No two card shuffles will EVER be the same. - Page 3

lumberjim · 02-04-2008, 10:26 PM

5?

Flint · 02-04-2008, 10:40 PM

Quote:

Originally Posted by Clodfobble

A five year old can shuffle a deck of cards. Since half of the population is not in a coma or under the age of five, doubling the work week will have a bigger positive effect than the negative effect of counting out those unable to shuffle.

But if you don't like that one, then how about you add in population growth, since people will have all this spare time to boink each other? Hey, you're the one who wants to make this happen, I'm just trying to think outside the box for you.

Basically, everyone on the Earth is not going to drop everything and shuffle cards all day. We couldn't even survive that for very long. So, in taking the total poulation of the Earth as my number, I'm making an impossibly generous concession, in order to imagine this actually happening. The 40-hour week is something familiar to us; I'm trying to put it in real terms.

If you like, I could go back to having each person shuffle an exponential amount of decks every second...

lumberjim · 02-04-2008, 11:08 PM

Quote:

Originally Posted by Flint

The 40-hour week is something familiar to us;

that's less than 1/3 of the hours in a week....what do you do with all of that free time? ya know....it sounds appealing....

Spexxvet · 02-05-2008, 08:06 AM

This site disagrees

Quote:

My interest with perfect shuffling started with a simple observation that the standard poker deck containing 52 cards will come back to its or original order if riffle shuffled precisely interleaving the two 26 haves 8 times.

So on the ninth time, the shuffle will be the same as the first shuffle.

He expects a "perfect riffle shuffle", though.

Shawnee123 · 02-05-2008, 08:06 AM

Quote:

Originally Posted by lumberjim

5?

SteveDallas · 02-05-2008, 08:28 AM

Quote:

Originally Posted by Flint

everyone on the Earth is not going to drop everything and shuffle cards all day. We couldn't even survive that for very long.

Why should you start injecting reality and common sense into this discussion at this late date?? You might as well start thinking about whether those monkeys with the typewriters have had touch typing classes or not.

Flint · 02-05-2008, 08:40 AM

Okay, I hear what people are saying. You want more shuffles getting done, okay. Let’s look at that.

I’m going by HLJ’s calculation (I’m too lazy to do it myself) that in 9.e+33 permutations you would have a 50% chance of repeating the same shuffle.

I’m using the entire population of planet Earth (6,648,429,413), and I’ll have them shuffle one deck of cards per second, year-round. It would take 42,925,646,062,489,266.972805985537223 years to get through 9.e+33 permutations.

How long is that? Well, the Earth is estimated to be 4.54 billion years old. It’s 9,454,988.1194910279675784109112819 times longer than that.

So, if every living person on the Earth shuffled one deck of cards per second, for 9 million times longer than the Earth has existed, there would be a 50% chance of the same shuffle coming up.

THE SAME EXACT SHUFFLE HAS NEVER HAPPENED, AND NEVER WILL HAPPEN. EVER.

lumberjim · 02-05-2008, 09:16 AM

unless it does...

Clodfobble · 02-05-2008, 10:04 AM

It totally happened to me the other day. Take my word for it.

HungLikeJesus · 02-05-2008, 07:52 PM

Would you settle for 1% chance?

kerosene · 02-05-2008, 07:55 PM

Flint, are you OCD?

Flint · 02-05-2008, 07:56 PM

Quote:

Originally Posted by HungLikeJesus

Would you settle for 1% chance?

If you're offering to calculate how many permutations of 52! you would have to go through to have a 1% probability of repeating a permutation...
I would love to know that.

HungLikeJesus · 02-05-2008, 10:30 PM

I'd better present my logic to see if anyone disagrees.

(n*(n-1))/(2*52!) = P; solve for P, where P = probability of 2 or more matching shuffled decks in n shuffles.

(n-1)^2 < n*(n-1) < n^2, so

(n-1)^2/(2*52!) < n*(n-1)/(2*52!) < n^2/(2*52!),
so the first equation can be simplified (for large values of n) as

n^2 ~= P*2*52!

n = square_root(P*2*52!)

If P = 0.5 (50%), n = 8.98e33
If P = 0.1 (10%), n = 4.0e33
If P = 0.01 (1%), n = 1.27e33

I just noticed a flaw in this logic. Can you see it?

classicman · 02-05-2008, 11:04 PM

lol - I can't even follow that!

lumberjim · 02-05-2008, 11:23 PM

pull my finger!

02-04-2008, 10:26 PM	#31
lumberjim I can hear my ears Join Date: Oct 2003 Posts: 25,571	5? __________________ This body holding me reminds me of my own mortality Embrace this moment, remember We are eternal, all this pain is an illusion ~MJKeenan

02-05-2008, 08:40 AM	#37
Flint Snowflake Join Date: Mar 2006 Location: Dystopia Posts: 13,136	Okay, I hear what people are saying. You want more shuffles getting done, okay. Let’s look at that. I’m going by HLJ’s calculation (I’m too lazy to do it myself) that in 9.e+33 permutations you would have a 50% chance of repeating the same shuffle. I’m using the entire population of planet Earth (6,648,429,413), and I’ll have them shuffle one deck of cards per second, year-round. It would take 42,925,646,062,489,266.972805985537223 years to get through 9.e+33 permutations. How long is that? Well, the Earth is estimated to be 4.54 billion years old. It’s 9,454,988.1194910279675784109112819 times longer than that. So, if every living person on the Earth shuffled one deck of cards per second, for 9 million times longer than the Earth has existed, there would be a 50% chance of the same shuffle coming up. THE SAME EXACT SHUFFLE HAS NEVER HAPPENED, AND NEVER WILL HAPPEN. EVER. __________________ **************** There's a level of facility that everyone needs to accomplish, and from there it's a matter of deciding for yourself how important ultra-facility is to your expression. ... I found, like Joseph Campbell said, if you just follow whatever gives you a little joy or excitement or awe, then you're on the right track. . . . . . . . . . . . . . . . . . . . . . . . . . . Terry Bozzio**

02-05-2008, 09:16 AM	#38
lumberjim I can hear my ears Join Date: Oct 2003 Posts: 25,571	unless it does... __________________ This body holding me reminds me of my own mortality Embrace this moment, remember We are eternal, all this pain is an illusion ~MJKeenan

02-05-2008, 07:52 PM	#40
HungLikeJesus Only looks like a disaster tourist Join Date: Feb 2007 Location: above 7,000 feet Posts: 7,208	Would you settle for 1% chance? __________________ Keep Your Bodies Off My Lawn SteveDallas's Random Thread Picker.

02-05-2008, 10:30 PM	#43
HungLikeJesus Only looks like a disaster tourist Join Date: Feb 2007 Location: above 7,000 feet Posts: 7,208	I'd better present my logic to see if anyone disagrees. (n(n-1))/(252!) = P; solve for P, where P = probability of 2 or more matching shuffled decks in n shuffles. (n-1)^2 < n(n-1) < n^2, so (n-1)^2/(252!) < n(n-1)/(252!) < n^2/(252!), so the first equation can be simplified (for large values of n) as n^2 ~= P252! n = square_root(P2*52!) If P = 0.5 (50%), n = 8.98e33 If P = 0.1 (10%), n = 4.0e33 If P = 0.01 (1%), n = 1.27e33 I just noticed a flaw in this logic. Can you see it? __________________ Keep Your Bodies Off My Lawn SteveDallas's Random Thread Picker.

02-05-2008, 10:04 AM	#39
Clodfobble UNDER CONDITIONAL MITIGATION Join Date: Mar 2004 Location: Austin, TX Posts: 20,012	It totally happened to me the other day. Take my word for it.

02-05-2008, 07:55 PM	#41
kerosene Touring the facilities Join Date: Nov 2002 Location: The plains of Colorado Posts: 3,476	Flint, are you OCD?

02-05-2008, 11:04 PM	#44
classicman barely disguised asshole, keeper of all that is holy. Join Date: Nov 2007 Posts: 23,401	lol - I can't even follow that! __________________ "like strapping a pillow on a bull in a china shop" Bullitt

02-05-2008, 11:23 PM	#45
lumberjim I can hear my ears Join Date: Oct 2003 Posts: 25,571	pull my finger! __________________ This body holding me reminds me of my own mortality Embrace this moment, remember We are eternal, all this pain is an illusion ~MJKeenan

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