what are the chances...

wimic

macrumors regular
Original poster
Aug 24, 2006
235
0
calgary, alberta
i thought of this the other day - a question of probability:

what are the chances, at any given time, that two decks of cards in the world have the exact same sequence of cards (not including new decks)?

i was thinking about what kind of ballpark this probability would be in (from a numerical point of view) and i compared it to the lottery. here in canada we have 6/49. which is 6 balls being chosen out of 49 balls (not in any specific order might i add) and the probability of matching all 6 numbers is approximately 1 in 30,000,000 (or something along those lines).

so how does this card problem compare? would you have less of a chance than the 6/49, or more of a chance since you're eliminating the odds of picking a specific 6 (since all 52 cards would be used), yet you're now considering the sequence (something that is neglected in the lottery).

anyone have any ideas as to how these odds can be calculated? i was thinking 52! (factorial) which would equal 1 in 8.06582E+67 or 1/80,658,200,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

i have a feeling that there aren't THAT many decks in the world... :rolleyes:
 

WildCowboy

Administrator/Editor
Staff member
Jan 20, 2005
17,369
1,325
You are correct in your calculation of the number of possible card orders...52! is a big number.

And no, there aren't that many decks of cards on Earth. In fact, 10^68 is a common estimate of the number of atoms in our galaxy. :cool:
 

jsw

Moderator emeritus
Mar 16, 2004
22,910
41
Andover, MA
Given that there are many people who will resort a deck of cards manually to get it into the "proper" order, I'd say it's virtually guaranteed that many non-new decks are in the same order right now.
 

WildCowboy

Administrator/Editor
Staff member
Jan 20, 2005
17,369
1,325
jsw said:
Given that there are many people who will resort a deck of cards manually to get it into the "proper" order, I'd say it's virtually guaranteed that many non-new decks are in the same order right now.
Also true...and I'm sure there are multiple decks in "reverse proper" order or in the various "numerically proper but suitally (I made that up...great word) improper" order, as well as various other patterns. But the chances that two randomly shuffled decks would be in the exact same order? Not so good.
 

®îçhå®?

macrumors 68000
Mar 7, 2006
1,826
2
The chance of winning the lottery here in the is 1/13,000,000. On my calculator, there is a button that works out probability but it is late and i am bored.
However i did find this maths problem earlier if you want to try it. cube root (13x +37) - cube root (13x -37) = cube root 2.
 

beatsme

macrumors 65816
Oct 6, 2005
1,204
1
wimic said:
what are the chances, at any given time, that two decks of cards in the world have the exact same sequence of cards (not including new decks)?
50/50...either they do or they don't :p
 
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