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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?

#21

Post by [deleted] »

HPsquared wrote: post #5

Quite 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…

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Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

#22

Post by fwlr »

HPsquared wrote: post #5

Quite 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…

If there is one card in this pile and no cards in the other, the probability of dropping the card from this pile is one. If instead there are some cards still in the other, a) the probability is less than one, and b) we move one step closer to the first state. So by construction it must be proportional - perhaps a poorly behaved proportionality, but that is still enough for the math to work.

Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

#23

Post by layer8 »

ecolonsmak wrote: post #17

"...unique tracking label for every card in the deck" I'd like more details on how this was accomplished on a practical level. Got me thinking about how to embed trackers thin enough to go into a playing card that would operate like a mesh network then the deck could self report once it's properly randomized making a green light go off indicating play may begin.

They didn’t do this practically, the “tracking label” is just an analogy to convey what they did mathematically. The word “barcode” is also only used because it might be more accessible to the layperson than “bit sequence”.

Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

#25

Post by empath75 »

capitol_ wrote: post #3

Shouldn't a perfect shuffle just reorder the cards without adding entropy? You would need sloppy ones to introduce randomness.

Yeah, a "perfect" shuffle is known as a faro shuffle and it's the basis of a lot of magic tricks, but it's a weird looking shuffle and it sort of ruins the tricks once you can recognize it.

Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

#27

Post by empath75 »

ecolonsmak wrote: post #17

"...unique tracking label for every card in the deck" I'd like more details on how this was accomplished on a practical level. Got me thinking about how to embed trackers thin enough to go into a playing card that would operate like a mesh network then the deck could self report once it's properly randomized making a green light go off indicating play may begin.

There are actually "marked" decks you can buy that come with an iphone app that tell you exactly where every card on the deck is by looking at the side.

Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

#28

Post by hdndjsbbs »

ecolonsmak wrote: post #17

"...unique tracking label for every card in the deck" I'd like more details on how this was accomplished on a practical level. Got me thinking about how to embed trackers thin enough to go into a playing card that would operate like a mesh network then the deck could self report once it's properly randomized making a green light go off indicating play may begin.

This is just the authors explanation to explain how to encode where a card ends up. The cards don't actually have barcodes, they have a binary-encoded number where a 0 indicates the left pile and 1 indicates the right pile during a specific round of the shuffle. The number encodes the journey that card makes during the shuffle. It's not an actual barcode.

Re: Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?

#29

Post by HPsquared »

tobr wrote: post #10
HPsquared wrote: post #5

Quite 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?

The randomness comes from sampling the probabilities. The strange assumption is that the probabilities are exactly proportional to number of cards currently in each stack.
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