[HN Gopher] The Math of Card Shuffling
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       The Math of Card Shuffling
        
       Author : Anon84
       Score  : 38 points
       Date   : 2024-07-03 16:32 UTC (3 days ago)
        
 (HTM) web link (fredhohman.com)
 (TXT) w3m dump (fredhohman.com)
        
       | matsemann wrote:
       | Once saw a talk by Roger Antonsen where he did various
       | visualizations of shuffles (but using 64 cards I think for the
       | even splits). Quitw cool images
       | https://rantonse.org/art/2018-07-25
        
         | veunes wrote:
         | The deep connection between mathematics, art and magic
        
       | slaymaker1907 wrote:
       | I wish the 7 shuffle thing would stop getting repeated
       | everywhere. It's based off a faulty model, particularly for
       | sleeved cards, since if we consider the deck as two piles left
       | (L) and right (R), Pr[L|R] (the probability of taking from the
       | left pile given the last draw was from the right), should be
       | about 0.5 but is nearly 1 in many cases.
       | 
       | The riffle shuffle also has to be one of the only things you
       | actually get worse at the more you practice it.
        
         | waynecochran wrote:
         | You get worse w more practice? Explain. I have been practicing
         | the riffle shuffle w/o using the table and keeping the cards
         | contained -- am I going to get worse at it?
        
           | slaymaker1907 wrote:
           | Yes, you'll get the alternating pile phenomenon more and more
           | often. In reality, big "clumps" of cards from one pile or the
           | other actually improve the randomization. In the extreme,
           | this becomes the Faro shuffle
           | https://en.m.wikipedia.org/wiki/Faro_shuffle
           | 
           | From a probabilistic standpoint, even if it isn't a perfect
           | Faro shuffle, almost-Faro shuffling clearly introduces far
           | fewer bits of entropy which is less than ideal.
        
             | cpeterso wrote:
             | To try to account for that, I purposely alternate thin and
             | chunky interleaving when I riffle shuffle (the customary
             | seven times :).
        
         | trombonechamp wrote:
         | Here is a bit more realistic model of the riffle shuffle. These
         | results show that you need between 3 to 8 riffle shuffles,
         | depending on your skill. Notably, the number of needed shuffles
         | actually does get lower as you get better, i.e., less clumping
         | is better:
         | http://blog.maxshinnpotential.com/2017/11/05/optimality-in-c...
        
       | waynecochran wrote:
       | I have played Pinochle w friends who always wanted the dealer to
       | shuffle the deck less since they believed that this would more
       | likely result in good/interesting hands (four of kind, straight,
       | pinochle...). This seems to stem from the notion that randomness
       | looks different or is less interesting. If all sequence of cards
       | are equally likely, the ratio of interesting hands to all hands
       | seems worse for a less shuffled deck since the cards are
       | interleaved throughout all the players.
        
         | remram wrote:
         | This is true if you deal one card at a time. If you deal 2 by 2
         | or 3 by 3 on the other hand...
        
         | less_less wrote:
         | There's a Dutch card game called Rikken that intentionally
         | incorporates bad shuffling. It's a trick-taking game, so the
         | cards get clumped by suit during the hand, and you shuffle very
         | lightly between hands. After shuffling, the cards are dealt
         | several at a time to each player, so players tend to get _much_
         | more suited hands than with a well-shuffled deck.
        
       | nyc_pizzadev wrote:
       | Check out Jason Ladanye. He's a magician who uses shuffle math to
       | place cards exactly where he wants them to be in the deck. Both
       | impressive and scary.
        
         | veunes wrote:
         | Jason Ladanye is a remarkable magician
        
         | khazhoux wrote:
         | Ha, came here to post about Ladayne. I've been watching all his
         | 2-minute shorts and I _still_ can't wrap my brain around the
         | mental /mathematical skill, or the astounding precision of his
         | fingers.
         | 
         | Another takeaway is the jaw-dropping amount of practice he's
         | put into it, and his total dedication to perfection (zero
         | mistakes allowed, ever). He speaks at length about this in
         | interviews, and in fact part of his act is to explain that it
         | is _not_ magic at all, but his full commitment to mastering the
         | craft. Something we can all reflect on.
        
       | veunes wrote:
       | Do not know why but still it's a problem for me to shuffle cards
        
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