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Stunninger Inner circle 2819 Posts |
One of the reasons I have developed a fondness for cartomancy is, once you learn the meanings of the cards, every reading is going to be unique.
Using a 52 card deck, there are over 130,000 possible combinations for a three card reading. This got me wondering, how many possible combinations are the for 52 cards? Paul Draper mentioned on his first Penguin live lecture there are more than 6 billion possible combinations of a 52 card deck. I wondered what the actual number was and it is quite difficult to believe: 80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, Apparently, if you pick up a deck of cards and shuffle it, and then deal all 52 cards out, that specific sequence of 52 cards likely has never been dealt before and likely never will be again for billions of years. https://gizmodo.com/there-are-more-ways-......53612843 52! Wow |
aligator Inner circle Canada 2044 Posts |
Even more possible combinations with 78 card tarot.
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John C Eternal Order I THINK therefore I wrote 12945 Posts |
52!
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Paul Draper V.I.P. Las Vegas, Nevada 245 Posts |
Absolutely! The number is astronomical! But I always like to say that there are more combinations than there are people on the earth so these cards are in an order created just for you, and no one else alive or who has ever lived!
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Shoreline99 New user 50 Posts |
This looks interesting if it can be useful presentation of NDO or triumph etc...
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tiptophat Loyal user Wesley 269 Posts |
52 X 51 X 50 X 49 and so on is how the answer is calculated. Just an FYI
Have a great day all |
Looch Inner circle Off by 3362 Posts |
It's called 52 factorial or 52! Or even 52 Shriek! - I have used this presentational angle for years. There are some fascinating stories about the mathematics behind it:
https://youtu.be/0DSclqnnC2s https://youtu.be/SLIvwtIuC3Y
Mentalism Products: https://www.readmymind.co.uk/ Learn Mentalism with the Pro's: https://www.mymind.rocks
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dyoung Special user 898 Posts |
Its true, unless you see a 9 of Diamonds on the bottom, then chances are it might've been in that order before
//Dan |
Tom Cutts Staff Northern CA 5925 Posts |
Except that there is one flaw in this deception of logic. All decks (or almost all) start out from the same point. It's not like you take a brand new deck and give it a couple shuffles and it all of a sudden has a unique order you will never see again in your life. Add to that the reality that the generally practiced "randomization" is actually somewhat ordered and limiting and you have a reality which does not follow the mathmatical construct. Even after a year in use the order will favor, albeit to a very small degree, a certain group of the possible outcomes because we start at the same point, new deck order, and we generally "randomize" in a structured somewhat ordered way.
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Philemon Vanderbeck Inner circle Seattle, WA 4694 Posts |
There's a mathematical proof that it takes a minimum of 6 riffle shuffles to put a deck in a random order, where every card has a chance of appearing at any position.
Professor Philemon Vanderbeck
That Creepy Magician "I use my sixth sense to create the illusion of possessing the other five." |
Stunninger Inner circle 2819 Posts |
Quote:
On Jan 21, 2019, Paul Draper wrote: Great BTW, your Penguin lecture on Cold Reading was outstanding. |
Emory Kimbrough New user Tuscaloosa, AL 94 Posts |
The number of shuffles to randomize a deck has been thoroughly studied, including work by Persi Diaconis, who is both a great mathematician and a great magician. There are several measures that are reasonable ways to judge the randomness (entropic, variation distance, separation distance). From those measures, five thorough riffle shuffles is close enough to random for most purposes. Seven thorough riffle shuffle produces a level of randomness that keeps mathematicians and statisticians happy - Thus, seven is the number quoted in a lot of popular-press articles on this subject. By the strictest measure (separation distance), eleven shuffles are needed. A message above in this thread hints that order gradually diminishes, but this is incorrect. There is a "cut-off phenomenon" in the shuffling of discrete objects, where there is a rather sharp transition between being surprisingly poorly shuffled if you're only a little short of the cutoff, but then essentially random when only a little past the cutoff. I agree that after the cutoff there is an asymptotic approach to absolute zero information at infinity, but that asymptotic tail is an extremely thin one.
To put some numbers on it: Unshuffled deck = 225.58 bits of information After one shuffle = 173.58 bits After two shuffles = 121.58 bits After three shuffles = 69.874 bits After four shuffles = 27.271 bits After five shuffles = 7.9452 bits After six shuffles = 2.0727 bits After seven shuffles = 0.5239 bits After ten shuffles = 0.0082 bits After transitioning to half a bit of information or less, the residual order soon just isn't worth talking about, and you're essentially certain to be producing unique orders in spite of the initial identical ordering of new decks. Overhand shuffles are EXTREMELY poor at producing true randomness compared with riffle shuffles - It takes THOUSANDS of overhand shuffles to produce the above levels of randomness. https://royalsocietypublishing.org/doi/p......000.0625 |
Tim Cavendish Inner circle 1404 Posts |
As Emory Kimbrough notes, it takes 7 riffle shuffles to reach approximately random distribution. Note the significant jump toward randomness between shuffles 5 and 7.
Persi Diaconis, who left home as a 14 year old to go on the road with Dai Vernon and Ricky Jay, and later earned a PhD from Harvard, proved this in 1992. Here's the link to the paper: https://statweb.stanford.edu/~cgates/PER......er92.pdf This page is more easily readable and summarizes some more recent wrinkles: https://www.math.hmc.edu/funfacts/ffiles/20002.4-6.shtml |
Mac_Stone Inner circle Miami, FL 1420 Posts |
Jared Kopf knows the number.
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Steven Keyl Inner circle Washington, D.C. 2630 Posts |
Here's the writeup of the video Looch mentioned above:
https://czep.net/weblog/52cards.html Given the time, I also have used this presentational angle. In most cases, however, I've found that it's too long to weave into a performance, so I usually just say "there are more ways to arrange a deck of cards than there are neurons in the brain... and there are 100 billion neurons in the brain... not 100 million, 100 BILLION!" The true number of 52! is ridiculously larger than 100 billion, but this gets the point across quickly and effectively.
Steven Keyl - The Human Whisperer!
B2B Magazine Test! Best impromptu progressive Ace Assembly ever! "If you ever find yourself on the side of the majority, it is time to pause, and reflect." --Mark Twain |
Rook Special user I went to the Magic Cafe and all I got were these lousy 834 Posts |
Quote:
On Jan 21, 2019, aligator wrote: Yep, for a full Tarot deck, 78 factorial is 1.132 x 10^115, or 11.32 septentrigintillion. You could just tell them "An 11 followed by 114 zeros."
Those who don't believe in magic will never find it.
-Roald Dahl |
Chris K Inner circle 2544 Posts |
Quote:
On Jan 23, 2019, Steven Keyl wrote: I agree with this. Steven's approach, which I cut out of the quote above because he should keep it to himself ;-) is great! There are times and places to get technical in my personal routines but a deck of cards isn't one. For one thing, cards are impersonal. Birthdates (and the numerological reduction of someone's birthdate) are great examples of how I introduce statistics. I use this approach to build a 6 digit number, which was predicted on cards that have been on the table since before anybody wrote/said anything. At that point I get into statistics, because the numbers have inherent personal value. Now, having said all that, I could totally see me saying something like "that's a 1 followed by 114 zeros" which is just a wonderful little image to bring up. A big thanks to Rook for that one! Great thread everyone, my sincere thanks! -Lem |
John C Eternal Order I THINK therefore I wrote 12945 Posts |
Quote:
On Jan 21, 2019, tiptophat wrote: really? |
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