Shuffling a deck
Asked by Ralzomic 1 year ago
Hi, what I usually do to make all my decks ready is to pile all lands, creatures and others separately. Then I take 1 card of each pile.
When this is done, I shuffle for a good 30 seconds.
Is this legal?
Rhadamanthus says... Accepted answer #2
The important thing is that the deck ends up randomized such that no one knows the order or general distribution of the cards anymore. If you can shuffle at a decent pace and are really going for 30 whole seconds (are you counting? If not, 30 seconds might be longer than you think) then that should be long enough for the cards to be mixed up in an unpredictable way. Like Gidgetimer said, the sorting you're doing beforehand is pointless if you're shuffling sufficiently and problematic if you aren't.
A "pile shuffle" is not a shuffle. It's just sorting. You need to shuffle for real after doing any kind of pile sorting. The Magic Tournament Rules allow for pile sorting once at the beginning of each game so you can count the cards in your deck but it isn't a valid substitute for shuffling.
The 7 riffles rule of thumb that Gidgetimer mentioned comes from a statistical study of "average" peoples' shuffling ability and the variances they introduce into the order and grouping of the cards as they're being shuffled. It doesn't really need to be scaled up for larger deck sizes, but if your shuffling tends to produce more large chunks than smaller ones then you might run into issues with cards that started out next to each other tending to stay next to each other, which could be a problem with regards to true randomization. In that case, go ahead and shuffle a few more times to make sure.
February 13, 2024 9:50 a.m. Edited.
Gidgetimer says... #4
The 7 shuffles comes from a mathematical paper called "Trailing the Dovetail Shuffle to its Lair" by Dave Bayer and Persi Diaconis. It is pure mathematics, which I can't focus enough to read fully at this point. The "shuffling" method they used was cutting in a binomial distribution and then cards are "dropped" from each heap with a probability proportional to the number of cards in the heap. There was an earlier statistical study on if this was a good approximation of how people shuffle and it was found to be a good approximation.
Late in the paper it mentions scaling to different sized decks and this is where I am having problems because it mentions that 8.55 shuffles are needed for a 52 card deck and 104 needs 10.05. I'm not sure if they are using a different criteria for that section than the commonly cited "7 shuffles", but it shows that scaling is necessary, though at a much lower rate than I said.
Persi was actually on a Numberphile video about 8 years ago explaining randomization of decks of cards if such a thing interests you.
February 13, 2024 7:35 p.m.
Rhadamanthus says... #5
Okay, I see now why there's scaling for larger deck sizes with the way they're measuring randomness based on runs, descents, the distance from the normal distribution and the guessing strategy they simulated. I had only read summaries of the result of the paper, not the paper itself, and made some assumptions based on gut feelings about what was going on. Since the marginal advantage from not shuffling as many times with a larger deck is based on knowing the order beforehand then yes, a sorted deck needs to be shuffled more if it's larger. Another reason why it's just better to avoid any sorting step before shuffling.
Gidgetimer says... #1
Depends on the speed at which you shuffle. 7 riffles (which are pretty interchangeable with mashes as long as you are doing full deck mashes) randomizes a 52 card deck, so I'd do 8 at the very least for a 60 card deck and 14 for a 100 card deck. As long as you thoroughly randomize your deck it is LEGAL to do whatever else beforehand.
However; if you are thoroughly randomizing your deck, no advantage is gained by anything you do before the randomization. If the first part does reduce variance, then you are cheating by not randomizing. If the first part doesn't reduce variance then you are wasting time.
Having said this, I do shuffle my graveyard and permanents together after a game before shuffling them into the deck. It makes my brain happy despite me knowing it does nothing and it takes like 2 seconds that I am willing to waste.
February 12, 2024 10:24 p.m.