Hacker News Reader

Comment by slaymaker1907 | Hacker News Reader

slaymaker1907

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.

View on HN

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...

The other thing is that the chaotic pile on the table, well-mixed, is about as fast as 7 riffles mixed with cuts and probably (my personal experience) equally mixed.

Just makes you feel like a child.

The other thing I don't like about it is that many cards will be flipped upside down which is very annoying for games like MTG.

If you take enough space on the table it's possible to do without flipping any cards. Still quite a palaver though.

Definitely haven't been getting worse at the riffle shuffle. But one of my more nerdy gaming buddies doesn't allow any of his cards to be riffled as it degrades the cards.

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?

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.

To try to account for that, I purposely alternate thin and chunky interleaving when I riffle shuffle (the customary seven times :).

I wish! Yes, the better you get at riffle shuffling, the more it will approximate a faro shuffle (meaning less "clumps" and more singles alternating) in some parts of the deck, but it's the repetition that makes it random. If you have accidentally mastered a perfect tabled faro without deliberate practice, I'd like to shake your hand and read your book (or video) on the technique!

Perhaps we can caveat that the person is not cutting perfectly at 26 every time and performing perfect out faros, then we can assume they'll be mixed enough. :-)

It's been a while since I've read Persi Diaconis' paper (who coined the 7 shuffles thing), but I believe all your main concerns were addressed. Not sure about the sleeved deck thing, that wasn't probably a consideration.

Yes, sleeves weren't much of a thing until the 2000s and they do seem to make a big difference in my experience.

Reply on news.ycombinator.com