Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Who really flipped the coin?

Hi

Two students were asked to flip a coin 120 times and record the heads as 1 and the tails as 0 and then hand it in.

Student A handed in:

1100 1011 0110 0100 0110 1010 0110 1001 0101 1011 0011 0111 0100 1001 1010
0110 1001 1010 1100 1110 0101 0100 0101 0101 0101 1001 0010 1100 1001 1011

Student B handed in:

1100 0011 1010 1111 1101 0001 1001 1010 1000 1101 0011 1010 0001 0111 0110
0111 0110 0111 1110 1101 0101 0000 0000 1001 1001 1110 1111 0101 1011 0101

One of them cheated and didn't flip a coin at all. Which one cheated and why?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Who really flipped the coin?

Makes a good point!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Who really flipped the coin?

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The Beginning Of All Things To End.
The End Of All Things To Come.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

Last edited by phrontister (2009-08-23 13:02:40)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Who really flipped the coin?

Hi phrontister;

None that I am aware of.

Hi MathsisFun and luca-deltodesco;

Correct.

Last edited by bobbym (2009-08-23 22:47:28)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

Hi Bobby,

I doubted that there would be runs such as in your findings and so I conducted my own experiment. Coin tosses were varied...left-handed, right-handed, caught, dropped, high toss, low toss, & some others.

Had to do it while my wife was out, because I'm "spending too much time on that maths forum".

My results:

0110 0110 1100 0011 0101 0111 0101 0111 1101 1011 1010 0001 0011 0000 1011
0101 1000 1111 1001 0010 1101 0001 0011 1101 0001 0101 1111 0111 1000 1011

Well...I'm surprised. It has 3 runs of 5 plus 5 runs of 4.

It also bears out luca's comment:

And no...I don't think there's a hidden message in my binaries.

I didn't analyse it any further...I just heard the front door open!

Last edited by phrontister (2009-08-24 00:58:50)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Who really flipped the coin?

Hi phrontister;

Why the heck didn't you program it! I just did one test on your data and I believe you flipped that coin. I remember doing a blackjack simulation by hand, a long time ago. It was before I got my first computer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

Hi Bobby,

Why the heck didn't you program it!

I don't know what possessed me! Sometimes I just start writing instead of typing, too!!

But I haven't yet descended to the depths of shop assistants and their utter reliance on calculators, even for the simplest of tasks.

Last edited by phrontister (2009-08-24 01:56:23)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Who really flipped the coin?

There is a purity in phrontister's sequence ... no need to worry about pseudorandom issues.

I wonder why noone has thought to include a "random" chip in a standard PC? Just a well-baked transistor would help!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Who really flipped the coin?

There are some computers that use radioactivity to obtain "truly random" numbers.
Something like drilling a hole in Schrodinger's box and timing how long it takes for the cat to die.

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Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Who really flipped the coin?

Hi;

  The trouble is flipping a coin is not truly random either, their is a bias to one side because of the uneven weight distribution. Pseudo-random numbers while not truly random, have the statistical properties of randomness.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

Hi Bobby,

The trouble is flipping a coin is not truly random either, their is a bias to one side because of the uneven weight distribution...

I doubt that there was much (any?) influence due to weight-distribution bias in my live experiment. Mixed in with the variations I mentioned above (left-handed, right-handed, caught, dropped, high toss, low toss) were catching-height variations, turning the coin over in my hand varying numbers of times before (and/or after) flipping it and varying the spinning speed. That's all I recall.

I also used varying combinations of those variations: eg, slow spin/high toss; fast spin/low catch/turn over catch.

I never used the same manoeuvre multiple times in a row...and maybe that makes my experiment not truly random.

Last edited by phrontister (2009-08-24 13:38:41)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Who really flipped the coin?

Hi phrontister;

I'm not saying the bias developed from the way you tossed the coin but from the fact that a coin is uneven in weight distribution (one side is heavier than the other). When a coin is spun it has a huge bias and when it is flipped:

http://www.codingthewheel.com/archives/ … roposition

Last edited by bobbym (2009-08-24 13:35:55)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

Hi Bobby,

Very interesting article...thanks! Next time there's some coin-flipping to do I'll toss and I'll call!

I hadn't considered the enormous influence that a weight-distribution bias of umpteen vigintillionths of a yoctometer (or any number of vigintillionths of a yoctometer, for that matter) might have on my experiment, otherwise I would have gone to much greater lengths than I did to try to achieve true randomness.

And it's just as well that the author didn't go down to one googolplexth of a yoctometre for the level of perfection in a coin's fabrication, or I might have thought he was just being silly!

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Who really flipped the coin?

Hi phrontister;

He sounds like a physicist and they are silly, they always worry about the smallest things.

But I haven't yet descended to the depths of shop assistants and their utter reliance on calculators, even for the simplest of tasks.

This is a really interesting and controversial point and deserves it's own thread.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

quittyqat

Member

Registered: 2009-04-08

Posts: 1,215

Re: Who really flipped the coin?

There is a purity in phrontister's sequence ... no need to worry about pseudorandom issues.

I wonder why noone has thought to include a "random" chip in a standard PC? Just a well-baked transistor would help!

Noone?

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I'll be here at least once every decade.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Who really flipped the coin?

Whatwaswrongwiththat?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Who really flipped the coin?

Hi;

Quittyqat, is the only person in this forum ever to catch me making a similar type error!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

Whatwaswrongwiththat?

"Whatwaswrongwiththat"...a syllabic-alliteration example.

Last edited by phrontister (2009-08-28 16:18:36)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

quittyqat

Member

Registered: 2009-04-08

Posts: 1,215

Re: Who really flipped the coin?

There is a purity in phrontister's sequence ... no need to worry about pseudorandom issues.

I wonder why noone has thought to include a "random" chip in a standard PC? Just a well-baked transistor would help!

Noone?

Whatwaswrongwiththat?

I see... When you wrote that, in your time, it was noon!

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I'll be here at least once every decade.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: Who really flipped the coin?

I see... When you wrote that, in your time, it was noon!

"noone"...the forbidden letter gives some nice, extra spice here.

Last edited by phrontister (2009-08-30 21:00:28)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson