Jackass Posted May 31, 2007 Share Posted May 31, 2007 I think this number would be "worst case" highest number. Even with shuffling the deck 7 or 8 times, there is a high probability that the top most cards would stay towards the top of the stack and the bottom most cards would stay towards the bottom. Just presuming that the top card always stays the top card, your number goes from 8.06e67 to 1.5e66. The 52! number presumes that any one card has the possibility to be in any 1 of 52 positions, but in practicality, the "randomness" is based somewhat on the initial order as well as the skill and technique of the shuffler. Quote Link to comment Share on other sites More sharing options...
Gopher Posted May 31, 2007 Share Posted May 31, 2007 I've heard that too...but if the probability of getting one ace is 4/52, then the probability of getting two aces is (4/52) * (3/52) ... take that percentage (0.452%) and divide it into 1, and you see that there should be pocket aces dealt once every 221 hands (not 212). Relatedly, since there are thirteen different cards, you should be getting a pocket pair of some type once every 17 hands or so. Wouldn't it be times 3/51, since one of the cards has already been taken out? I think that might be where they get the 212. Quote Link to comment Share on other sites More sharing options...
muck Posted May 31, 2007 Share Posted May 31, 2007 (edited) Wouldn't it be times 3/51, since one of the cards has already been taken out? I need more sleep. Of course you're right. I had a typo. I think that might be where they get the 212. However ... I did do the math correctly in excel. It's still 221 hands. (4/52) * (3/51) = 0.00452489 1 / 0.00452489 = 221 ...another way to look at it is that once in every 13 (i.e., 52/4) hands you'll get at an ACE (or ten, or four, or whatever) for the first card face down ... and that one in 17 (i.e., 51/3) hands you'll get another card of the same type face down. 13 * 17 = 221 ...or, every 17 hands (on average, over a VERY long session) you should have pocket pairs... Edited May 31, 2007 by muck Quote Link to comment Share on other sites More sharing options...
isleseeya Posted May 31, 2007 Share Posted May 31, 2007 Looks like a math convention broke out in this thread Quote Link to comment Share on other sites More sharing options...
wiegie Posted May 31, 2007 Author Share Posted May 31, 2007 (edited) Looks like a math convention broke out in this thread It is my goal to have math added to the listed of banned tailgate topics. Edited May 31, 2007 by wiegie Quote Link to comment Share on other sites More sharing options...
Egret Posted June 1, 2007 Share Posted June 1, 2007 I'm guessing you were made to play 52 card pick-up. More than once. Quote Link to comment Share on other sites More sharing options...
Big John Posted June 1, 2007 Share Posted June 1, 2007 It is my goal to have math added to the listed of banned tailgate topics. Did you calculate the odds if having this subtracted? Did the conclusion add up? Is the divide going up expotentall? Or are there multiple possibilities? :oldrazz: Quote Link to comment Share on other sites More sharing options...
jaxfactor Posted June 1, 2007 Share Posted June 1, 2007 I didn't want to get that picky, but if you insist.........it would be every 221.238938053097 hands. Calling Captain Kirk and Tim C! I think we found Mr. Spock. Quote Link to comment Share on other sites More sharing options...
irish Posted June 1, 2007 Share Posted June 1, 2007 It is my goal to have math added to the listed of banned tailgate topics. You wouldn't be able to survive without it. Quote Link to comment Share on other sites More sharing options...
Grits and Shins Posted June 1, 2007 Share Posted June 1, 2007 Hey! Somebody told me I wouldn't have to do no math. Quote Link to comment Share on other sites More sharing options...
untateve Posted June 1, 2007 Share Posted June 1, 2007 Each time someone fairly shuffles a deck of cards it is almost certain that the resulting sequence of cards has never occured before and will never occur again. You see, there are approximately 80,658,175,170,940,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible different outcomes that could occur when shuffling a standard 52-card deck of cards. To put this in perspective, if 10 billion people had been shuffling cards at a rate of one shuffle per second since the start of the universe 14 billion years ago, they would still have only shuffled less than 1 billionth of 1 billionth of 1 billionth of 1 quadrillionth of the possible shuffling outcomes. Have a nice day as you ponder your own insignificance. This is BS. I just shuffled a deck 5 times and on three occasions, I got the exact sequence of cards. Quote Link to comment Share on other sites More sharing options...
Caveman_Nick Posted June 1, 2007 Share Posted June 1, 2007 It is my goal to have math added to the listed of banned tailgate topics. Do some work on the probability that the 82nd player taken in this year's upcoming draft will be better than Reggie Wayne. That will get Bronco Billy in here, and then you are halfway to your goal. Quote Link to comment Share on other sites More sharing options...
TimC Posted June 1, 2007 Share Posted June 1, 2007 Calling Captain Kirk and Tim C! I think we found Mr. Spock. My head just exploded after proofing that math. And not with the Earth-shattering boom I was expecting but more like a little puff of smoke from one of those old candy cigarettes... Quote Link to comment Share on other sites More sharing options...
The Irish Doggy Posted June 1, 2007 Share Posted June 1, 2007 Wouldn't it be times 3/51, since one of the cards has already been taken out? I think that might be where they get the 212. ahem Quote Link to comment Share on other sites More sharing options...
isleseeya Posted June 1, 2007 Share Posted June 1, 2007 I am a poor shuffler of cards but still manly Quote Link to comment Share on other sites More sharing options...
Savage Beatings Posted June 1, 2007 Share Posted June 1, 2007 To put this in perspective, if 10 billion people had been shuffling cards at a rate of one shuffle per second since the start of the universe 14 billion years ago, they would still have only shuffled less than 1 billionth of 1 billionth of 1 billionth of 1 quadrillionth of the possible shuffling outcomes. This scientific-ish place begs to differ! Quote Link to comment Share on other sites More sharing options...
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