In Defense of Not Pile Shuffling

This article is a response to In Defense of Pile Shuffling. If you haven't already read it, I'd recommend you do so now, before reading any further in this article.

Every statement in that article was completely accurate. However, it left most readers with a much rosier view of pile shuffling, and of my personal opinions on pile shuffling, than would be justified. I published it on April Fool's day, and it was a demonstration of what's known as paltering; the use of technically-true statements to mislead people into believing something false.

The actual state of pile shuffling

All of the positives I mentioned in the previous article are in fact true positives about pile shuffling, but there are many negatives that outweigh them.

First off, while pile shuffling can indeed randomize a deck by helping the owner forget what cards are where, it's an extremely slow method of doing this. I just tested, and in one minute, I can mash shuffle 26 times. In that same amount of time, I can pile shuffle... once. A faster pile shuffler than me might get that up to 2, but it's never going to come anywhere close.

Pile shuffling also has a tendency to produce patterns. If the player is doing their best to choose the piles randomly, then it will in fact randomize the deck. But most players lay out the cards in a regular pattern instead, such as "top left, top middle, top right, bottom left, bottom middle, bottom right, repeat". These patterns can persist across any number of shuffles, as this image album does a great job of showcasing.Also, funnily enough, this Reddit post by a programmer who wrote a simulation to try to prove what kind of pile shuffling is most effective at randomizing their deck, and ended up proving that none of the options do it successfully.Reminds me of this video.

So while pile shuffling is indeed a method of randomization, it's an extremely slow and inefficient one. It has pretty much no randomization benefit over mash shuffles.

The non-randomization benefits I mentioned are valid ones, but some of them don't matter much (e.g. less likely to break sleeves is not a big deal given how cheap replacement sleeves are), and others often aren't actually used in reality. For example, many people claim that pile shuffling helps them count their deck, yet use piles of 7 rather than a factor of 60 like you'd want to do if counting were the primary goal. (And there are faster ways to count a deck anyway.) Experienced pile-shufflers also tend to pile shuffle very quickly, and likely won't notice damaged sleeves while they're doing so. Counting the deck and checking for sleeve issues can also be done before the match begins; no need to do it in front of the opponent.

Overall, I stand by the traditional perspective that pile shuffling is a waste of time. While it can in theory have some benefits, most players are doing it out of superstition and habit rather than because it actually benefits the tournament. Given how often players complain about slow play and their rounds going to time, I think banning it outright would be an overall benefit.

How did I convince people otherwise?

It's pretty easy to come up with convincing arguments for any conclusion, regardless of that conclusion's accuracy.

I started off the article by trying to create a sense of pile shufflers being forced into silence. I gave a bunch of examples of people who disliked pile shuffling, and framed them as bad and/or stupid people, intentionally cherry-picking the worst examples I could find. There are a lot of Magic players in the world, and if you look hard enough there will always be examples of poor behavior from any group, regardless of whether that group on average behaves any worse than other groups.

I also used the emotive conjugation of words to frame these actions as negatively as possible. For example, "bashing" and "disparagement" rather than "disagreement" and "criticism". In reality, while those tweets are a little rude, they're not really that bad.

All the framing here was maximally one-sided. Consider this quote:

"At times, well-intentioned people have tried to defend pile shuffling. It usually doesn't go well."

The phrase "well-intentioned" has a positive connotation, so the first sentence tries to frame these people as being "the good guys". By talking about them "defending" pile shuffling, I give the situation an adversarial framing, with them as the plucky underdogs. And then "it doesn't go well" is a very vague statement. It's true in that they usually fail to convince people of their argument (because it's wrong), but people are likely to interpret it as them suffering some negative consequence.

Overall, this first section was effectively an appeal to emotion/Ad hominem attack (or more specifically, a bravery debate), where I present a bunch of completely irrelevant information just to try to get people to sympathize with the pile shufflers.

I end the section by saying:

But of course all of that is tangential to the question of whether pile shuffling works. While observing the psychology of the detractors of pile shuffling can give us an idea of how they may have arrived at their conclusions, a bad reasoning process doesn't guarantee a false conclusion. So let's look at the object-level arguments here.

This was apophasis; I claimed to not want to engage in a certain type of rhetorical tactic (bulverism), but by making that statement, I actually do it anyway and just lampshade it to give myself a veneer of rationality and objectivity.

I then move on to discussing probability. My main approach here is to say a bunch of smart-sounding things about randomness that are true but irrelevant.

For example, I point out that pile shuffling increases the randomness of the deck by helping people forget what cards are where. You know what also increases the randomness of a deck by the same metric? Just sitting there and doing nothing! The player will start to forget what cards are where after enough time has passed. Just increasing the uncertainty about the deck configuration is not enough to justify a certain type of shuffling; it has to do it efficiently, and the level of randomness must be tending towards "completely random" rather than towards some other semi-random distribution.

The next section then goes even further into the "say true but completely off topic things". I use the examples of two decks that each start out like this:



And then we shake the letters around a bit randomly and get:



Then then I explain that the second deck is more random than the first. All true, but I conveniently failed to mention that the "shuffle" I performed on these decks is nothing at all like any shuffle a Magic player might use. "Any card has some chance of being moved up or down a few positions" is not something that can easily be implemented in a real life shuffle. If instead I performed a mash shuffle on those decks, where i split the deck in half and interweave the halves, the results would look more like this:



The first deck is still worse because there were fewer lands than spells, so there's still a clump of spells at the end, but this pattern will go away after the second mash. And the second deck is subtly bad too, because there's no chance of getting three lands in a row, since they were spread out in a regular pattern beforehand that isolated them from each.

Basically, what I did here was invent a completely new type of terrible shuffle, and point out that performing a pile shuffle followed by my new terrible shuffle is better than just doing my new terrible shuffle on its own. It has pretty much no relevance to actual card shuffling, where mash/riffle shuffles are effective enough that the additional randomness you'd get from a pile shuffle beforehand is a negligible rounding error. This whole section was a red herring.

In a general sense, my arguments were overstating the importance of Bayesian probability theory vs. frequentist probability theory.

Frequentist probability is the interpretation that gives items some fundamental property of randomness, and the outcome is drawn from that distribution. It's a useful mathematical idealization, but runs into a lot of problems both philosophical and practical when people try to apply it to the real world. Bayesian probability is an improvement over frequentist probability that allows the world to be deterministic, and defines randomness as our lack of knowledge of what the outcome will be.

As I explained in the previous article, Bayesian probability is the philosophically-correct way of thinking about a real-life deck of cards, since frequentist interpretations don't make sense. But there are some subtleties to the concept of "knowing the location if a card in the deck", and it's easy to take a too-simplistic view of things and end up going wrong.

The relevant one here is that players need to use a shuffling method that doesn't allow the player to assign a more informative prior distribution across deck configurations than they should otherwise have access to. Say that a player doesn't know anything in particular about their deck's order. They then start drawing some cards, and notice that their last 9 draws have been "LSSLSSLSS". If they know that the deck was shuffled properly, then this shouldn't give them any information about the next card they draw. But if they know that the deck was shuffled using a method that's likely to produce a regular pattern, then they can justifiably assign a higher probability to the next card being a land. We need players to use shuffling methods that result in every possible deck configuration having an equal chance of occurring as a result, so that players truly have no information about the deck's ordering.

Bayesian probability is very useful for more complex situations such as interpreting medical tests and reasoning under uncertainty, but when it comes to decks of cards and rolling dice, frequentist approaches are going to be less likely to lead you astray.

I also threw in some rhetorical slight of handSlight of mouth? such as in:

"This article on the Magic judges blog correctly states that pile shuffling is an optimal randomization method if we start from an unknown deck configuration".

The linked article does in fact state that, and it is technically correct, but it's a completely inane statement. If you're starting from an unknown deck configuration, then the deck is already randomized! Any shuffling method after that point would be "optimal", since you can't increase the randomness of the deck any further than the "completely random" it started as. I have absolutely no idea what the writers of that article were thinking when they wrote that sentence, but I thank them for giving me such an amazing opportunity to mislead people.

I finish off the article with various appeals to authority. Pi Fisher and Jacob Cohen are both real people who have the stated credentials, though as with everything else, I present those credentials as being more impressive than they are. "Google employee" has very little relevance to a math articleAs a funny coincidence, while writing this article I stumbled across this video that talks about how a programmer at Google misunderstood the extremely basic and foundational concept of function growth rates, and refused to listen to an explanation of how it actually worked., the textbook contributions were fairly minor (like teaching the author how to create their diagrams), and Jacob's only contribution to the New York Times was getting some of their puzzles included in the NYT's puzzles page. (Notice how "a New York Times published mathematical writer" strongly implies that it's the writing that was published in the NYT, but doesn't state it outright.)

They were both in on the joke, of course. They happily signed off on "every statement you made in this article is technically accurate" and told me how to inflate their resumes to seem more impressive.Jacob suggested that I conflate them with the famous statistician also named Jacob Cohen, but I didn't see a convenient way to do that that wouldn't be crossing the line into outright lying. Very tempting though.

I also said:

For example, I remember talking to a player in my LGS several years ago and asking them to stop pile shuffling. At the time I was against pile shuffling, but they explained to me that it was a useful method of randomizing the deck, and backed this up by mentioning that they were a statistics student at the University of Florida. After that interaction, I looked into the matter further, and found out many of these arguments in favor that I had previously been unaware of.

It's important that we're able to admit our mistakes and change our minds when presented with new evidence.

That interaction did happen, but that player's arguments were exceedingly bad, and their net effect on me was just to lessen my opinion of the average quality of university statistics instructors. It's true that "after that interaction I looked into the matter further", but there was no causal connection between the two; I just enjoy learning about statistics.

I finish the argument by pointing out that "It's important that we're able to admit our mistakes and change our minds when presented with new evidence", strongly (but falsely) implying that that's what I did in response hearing that player advocate for pile shuffling, and making the reader associate open-mindedness with "agreeing with what I said in this article", encouraging them to change their mind as well.

Was this a good idea?

Not sure. I'm generally pretty strongly against deception, but "help people learn how to spot deception" seems like as a good a reason to deceive people as you're gonna get. (Since it'll ideally make deception less effective and therefore less common overall.)

One concern was that of contributing to misinformation. If somebody saw only my first article and not this follow-up, they could leave with the impression that pile shuffling is good, and now I've made the world worse.A few players commented on the article with things like "thanks for posting this, now I feel vindicated". This is a concern I take seriously, but much more popular content creators than me have advocated for pile shuffling (all the way up to Wizards of the Coast themselves), so my article seems like it would be naught but a drop in the bucket. (And of course I've edited the previous article to include a link to this one at the bottom, so other people can't effectively link it to people as a justification for pile shuffling.)

I did make one significant mistake here, which was posting the April Fools article in the main Magic subreddit. All the other locations I distributed it (my email subscriber list, my Facebook, my Twitter, and the MTG Judge subreddit) are all small fora where people know me and will see a follow-up article. But the main Reddit is much larger, and it's highly likely that someone could see the original post and then never see me posting this response article. So that was bad, and I deleted the post a few hours after making it once I realized the problem.

The other concern is whether I may have offended or embarrassed people by deceiving them. For example, a friend and L2 judge posted this glowing review in a public discord server:

A discord message saying '@IsaacKing has successfully changed my mind about pile-shuffling: I didn't have a very strong conviction that pile shuffling was very bad before, though. Just that it 'seemed off.' Glad to see statisticians agree it's pretty darn good at randomizing your deck. Thinking about randomness differently is hard, so I appreciated the example of riffle-shuffling faceup vs facedown.'

I reached out to them to let them know that the article wasn't serious, and they were, well, a little miffed.

I'm not sure whether this is a positive. It's very easy to be convinced by a well laid-out argument in favor of a false conclusion, and we should be wary of trusting such individually-compelling arguments that go against a general consensus among subject-matter experts, and I think this demonstrates this very well. I'd rather people didn't just accept anything they read from a contrarian source they trust without first seeking out counterarguments.

At the same time, I'm sorry for any upset I caused. I set out to write a convincing piece of disinformation, and I didn't properly consider what would happen if I succeeded. My hope is that this can be a useful learning experience to help people understand their own susceptibility to flawed arguments.I'm reminded of the AI box experiment, where people confidently claim that they could never be convinced to let a malicious superintelligent AI out of a contained environment, then consistently fall prey to arguments they hadn't thought of and let it out anyway. Most people who use these sorts of manipulative rhetorical tactics aren't going to tell you about it afterwards, so it's important that we're able to notice them on our own. (One concern here is that people overfit on the experience and start only being more skeptical of what I personally write, without giving the same scrutiny to anyone else. That would obviously be a pretty unhelpful lesson to learn, but it's very common for people to laser-focus on the exact issue they just experienced and fail to draw the general lesson.)

My general point here is that knowing what's true is hard. Any topic that's complicated enough to argue about is also complicated enough that most people won't have a complete understanding of it. Randomness is actually a pretty involved concept, and even people who are professionally familiar with it can easily get it wrongEven Paul Erdős had trouble with it.Pigeons, however, have got this down.. This is of course true for both sides of any issue; many people objected to my April Fools article and continued to claim that pile shuffling is bad, but did it on incorrect reasoning.

This is true even when everyone is speaking in good faith with an intent to find truth, but it gets so much worse once one side has already decided on their conclusion and goes looking for arguments to support it like I did there. The sort of nutpicking/weakpersoning like I did in the first section is the standard approach to any heated debate among large groups; just find the dumbest people out of a group of millions, and claim that those people represent the entire group. The paltering in the second section is also an extremely common approach any time someone wants to mislead people while retaining enough plausible deniability to deflect accusations of lying. And of course arguments from authority get misused all the time.

The judge community in particular tends to struggle with this. We claim to (aspire to) be impartial arbiters, tasked with resolving disagreements and investigating adversarial situations to determine which player (if any) is mistaken, cheating, or lying. And with such a large amount of power over players, judges bear significant incentives towards abuse and malpractice, and must self-regulate with no oversight. Yet Judge Academy provides no guidance on avoiding basic misinformational practices like these, nor do most members of the community make any attempt to avoid it, and they often intentionally engage in them for personal gain.For example, a female-presenting judge once publicly claimed that I had "told them I don’t need their consent to do what I want with them". There is indeed a very convoluted reading of this that's technically true, in the pedantic sense that judges don't need players' consent to give them a penalty they didn't want to receive, but what this judge was obviously trying to do was falsely imply that I was in favor of or had threatened to sexually assault them. They received no consequences for this accusation, and were shortly thereafter hired by Star City Games.

If we want to live up to the trust placed in us by players, we need to hold ourselves up to a higher standard, and right now we're not doing so great. My pile shuffling article was "easy mode"; It was published on April Fools, about a non-emotionally-charged subject, contradicting my previous article on shuffling and many of my own statements on Twitter, using bad faith rhetorical tactics that I frequently denounce and would never use in a serious context, and the header image was the card "Disinformation Campaign". Yet many people still accepted it uncritically.

We need to get better as a community at figuring out what's true and what's false, noticing when people are trying to mislead us, and clearly communicating about what's happening.

Together, we can rid the world of pile shuffling.