How Many Ways Can You Arrange a Deck of Cards
New user
81 Posts
Posted: Mar 30, 2022 08:37 pm
0
Also depends on what purpose we're applying for. In Blackjack suits don't matter, so I remember its 312!/4 (hopefully? I recall?)
In whatever case, the nearly precise answer for a magicians purposes is "lots and lots."
Special user
Tampa, FL
741 Posts
Posted: Mar xxx, 2022 x:54 pm
0
Keen patter in this lesson to use for Anton James' "Unshuffled"!
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Special user
Never a dull moment with
942 Posts
Posted: Mar 31, 2022 06:28 am
0
iii...comments until someone mentioned the correct answer. 52 factorial.
Custom Props Designer and Fabricator equally well as Performer from Indiana, U.s.
Inner circumvolve
3894 Posts
Posted: Mar 31, 2022 06:xl am
0
2 comments, in fact[orial].
Veteran user
389 Posts
Posted: Mar 31, 2022 07:12 am
0
Quote:
On Mar thirty, 2014, trampabroad wrote:
Actually all wrong. While 52! is correct for a normal shuffled pack of cards, it doesn't include whether or not the card is confront up or confront downward. Which means(for, for example, a triumph-type shuffling) the actual number is more than like 52! ten ii^52
That'due south what I was getting at when I said "I'grand pretty sure information technology'south more than that". Also, some cards (22 in all I recall" announced unlike if rotated 180 degrees , which multiplies the number of possibilities by a further ii^22
So that's 52! x 2^52 ten 2^22 would be the number of distinguishable ways to arrange a standard deck of 52 cards and nonetheless get them back in the box.
Special user
French republic
742 Posts
Posted: Mar 31, 2022 12:26 pm
0
Adept video for those like me who like mathematic ... and maybe for the other people
Regular user
136 Posts
Posted: Mar 31, 2022 12:32 pm
0
R.E. Byrnes - haven't read the book, only am guessing his reasoning maybe to give the number of different orders the cards could be in, ignoring where the top of the deck lies. Or how many orders 52 cards could be in in a circular fashion, rather than in a specific bill of fare box. For example the number of orders half dozen people may sit round a circular table is fewer than the number of ways they could stand in a line. And then in a memorised stack, if y'all say by putting the acme card to the bottom the stack is still fundamentally the same, the number of possible stacks is (I believe) 51!. But mathematicians please bound in if I'm wrong.
Inner circle
Midwest
2924 Posts
Posted: Mar 31, 2022 12:52 pm
0
The number of arrangements of 52 different things is 52! At that place must be some misunderstanding of what Prof. Diaconis is saying if it seemed that he's contradicting that. It's a full general principle not specific to a deck of cards. The number of arrangements of n dissimilar items is northward! Nosotros're not talking about face upward and confront down or face up and sideways or confront and rotated to a specific angle. Nosotros're assuming that the deck is existence used for a carte du jour game in which all the cards face up the aforementioned management. Otherwise it'southward going to get nutty.
Imagine that in that location are 52 slots numbered 1 to 52. With your 52 card deck in hand, the question is "how many choices are there for what bill of fare goes in slot one?" The answer conspicuously is 52 since you can use any of the 52 cards. At present the question is "how many choices are there for slot 2?" Clearly the answer is 51 since there are 51 dissimilar cards remaining to choose from. At that place are 52x51 possible options for these 2 slots. The logic continues for the remaining slots which leads to the 52x51x50....x3x2x1 value. This is one of the about basic counting principles in probability and statistics.
Mike
New user
Charlotte, NC
54 Posts
Posted: Mar 31, 2022 02:58 pm
0
Guess that explains why I never get dealt Pocket Rockets in Hold'em.
Inner circumvolve
Landrum, S.C. by way of Chicago
3413 Posts
Posted: Mar 31, 2022 03:46 pm
0
52! Dang, I knew I was missing one!!!
Stanyon
aka Steve Taylor
"Every motion a move!"
"If y'all've enjoyed my operation half as much as I've enjoyed performing for you, and so you've enjoyed it twice as much as me!"
Inner circle
Midwest
2924 Posts
Posted: Mar 31, 2022 04:25 pm
0
I don't play Texas Holdem' so I might screw this upwardly. Only if yous're getting the outset ii cards dealt in Holdem, the probability of getting two aces would exist (4/52)*(3/51) since there are four possible aces for the first bill of fare and 3 for the second carte du jour. That's .004 or iv out of yard hands (ane in 250). I'k assuming that all cards are face up down and that yous get the first two cards in a row. I think that's what happens in Holdem.
Mike
Inner circle
Considering Stopping At Exactly
5207 Posts
Posted: Mar 31, 2022 04:46 pm
0
You don't become 2 in a row in Concord-Em. They deal twice around to all players before dealing the "community" cards. I saw a stat one time that yous have a 1 in 16 chance of being dealt a pair though. (dont call back the number of players though)
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Special user
Toronto
569 Posts
Posted: Mar 31, 2022 07:50 pm
0
Quote:
On Mar 29, 2014, WilburrUK wrote:
Quote:
On Mar 29, 2014, j100taylor wrote:
52 factorial
I'1000 pretty sure it'due south more that.
It is. 52! is just the number of permutations of the entire deck sans jokers. If yous go through and add in all of the possible subsets of i through 51 cards selected from the whole deck (taking gild into account if this is relevant), there are fifty-fifty more possibilities yielded by a standard deck.
Special user
Toronto
569 Posts
Posted: Mar 31, 2022 07:59 pm
0
Veteran user
389 Posts
Posted: Apr 1, 2022 07:47 am
0
Quote:
On Apr 1, 2014, lcwright1964 wrote:
Quote:
On Mar 29, 2014, WilburrUK wrote:
Quote:
On Mar 29, 2014, j100taylor wrote:
52 factorial
I'k pretty certain it's more than that.
Information technology is. 52! is simply the number of permutations of the unabridged deck sans jokers. If you become through and add together in all of the possible subsets of 1 through 51 cards selected from the whole deck (taking guild into business relationship if this is relevant), at that place are even more than possibilities yielded by a standard deck.
Then there must just be 2 ways to "accommodate" 2 lego bricks I guess, despite the fast that kids everywhere no this to be imitation.
Inner circle
Midwest
2924 Posts
Posted: Apr ane, 2022 09:30 am
0
I must exist missing something re: taking subsets into account?? Aren't we talking most a deck of 52 different cards, all face downwards with ane on peak of the other similar a normal deck would exist after a shuffle?? If and so, how do you go a greater number of orders than 52!?? Please show an ordering of the deck that's not amidst the 52!
With a 4 bill of fare deck say with letters A, B, C and D printed on them, you can hands show all 24 orderings permit'southward say starting with A on pinnacle followed by B, then C and finally D. There are no more these 24 or iv! orders to the deck.
Delight elucidate on the concept of more than 52! orderings to a deck.
Mike
Inner circle
Washington, D.C.
2593 Posts
Posted: Apr 1, 2022 10:40 am
0
Here'due south a site whose content I've used equally the ground for a bill of fare presentation. It helps put into perspective exactly how big 52! actually is.
http://czep.net/blog/52cards.html
Inner circumvolve
middle world
1077 Posts
Posted: Apr 1, 2022 11:52 am
0
Cool site Steven. What I gain from the site is 52! is "beyond astronomically big! "
Inner circle
Midwest
2924 Posts
Posted: April 1, 2022 03:00 pm
0
That's the coolest one Steven. I love pointing out that 14 steps the first time effectually the world is the entire age of the universe i.e. nearly 14 billion years. Very cool. I was going to signal that i out, merely I wanted to go on information technology for myself.
Mike
Inner circumvolve
Washington, D.C.
2593 Posts
Posted: Apr one, 2022 05:26 pm
0
I approach information technology from the other terminate, Mike. I say that you lot could only movement 5 steps earlier our sun burns off the sea and vaporizes the temper. Quite a short trip on the way to plumbing the depths of 52!
In either example it's great presentational provender.
Source: https://themagiccafe.com/forums/viewtopic.php?topic=548332&start=20
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