Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
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Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#2The paper: https://arxiv.org/abs/2510.22783
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#3Shouldn't a perfect shuffle just reorder the cards without adding entropy?
You would need sloppy ones to introduce randomness.
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#4And 8 perfect shuffles resets it back to starting order (perfect being cards interlaced 1 by 1)
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#5Quite the assumption here: "cards are randomly interleaved from the left or right pile one by one. (Each card gets dropped from either the left or the right pile with a probability that’s proportional to the number of cards remaining in that pile."
... Why would it be proportional to the number of cards in each pile? (Edit: I suppose the person doing the shuffling might adjust the rate of cards coming from each hand ... But not perfectly and continuously)
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#6Upper limit of 14. I’m curious then - when playing cards with friends we start with a semi -random, but definitely clumped, deck. It gets shuffled a couple times.
How random is that deck? How many “cold spots” does it have? Just how not random of decks are people playing with, and ultimately does that even matter if players lack the knowledge or skill to change their play because of that knowledge?
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#7Shouldn't a perfect shuffle just reorder the cards without adding entropy? You would need sloppy ones to introduce randomness.
I don’t know on perfect shuffles but for the sloppy shuffles, the deck is cut at a random location between each shuffle.
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#8Shouldn't a perfect shuffle just reorder the cards without adding entropy? You would need sloppy ones to introduce randomness.
See the paragraph beginning "Yet terms and conditions also apply."
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#9Shouldn't a perfect shuffle just reorder the cards without adding entropy? You would need sloppy ones to introduce randomness.
It's modelled with randomness, each card is taken from left or right with a probability, it's not a deterministic model.
Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
#10Quite the assumption here: "cards are randomly interleaved from the left or right pile one by one. (Each card gets dropped from either the left or the right pile with a probability that’s proportional to the number of cards remaining in that pile." ... Why would it be proportional to the number of cards in each pile? (Edit: I suppose the person doing the shuffling might adjust the rate of cards coming from each hand…
> But not perfectly and continuously
Isn’t that where the randomness comes in?