Chatter of the Squirrel – The Truffle Shuffle

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Wednesday, October 1st – This article would not help you win a single game of Magic if everyone played games exclusively via MTGO. Fortunately, those of us who don’t play World of Warcraft are still relatively familiar with the phenomenon known as “real life,” and thus we sometimes occasionally every once in a while maybe just maybe interface with living, breathing human beings. If this happens in a Magical context, we might even shuffle up a physical deck of brown-backed insignia-inscribed trading cards.

… Okay, minus the truffle. That moniker is reserved for a certain dance a Mr. Cody Peck performed at a New Year’s Eve celebration at Petra restaurant. The “shuffle,” though…

This article would not help you win a single game of Magic if everyone played games exclusively via MTGO. Fortunately, those of us who don’t play World of Warcraft are still relatively familiar with the phenomenon known as “real life,” and thus we sometimes occasionally every once in a while maybe just maybe interface with living, breathing human beings. If this happens in a Magical context, we might even shuffle up a physical deck of brown-backed insignia-inscribed trading cards.

It is my experience, at the local level especially, that most people do not sufficiently randomize the position of these physical cards before they present their deck at the beginning of a match. This can lose a player a huge amount of games over the course of a career, completely preventable losses, but because his shuffling technique is almost never called to attention this type of player can go years without ever even realizing what he is doing. I watched a number of players shuffle their deck completely inadequately at this last weekend’s prerelease, only to lose as a result due to repeated successive mulligans, and it occurred to me that the phenomenon is probably not localized to Malaysia. A lot of people just don’t give shuffling much thought.

First, though, some background. I believe Zvi has written about shuffling technique awhile ago, but I can’t for the life of me find the link. There are a number of players, myself and Sam Black included, who are occasionally criticized for “over-shuffling” a deck. As long as you do it in a reasonable amount of time, I don’t think there is such a thing as over-shuffling a deck, but that is neither here nor there. In truth, there are a lot of misconceptions about the role of randomness in regards to things like mana screw and mana flood, and I want to dispel some of those myths right now.

The first, of course, is that the more you randomize your deck the less likely you are to get mana screwed. People frequently conflate “regular distribution” with randomness when they are in fact almost entirely the opposite. A mana-woven and then slightly shuffled deck is a deck with a very ordered pattern to its cards, even though “you never know what you’re drawing so it can’t be illegal” (an actual argument made to me a few years back). In fact, while people mana weave with much less regularity these days, understanding the importance of randomization can help you to understand why you need to thoroughly shuffle an opponent’s deck before you play, even if you have absolutely zero suspicion whatsoever that they are cheating.

The second myth, though, is just as dangerous: that because you get manascrewed a measurable percentage of the time with a thoroughly-shuffled deck, there is nothing really you can do to prevent this from happening. Magic Online shuffles – oh, the notorious shuffler – and you still get screwed. So what difference does it make?

The truth is that there’s a scale you can construct for the degree of randomness an average physical deck possesses. In order to understand this scale, you have to realize that strictly speaking there is nothing “random,” nothing that in actuality exists as a measure of probabilities, about the composition of cards in your deck relative to one another. When you present your deck each card is predetermined to be in a certain position based on the series of manipulations you executed upon it in the interval between now and your last match. The reason probability still governs the percentage chances we have of drawing certain cards is of course because we don’t have access to the information about where, say, my four copies of Bitterblossom are sitting in actuality, so we have to use probabilistic methods to determine what our best course of action should be given the amount of information we possess.

I know a lot of this is obvious, but I need to re-hash the very basics so you can get an understanding of where I’m coming from to construct this scale. The point is that after a given game of Magic your deck typically possesses a very high level of order, and it will not lose that order and tend towards randomness until you make it so – and that the typical sort of order a deck possesses is very bad for you when you’re drawing opening hands.

The reason for all of this is that at the end of a normal game of Magic, what do we usually do? We scoop up our permanents, grab our graveyard, put them on the top or bottom of our deck, and start riffle shuffling. Therefore at the instant the shuffling commences, approximately half the lands in our deck (in a given game of Limited) are positioned adjacent to one another, as are a considerable portion of our spells. These are not the type of opening hands you want to draw.

Of course, it is important to remember that in a completely randomized deck, our cards could retain this exact same configuration. However — and this is probably what my thesis boils down to ultimately — it is more likely in any given game that this type of uneven distribution, given many players shuffling habits and the time constraints imposed, is a result of insufficient randomization than it is the natural variance across the set of randomized deck configurations. This is simply Occam’s Razor. The “scale,” then, is the set of possibilities ranging from the very “bad-for-you” “clumped” lack of randomness at which we frequently end games, and total randomness, which for our purposes is ideal (“good for you” randomness is the set of possibilities extending to the other side of random, that is to say “sequenced distribution” instead of “clumped distribution,” but unfortunately such sequenced distribution is very illegal — and I know, my terms are very technical, heh).

You may not believe that it’s all that difficult to truly randomize a deck from this typical end-game position, and that in fact it isn’t terribly likely that an appreciable percentage of “clumping” results from insufficient randomization. But consider: in order to actually be randomized, a sufficient number of operations have to be executed upon each one of the forty cards in a given Limited deck so that it is no more likely that any card is closer in proximity to the cards it began the shuffling process “grouped with” than it is to be in close proximity with any other card in the deck. Now think of how many operations have to be conducted for this statement to be realistically true.

Because of this reality, it’s important to economize one’s operations so that you allow the maximum number of iterations of a process within a given time frame.

Let me explain what I mean by that.

There’s a process that I refer to as “brick shuffling,” because you’re layering different clusters of the deck as if laying bricks, but I really have no idea how you’re actually supposed to refer to it. We all know what I’m talking about, though: it’s where you hold the deck in one hand, grab it either lengthwise or by its end if you are Asian*, and move an undefined portion of the deck from either the bottom or the center to the top. Usually you can execute this technique seven or so times before you’re “done” with all the cards and have to pick the whole deck up and do it again. You sort of dump a clump of cards from one part of a deck to the other. A whole lot of people riffle shuffle the deck two or three times and then just do this a bunch until they present the deck.

The problem, though, comes when you think about what you are doing. Every time you pick up a chunk of the deck and relocate it, you are only actually re-ordering a small percentage of the cards relative to one another. Say you cut a deck and grab each half before you do this. Then the part that was on the bottom you, you know, “shake” a portion of the cards onto the top of the other pile. It’s usually like eight or nine cards. But you’ve actually only affected the relative position of five of the cards in the deck: the former “bottom” of the deck, the new “bottom,” the former “top,” the new “top,” and the last card in the “clump” whose position is being relocated (the first card in the “clump” is also the new top, and the card atop which the new pile is being placed was also the top card of the deck). It sounds complicated when I explain it here but we all know what I’m talking about: the type of shuffle you do when you’re not riffling. In any case, you only affect the relative position of a small number of cards, and you only really vary that relative position by a card or two.

It should become clear, then, that as a method of randomizing a deck completely, you’re not going to really get far. That is not to say it has zero usefulness; in fact, it’s very good at changing the relative position of a large portion of cards from one part of the deck to the other, which is useful after a long span of riffle shuffling because you rarely alter the position of the first and last few cards.

Then, of course, there is pile shuffling, which we all do. The “shuffling” part of pile shuffling is actually a misnomer, at least insofar as “shuffling” connotes “randomizing,” because you’re in fact laying the cards out in a very organized, very defined pattern. Nevertheless, I recommend pile shuffling both because it ensures that you are presenting a legal deck, and because it apportions your deck into smaller units upon which more iterations of a riffle can be conducted. This is simply due to the reality of their physical dimensions: especially in sleeves, it’s easy to do two or so riffles per second on two out of five piles of eight cards, and it’s also possible to get a higher degree of variance per “brick shuffle” because you’re more likely to shuffle smaller, less sequenced groupings due to the limited space available**. In order to capitalize on this, though, it’s essential not to just pile shuffle and stack the cards on top of one another. I usually take three of the piles and shuffle them independently, take the other two piles*** and shuffle them independently, then riffle the two groups into one another.

Riffling, of course, is the most “efficient” shuffling technique, since you’re actually rearranging the relative order of almost every one of your cards with each iteration. Even it has its limitations, though, and it’s important to recognize them.

First, if you’ve been playing Magic forever like I have, you’ll probably get to the point where (unsleeved anyway) you can execute almost perfect riffle shuffles without even attempting to do so. This is problematic because such a technique, like pile shuffling, is actually far from random even if it is more intricate. There is an equation I used to know that describes the relationship of every sequenced card in the deck (numbered 1 to N, where N is the total number of cards in the deck) for X perfect riffle shuffles, but irrespective of that the point is that this type of order is exactly what you’re not going for. Furthermore, it’s frequently very easy to unconsciously keep the top three or four cards on both the top and bottom of the deck at either the top or bottom of the deck, especially if you’re in the habit of unconsciously looking at the bottom of your deck like many of us were doing before the Ruel suspension made us much more aware of it****. Point is that I had to start intentionally riffling different-sized portions of the deck, and brick-shuffling every five or so shuffles to vary the positions of the top and bottom cards. Alternatively, you can use sleeves, which makes it easier, and again grab different sizes of deck to shuffle into one another each time, and make sure you’re not evenly spacing the interlocking of cards, if that makes sense – like, when you cut the deck and have “halves” of twenty-five and fifteen cards, or whatever, make sure the fifteen aren’t going “into” the twenty-five every two cards with however many left over.

What’s my technique?

First of all, I shuffle all the cards I had in play with one another, and then I shuffle them into my graveyard before placing any of them into my deck. Technically this shouldn’t matter but as I said earlier it’s easier to conduct a greater number of operations on a smaller group, so I’ve found this to be more efficient. Then I riffle shuffle the deck five or so times, at which point I sideboard. After sideboarding, I riffle five or so more times and then pile shuffle the deck into piles of five – doing it after boarding to make sure I de-boarded correctly. After I pile shuffle my deck I verify my sideboard visually to make sure I didn’t leave a card laying around somewhere. I then choose two of the piles at random and riffle them into one another, and then take the other three piles and riffle those into one another. I then riffle the two bigger piles, brick shuffle them every five riffles or so, and conduct probably twenty-five unsleeved or sixty sleeved riffles on the final product before I present it to my opponent. Limited I typically, for spatial reasons above all else, shuffle more than Constructed even though this is not ideal.

The reasons I have chosen to devote an entire week to shuffling technique are that 1) it’s incredibly dangerous if you don’t know you’re doing anything wrong, losing you countless games before they even start, and 2) the habit negatively reinforces itself. You get manascrewed, you get upset, you throw the hand back and half-assedly shuffle maybe a few times only to present the deck again to your opponent’s cut, and unsurprisingly your hand of cards, while physically a different hand than before, is still sequentially organized and is therefore vulnerable to the same patterns.

Finally: I mentioned earlier some of the reasons why you should always shuffle your opponent’s deck. Many of those reasons have to do with wanting to avoid deliberate reorganization of the deck, or because you don’t want to combat an opponent’s mana-weaving, or because you’re playing at a prerelease or something and you know your opponent hasn’t shuffled properly, but you want everybody to have fun and so you shuffle a bunch to ensure you’re playing a real game*****. Another reason is that it’s illegal at high levels of play for you not to shuffle the opponent’s deck at first. I bring this to everyone’s attention because there are several occasions at a high level of play, especially after the opponent has mulliganed, where it is to your advantage actually not to shuffle their deck, instead only choosing to cut it, because they have mulliganed a hand and only made a halfhearted attempt to randomize their deck afterwards. Again, by not shuffling you’re not by any means gaining a sure advantage. Their deck could be sufficiently randomized and the bad draw due entirely to variance. But it could also be that their deck is insufficiently randomized from a previously-clumped position, and therefore it is to a player’s benefit to preserve that lack of randomization and hope his opponent draws the worse for it.

This is illegal, and I hope again at high levels that judges are enforcing the rule of mandatory shuffling from the opponent. For one thing, this reinforces positive habits at lower levels of play, and saves people from the awkward “why are you shuffling my deck?” comments at FNMs and the like. But it also prevents people from exploiting any advantage they could gain from the knowledge that an opponent’s deck is insufficiently randomized, while at the same time (for people who aren’t even thinking of things in these terms) gradually ensuring that everyone shuffles everyone else’s deck regardless. Once shuffling becomes accepted at all levels of play to be as much a part of the game as the draw step or the die roll, it exponentially discourages deck-marking and other cheats related to the deliberate ordering of the deck.

A final point re: judging: why is it that an opponent gets to be the last person to touch the deck before he draws his cards? There is really no means of intentionally “screwing” an opponent that couldn’t be lumped under other infractions, e.g. “Looking at an opponent’s cards” or whatever. But I always get really suspicious of anyone that takes a moment to cut his deck after I shuffle. What reason would he have for this? Whenever he hesitates even a moment I check the deck for obviously-marked cards and almost always want to call a judge, even though based on the rules he has committed no infraction. Can we get rid of this archaic practice once and for all?

Until next week,


* Oddly enough I actually mean this statement at face value. So far it’s the only behavioral racial characteristic I have observed to be unequivocally, universally true across an extremely high N of samples. There is seriously a graduate thesis to be written on this topic. White people grab the deck from the side, usually between the index and middle fingers and the thumb, and shuffle the wide ends of the cards into one another in layers. Asian people, on the other hand, usually grasp the narrow end of the deck in a manner resembling a pencil, and shuffle either the tops or bottoms of the cards into one another. Now that I pointed this out, watch for it. It’s seriously uncanny.

** That’s a complicated way of saying that when we brick-shuffle we would look really stupid using the eight-or-so-card piles we normally do out of sixteen (instead of forty) total cards, so we only do it in groups of three or so, which actually works out for the better.

*** I use five-card piles because of their ease of counting, but some prime number like seven apparently produces less suspicious piles, reason being it’s very easy to retain the grouping of the deck across multiple five-pile shuffles.

**** This is/was frequently entirely unintentional; the thing is you don’t want to show your deck to the opponent, but you don’t want to screw up a shuffle and send your cards flying, so the most natural place to look it as your deck, which is frequently facing one side or the other – and you have to look somewhere. It took a great deal of training for me to avoid this habit.

***** This happened to me last weekend, where an opponent literally scooped all of his cards into a pile, put them on the bottom of his deck, riffled maybe three times, and then presented.