MichaelBluejay
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November 29th, 2022 at 9:30:39 PM permalink
The number of distinct results for shuffling a deck of cards is 52!, or 52 x 51 x 50 x 49, etc.

That's about 8.07 x 1067, or 8 with 67 zeroes after it.

If a million people each shuffled a million decks of cards every second from now until the end of the earth (best guess = 8 billion years), that would be only 2.56 x 1029 decks. With all those decks, in all that time, it's unlikely that exactly there would ever be two matching decks of cards.

Another large number is the possible number of Bitcoin addresses: 1.4 x 1048. Anyone can generate a new Bitcoin address using random data (or have a service do it for you), but how do you make sure you didn't choose an address that someone else already chose? For example, if someone created a paper wallet but has never used it, it won't appear on the blockchain, so how do you know whether someone else already chose your address? The answer is you don't need to know: If a million people each created a million new Bitcoin addresses every second for billions of years...same principle. Created randomly, no one will ever create a random Bitcoin address that someone else already created.

Yeah, a collision is possible, but not like winning the lottery is possible. Far, far longer than that. It's like winning Powerball six times in a row.
I run Easy Vegas ( https://easy.vegas )
rainman
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MichaelBluejay
November 29th, 2022 at 9:47:12 PM permalink
Good stuff MB. I am fully willing to admit your brain is significantly more powerful than mine.
I read this and all I can think is lets do it. You create the data post it here with a deployment
date & time and we will see how many we can get to participate in the Great Bitcoin Wallet
Collision of 2022.
MichaelBluejay
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November 29th, 2022 at 10:40:19 PM permalink
Quote: rainman

Good stuff MB. I am fully willing to admit your brain is significantly more powerful than mine.

link to original post

Not really, I used a calculator.
I run Easy Vegas ( https://easy.vegas )
odiousgambit
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November 30th, 2022 at 6:14:37 AM permalink
for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
aceside
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November 30th, 2022 at 7:32:10 AM permalink
Quote: MichaelBluejay

The number of distinct results for shuffling a deck of cards is 52!, or 52 x 51 x 50 x 49, etc.

That's about 8.07 x 1067, or 8 with 67 zeroes after it.
link to original post


Although this number sounds gigantic, it is not horrible. In a blackjack game, it’s much smaller because card suits do not matter at all. What is the number of possible deck compositions for a one-deck blackjack game?
gordonm888
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November 30th, 2022 at 8:40:54 AM permalink
Quote: aceside

Quote: MichaelBluejay

The number of distinct results for shuffling a deck of cards is 52!, or 52 x 51 x 50 x 49, etc.

That's about 8.07 x 1067, or 8 with 67 zeroes after it.
link to original post


Although this number sounds gigantic, it is not horrible. In a blackjack game, it’s much smaller because card suits do not matter at all. What is the number of possible deck compositions for a one-deck blackjack game?
link to original post



If you ignore suits and consider the 52 card deck to be comprised of 13 ranks with four identical cards per rank then the number of possible deck compositions is (I think) = 52!/ (13*4!) = 2.6 x 1065.

Someone needs to check me on this.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
aceside
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November 30th, 2022 at 8:48:57 AM permalink
Quote: gordonm888

Quote: aceside

Quote: MichaelBluejay

The number of distinct results for shuffling a deck of cards is 52!, or 52 x 51 x 50 x 49, etc.

That's about 8.07 x 1067, or 8 with 67 zeroes after it.
link to original post


Although this number sounds gigantic, it is not horrible. In a blackjack game, it’s much smaller because card suits do not matter at all. What is the number of possible deck compositions for a one-deck blackjack game?
link to original post



If you ignore suits and consider the 52 card deck to be comprised of 13 ranks with four identical cards per rank then the number of possible deck compositions is (I think) = 52!/ (13*4!) = 2.6 x 1065.

Someone needs to check me on this.
link to original post


Why not 52!/[(4!)^13].
Dieter
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November 30th, 2022 at 6:13:12 PM permalink
Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post



I think it depends on what you consider a meaningful equivalence.

If you outright ignore suits, and 10 J Q K are all interchangeable, you get a surprisingly low number of "different" shuffled decks.

In some games, suit and the X ranks are significant, and you get a different answer.

If one J♣ is not equivalent to any of the others, then I think it should be 312!. This is a very large number followed by 76 zeroes.
May the cards fall in your favor.
aceside
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November 30th, 2022 at 6:56:09 PM permalink
Quote: Dieter

Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post



I think it depends on what you consider a meaningful equivalence.

If you outright ignore suits, and 10 J Q K are all interchangeable, you get a surprisingly low number of "different" shuffled decks.
link to original post


Consider a one-deck blackjack game, there are
51!/[16!x(4!)^9]
different shuffles.
Is this calculation correct?
Ace2
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November 30th, 2022 at 7:12:36 PM permalink
(52/e)^52 * (2pi52)^.5 = 8.053 x 10^67. Within 20 relative bips of the exact answer
It’s all about making that GTA
aceside
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November 30th, 2022 at 7:17:36 PM permalink
I don’t know what the above number is, but for a one-deck blackjack game, there should not be many different shuffles.
Dieter
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November 30th, 2022 at 7:26:10 PM permalink
Quote: aceside

Quote: Dieter

Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post



I think it depends on what you consider a meaningful equivalence.

If you outright ignore suits, and 10 J Q K are all interchangeable, you get a surprisingly low number of "different" shuffled decks.
link to original post


Consider a one-deck blackjack game, there are
51!/[16!x(4!)^9]
different shuffles.
Is this calculation correct?
link to original post



I'm not a combinatoricist. That said, the parts all seem to make sense.

I get stuck trying to count beyond 99 on my fingers, so someone smarter should verify.
May the cards fall in your favor.
Ace2
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odiousgambit
November 30th, 2022 at 8:09:05 PM permalink
Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post

6 * 52 / e = 1.15 * 10^2 = a

a^312 = 4.75 * 10^18 * 10^624 = 4.75 * 10^642 = b

b * (2pi312)^.5 = 2.10 * 10^644 =~ 312!

That will be even more accurate than the 52! calculation, which was within 17 relative bips of the exact answer, assuming my late-night arithmetic is correct.
Last edited by: Ace2 on Nov 30, 2022
It’s all about making that GTA
Dobrij
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December 1st, 2022 at 2:55:22 AM permalink
Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post



If I am not mistaken, number of combinations the player's first two cards is: 48516. Player's first two cards + dealer's card: 5013320
odiousgambit
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December 1st, 2022 at 3:25:11 AM permalink
Quote: Ace2

Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post

6 * 52 / e = 1.15 * 10^2 = a

a^312 = 4.75 * 10^18 * 10^624 = 4.75 * 10^642 = b

b * (2pi312)^.5 = 2.10 * 10^644 =~ 312!

That will be even more accurate than the 52! calculation, which was within 17 relative bips of the exact answer, assuming my late-night arithmetic is correct.
link to original post

pi is in that? amazing

a google is 10^100 and so the answer has 544 more zeroes, so to speak, than a google if your late night crunching is right
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
Ace2
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December 1st, 2022 at 9:01:19 AM permalink
For a rough estimate of 312!, take (312/e)^312, even rougher take 100^312 which would be 10^624
It’s all about making that GTA
Ace2
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December 1st, 2022 at 10:43:05 AM permalink
Quote: Ace2

Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post

6 * 52 / e = 1.15 * 10^2 = a

a^312 = 4.75 * 10^18 * 10^624 = 4.75 * 10^642 = b

b * (2pi312)^.5 = 2.10 * 10^644 =~ 312!

That will be even more accurate than the 52! calculation, which was within 17 relative bips of the exact answer, assuming my late-night arithmetic is correct.
link to original post

Amendment: I think you’d have to divide by 6!^52 to get the number of distinct ways to shuffle six decks (52 unique cards per deck). So divide 312! by 3.81 * 10^148. Which is still infinity for all practical purposes
It’s all about making that GTA
aceside
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December 1st, 2022 at 11:46:36 AM permalink
Quote: Dobrij

Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post



If I am not mistaken, number of combinations the player's first two cards is: 48516. Player's first two cards + dealer's card: 5013320
link to original post


The player's starting two-card hand number is as small as 55. The player's first two cards + dealer's upcard combination is as small as 550.
Dieter
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December 1st, 2022 at 11:53:23 AM permalink
Quote: aceside

Quote: Dobrij

Quote: odiousgambit

for the often seen 6 decks in BJ, my usual online calculator refuses to guess how many combinations there are

maybe if you have a powerful computer with a program that runs for days?

https://web2.0calc.com/
link to original post



If I am not mistaken, number of combinations the player's first two cards is: 48516. Player's first two cards + dealer's card: 5013320
link to original post


The player's starting two-card hand number is as small as 54. The player's first two cards + dealer's upcard combination is as small as 702.
link to original post



Why 702 instead of 540?
Do the same equivalencies not apply to the dealer hand?
May the cards fall in your favor.
aceside
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December 1st, 2022 at 11:57:21 AM permalink
You are right. I revised these numbers.
Dieter
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December 1st, 2022 at 6:27:58 PM permalink
Quote: aceside

You are right. I revised these numbers.
link to original post



OK... why 550 instead of 540?

(I'll assume tpyo instead of logical error.)

As it's been grinding in my brain, I also don't understand the 51! from earlier. (I'll assume another tpyo. I swear, I'm not trying to bust your chops.)
May the cards fall in your favor.
Deucekies
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MichaelBluejayodiousgambit
December 1st, 2022 at 6:34:10 PM permalink
Quote: MichaelBluejay

The number of distinct results for shuffling a deck of cards is 52!, or 52 x 51 x 50 x 49, etc.

That's about 8.07 x 1067, or 8 with 67 zeroes after it.

If a million people each shuffled a million decks of cards every second from now until the end of the earth (best guess = 8 billion years), that would be only 2.56 x 1029 decks. With all those decks, in all that time, it's unlikely that exactly there would ever be two matching decks of cards.



My favorite way of describing how big 52! is...

If every star in the Milky Way had a trillion planets...
And each planet had a trillion people...
And each person had a trillion decks of cards...
And they were shuffling all of them 1,000 times a second...
And they've been doing that SINCE THE BIG BANG...
...they'd JUST NOW be starting to repeat permutations.
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
aceside
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December 1st, 2022 at 6:57:03 PM permalink
Quote: Dieter

Quote: aceside

You are right. I revised these numbers.
link to original post



OK... why 550 instead of 540?

(I'll assume tpyo instead of logical error.)

As it's been grinding in my brain, I also don't understand the 51! from earlier. (I'll assume another tpyo. I swear, I'm not trying to bust your chops.)
link to original post


I looked back into a few posts and found some problems. Let me correct them all now.

For a blackjack game, the player's starting two-card hand number is 55. The player's first two cards and dealer's upcard combination number is 550.
If we consider a one-deck blackjack game, there are these many different shuffles:
52!/[16!x(4!)^9] = 8.20752E+13
Dieter
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December 1st, 2022 at 7:25:10 PM permalink
Ok, I see it now.

Thanks!
May the cards fall in your favor.
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