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The Math of Card Shuffling (2018)

fredhohman.com

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Re: The Math of Card Shuffling (2018)

#11

Post by e12e »

b0rsuk wrote: post #8

What 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…

On the other hand, with sleeved cards - you can do a "direct" rifle by "cutting" one half of the deck directly into the other (looks a bit like the overhand shuffle, acts more like a riffle).

Something like the second method here ("smash"? Shuffle). Note that the riffle shuffle is also pretty easy with sleeved cards, you just need to modify the technique a bit.

https://youtu.be/nnVABY_a6IQ?t=2m21s

Re: The Math of Card Shuffling (2018)

#12

Post by [deleted] »

b0rsuk wrote: post #8

What 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…

[deleted]

Re: The Math of Card Shuffling (2018)

#14

Post by tridentboy »

strogonoff wrote: post #10
b0rsuk wrote: post #8

What 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? [0] https://arxiv.org/abs/math/0501401

Well, it seems that his point still stands. Overhand shuffle is terrible for actually shuffling a deck of cards.

Re: The Math of Card Shuffling (2018)

#16

Post by OisinMoran »

have_faith wrote: post #7

There'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.

Yes it's 8 perfect riffles. What the article doesn't seem to stress is that there are two different riffles—an in shuffle (top card moves to second) and an out shuffle (top card stays on top). It's only 8 with an out shuffle I think, but 52 with an in shuffle. So presumably their figure of 7 is referring to the in shuffle (as being 1 shuffle away from the original order doesn't sound too shuffled to me).

The in shuffle is n shuffles in general to get back to the start but the out shuffle isn't such a simple pattern.

If you want to make a shuffle that will take _even longer_ to get back to it's starting point, the best you can do is the Landau function which as you can see can get very big: https://oeis.org/A000793/list (I have a calculation of g(52) but not on me right now)

Re: The Math of Card Shuffling (2018)

#17

Post by mcguire »

have_faith wrote: post #7

There'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.

The Faro shuffle (https://en.wikipedia.org/wiki/Faro_shuffle?wprov=sfla1).

Re: The Math of Card Shuffling (2018)

#18

Post by dghughes »

An interesting bit if history. Electronic card shuffles were invented by a former truck driver. Casinos rented the devices from his company I don't think any were sold (their value was approximately $20,000 each).

I haven't worked at a casino for four years but at that time I beleive the market opened up. It sounds like a patent expired or maybe the fisr card shuffle company was sold.

Re: The Math of Card Shuffling (2018)

#19

Post by jonplackett »

The link in this to another article about the number of different combinations of cards is mind blowing.

I mean, I know I should probably have realised that really, but I didn't think it would be such a beyond-astronomical number of potential orders.

Re: The Math of Card Shuffling (2018)

#20

Post by jonplackett »

I'm designing a card game at the moment and have been pondering this because I'm doing play testing online, so the shuffling is done by a computer and is therefore perfectly random.

I'm wondering how having non-perfect shuffling will affect the game play when it's a real world game and card combinations end up being left together.

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