The Math of Card Shuffling (2018)
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The Math of Card Shuffling (2018)
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Re: The Math of Card Shuffling (2018)
#2Why can't I keep riffling once the King reaches the top?
I thought I had found my next idle clicker.
Re: The Math of Card Shuffling (2018)
#3I love articles that marry prose and interactive simulations to make a point.
Re: The Math of Card Shuffling (2018)
#4Why does every card, on average, need to be ruffled in order for the dev to be randomized?
Re: The Math of Card Shuffling (2018)
#5Seems a good opportunity to link to this again:
Re: The Math of Card Shuffling (2018)
#6The explanation of the 1-card riffle looks fine on a purely mathematical (computer) simulation, but what about an actual human trying to do it manually? I'd presume one would be much more likely to insert the top card somewhere near the middle of the deck, and almost never at or near the top, nor at the bottom of it. Would the calculation still stand, or should one need more riffles to reach a truly random state?
Re: The Math of Card Shuffling (2018)
#7There's a sort of magic trick involving doing perfect riffle shuffles where the whole deck retains it's order. If my memory is correct if you perform 8 perfect riffle shuffles (split deck 50/50, riffle one for one card correctly) then the order resets itself after 8 shuffles. It's usually only performed as a demonstration of skill by experienced card magicians than as a standalone trick.
Re: The Math of Card Shuffling (2018)
#8What the article failed to mention is that a very common shuffling method - overhand shuffle - is terrible. You need about 10000 (ten thousand) of them to shuffle an ordinary deck of 52 cards. This can seriously impact you when playing board games, and collectible card games like Magic: the Gathering. In competitive CCGs it can make the game unfair. In non-competitive games it just makes it boring because the same situations tend to occur.
Smushing is a great way to shuffle cards (used on poker tournaments) but it doesn't work if they're sleeved.
For this reason I really appreciate board games which use bags and tokens as card substitutes. It's really the best shuffling method, except that token-sized cards don't have room for text on them. Now that I mention it I'm surprised there are no playing cards in the form of bag and tokens. Probably because ordinary playing cards are so cheap.
Re: The Math of Card Shuffling (2018)
#9There's a sort of magic trick involving doing perfect riffle shuffles where the whole deck retains it's order. If my memory is correct if you perform 8 perfect riffle shuffles (split deck 50/50, riffle one for one card correctly) then the order resets itself after 8 shuffles. It's usually only performed as a demonstration of skill by experienced card magicians than as a standalone trick.
Yup! That's correct, here's a demonstration:
https://www.youtube.com/watch?v=rEoYwyHddLc
Explaining why it works is an exercise in number theory. For example, card 1 stays in place; card 2 goes to position 3, then 5, then 9, then 17, ... In short, the reason why it works is that 2^8 - 1 is divisible by 52 - 1.
Re: The Math of Card Shuffling (2018)
#10What the article failed to mention is that a very common shuffling method - overhand shuffle - is terrible. You need about 10000 (ten thousand) of them to shuffle an ordinary deck of 52 cards. This can seriously impact you when playing board games, and collectible card games like Magic: the Gathering. In competitive CCGs it can make the game unfair. In non-competitive games it just makes it boring because the same si…
> You need about 10000 (ten thousand) of them to shuffle an ordinary deck of 52 cards.
My source[0] says the lower bound for full overhand shuffle is number of cards squared, so less than 3000 shuffles for 52 cards. Upper bound around 5000.
Your source?