run #95 and #100.

At run #95 the running average is 50.0001 and 49.9999

If your assertions had any validity whatsoever... the next run of 50,000,000 coin flips ought to have made it even closer to 50%... no.

But as can be seen by just looking...

At 950,000,000 flips the running average was 50.0001% to 49.9999%
At 1,000,000,000 flips the running average is 50.0010% and 49.9990%

That is a factor of 10 jump IN THE WRONG direction.

At run #95 there was 950 more heads than tails. At run #100 there was 10,000 more heads than tails.
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.

So no... the FACTS rive to smithereens your BARE ASSERTIONS.... no matter how many times you insist on repeating the error it will not ever converge onto truth.

[IMGW=550]http://godisadeadbeatdad.com/CoinFlipperImages/NotConvergent.png[/IMGW]
​

 

[jsfisher]

I did not say you made the results up...

Yeah, you did.

...not the one you made up...

 

[jsfisher]

You evidently have not looked at the screen at all... it does exactly that... I suggest you look better next time.

No it does not. It gives the heads and tails percentages for each of the past ten or so individual runs. It also gives the running average percentage as of the last run.

I was suggesting displaying the running percentages as of each trial instead of the individual trial percentages. Then, a single screen shot would show the evolution of the running averages for the past ten trials, not just the current averages.

 

[Leumas]

....
The point I was raising was the usability of the pseudorandom number generator for a sequence of one billion or more values. Yes, it will provide that many values, but at what point do the values no longer have the required properties?

The PRNG is not asked to provide 10⁹ values.

It is asked to provide ONE value for each flip to decide the flip result.

Each flip is independent of the previous or any other flip.

Doing 10⁷ flips is just like doing one flip 10⁷ times.

And doing 100x10⁷ is just like doing one flip at a time for 10⁹ times.

The PRNG is not asked to produce more than one random number at a time each time there is a flip.

And each time the flip is done a new seed is used so a new sequence is generated from which one result is used for the flip.

So doing 10 flips the PRNG is asked 10 times each time anew to generate a new random number with a new seed.

Doing that 1000 times or 10⁹ is the same.

In your QBasic it is like doing a RANDOMIZE TIMER before each time you use the Rnd function.

 

[Leumas]

Yeah, you did.

You made the table... that is what I meant... and the made up table is worthless... and thus the results in it are worthless too.

But in any case I suggest you look more closely at the sample runs I gave in this post.

They irrefragably debunk your claims.

 

[Leumas]

No it does not. It gives the heads and tails percentages for each of the past ten or so individual runs. It also gives the running average percentage as of the last run.

I was suggesting displaying the running percentages as of each trial instead of the individual trial percentages. Then, a single screen shot would show the evolution of the running averages for the past ten trials, not just the current averages.

Well... that might be a good addition for the next version... but unless you apologize for your false slander of me... I do not see the point of ever doing anything for you.


But... you can always take a screen shot after each trial because the running average is right there before the next run.

But regardless... the results in the screen shots in this post show that your claims are not true anyhow.

 

[Leumas]

....

Why have you not answered the questions paused below.... is it because they demonstrate how wrong you are about the inherent randomness of the process???

...

But... let's see if you can answer these questions

Let's say that one picks the 20th card from the right side of a shuffled and spread out deck of cards every time.

That is not just deterministic... it is not even random

But the deck is shuffled before one picks the 20th card from the right.

Now the deck is not even random numbers... it is the same deck of cards... no?

Do you think anyone can determine whether a red (diamonds/hearts) or black (clubs/spades) card will be drawn??

So

• We have the same deck of cards... no random numbers or changing at all.
• We have the same card position picked every single time... not random or not even unknown... fully determined
• But the cards deck is shuffled before every pick... from the same deck... from the same position

Is the resulting pick (red or black) random?

Is it deterministic? If you say yes... then by whom or what?

 

[Thermal]

To respond to the card question (and coin flipping for that matter), it appears random. It is not, really. A simple thought experiment:

You have two cards, one red and one black. You take note of which is which before they are inverted and slowly "shuffled". You are able to track which is which, and "guess" correctly which will be drawn.

The same principle applies to a full deck of cards. If you know enough about the physics of each, you can determine not only the 50/50 odds, but exactly what card it will be.

However, we don't practically know enough, so we call it random, even though it was entirely deterministic, at least in theory.