When we go to a Magic tournament, everyone is playing the same game by the same set of rules (we hope). Even with this imposed uniformity, there are a lot of unique people at Magic tournaments. At one level, the game itself, the deck we are playing makes us unique. Deck choice could be a product of what we think the metagame is, the type of deck you like to play or, in the case of poor graduate students like myself, what good rares we happen to have at the time. But there are a number of other ways that people can distinguish themselves from the rest of the players in the room: The sleeves we use, the way we keep score, the good-luck charms, the way we lay out or cards, the clothes we wear, etc.
But one way you shouldn't set yourself apart from the crowd is your shuffling technique.
One example of this happened this past weekend in the Top 8 of the U.S. Nationals. Casey McCarrel was disqualified in the quarterfinals for manipulating cards (go here for details). McCarrel apparently handed back to his opponent, Brian Hegstad, a deck in which the first eleven cards were all spells. Obviously, this puts Brian at a disadvantage, because he would have to mulligan at least once. I have no clue how Casey managed this if it was intentional, and as I write this, I have not read any descriptions as to how this might be accomplished. McCarrel was disqualified from the tournament.
A second shuffling related incident occurred at the Sunday Detroit Apocalypse pre-release. It was the second round, and I was playing G/W/U with Treva, three tappers, and two Temporal Springs combined with a fair number of flyers. My opponent was very talkative but unfortunately, he wasn't talking to me. He was talking to anyone who would listen, which was the person next to him. This may have been a friend, and if it was you would have assumed that he had already heard the story about how he won the last thirty-two-person flight he was in at the Planeshift pre-release with a really good control deck, but maybe his friend had forgot. Anyway, I lost the first game after casting my Treva four times, because the first three times I cast it Treva was Temporal Spring-ed (Temporal Sprung?) to the top of my library. I lost the second game after he used a painland to cast a back-to-back Rith and Spiritmonger. I quickly scooped.
If we ignore for a minute that at least three of his six rares were a Rith, a Spiritmonger, and a painland, and that from three Apocalypse packs he got three Temporal Springs (one foil), my opponent had a very unique method of shuffling. As he was talking to his neighbor, I was shuffling my own deck, and didn’t watch him shuffle. But as he handed me his deck to cut, he cut it first. I thought about this for a second... But just cut the deck and handed it back to him. In between the first and second game, I watched him shuffle and saw him do the following:
1. Separate cards into seven piles, and pull each one off the table into his stomach below the table.
2. Riffle shuffle a few times.
3. Overhand shuffle very quickly, but with the cards turned 90 degrees, so the short end of the cards were in his palm.
4. Cut the deck and then hand it to me.
Now if he was stacking the deck, cutting the deck would put the cards at the top of his deck in the middle, therefore increasing the odds of those cards being on top if I only cut the deck. Needless to say for the first time in two years of playing Magic, I shuffled an opponent’s deck versus just cutting it. I was not the only one who noticed the player's shuffling technique; my wife Natalie sat next to the same person later in the day, and his opponent questioned his shuffling to the judge, including the orientation of the cards (i.e., land in one direction, spells in the other). One of the things Natalie overheard after the match is that you should always shuffle your opponents deck, so that you never get an opponent saying,"Hey, you didn't shuffle your last opponents deck. Do you think I am cheating?" Am I accusing of this person of cheating? Yes (although I have no proof), and so did at least another person and as much as I hope prereleases are relaxed, fun environments, when eighty or more dollars worth of product is on the line, people will cheat.
The lesson to be learned from all this is: Don’t draw attention to yourself by shuffling you cards in a unique, non-standard way. If you shuffle your deck in a funny way and you find people questioning how you shuffle, change. It will save you, and your opponents, lots of grief. If you continue to shuffle you deck in a funny way, then people will assume you are cheating, and they will continue to question you. There are numerous articles on the web for what to look for when someone is stacking their deck via shuffling. Here is one more: http://www.ehow.com/eHow/eHow/0,1053,4402,00.html.
So now that we know how not to do it, we must then ask another question: What is the best way to shuffle a deck in a standard way that ensures a random distribution of cards? In Magic, there are three main ways of shuffling: The riffle shuffle, the overhand shuffle, and the pile shuffle. The riffle and overhand are carryovers from other card games, and descriptions can be found at http://www.ehow.com/eHow/eHow/0,1053,4353,00.html for the riffle and http://ps.superb.net/cardtric/sleights/overhand.htm for the overhand (as well as more ways to keep cards in certain places). The pile shuffle occurs when a deck is dealt into two or more piles and then stacked on top of each other.
There exists a paper that says the optimal number of times you should riffle shuffle a 52-card deck is seven times. A copy of this paper by Brad Mann can be found here but be forewarned, this is a very technical probability paper and is a tough read. The rule of seven would work for a standard a 60 card Magic Deck as well. It should be noted that probability model used does not assume a"perfect" riffle shuffle that is, the deck is split evenly into two piles, and one card at a time is riffled together. The model actually takes into account different size piles and the fact that all riffles are not perfect. The paper also discusses alternative opinions as to how many shuffles, offering eleven or twelve, depending on what you consider random is (more on that later). By the way, if you could riffle shuffle a 250 card 5-color deck, the approximate number of riffle shuffles to make it random is nine.
One of the above links describes different ways the overhand shuffle can be abused, and the riffle shuffle can be abused as well. One interesting link is http://www.math.hmc.edu/funfacts/ffiles/20001.1-6.shtml, which talks about"perfect" shuffles. And if you can shuffle perfectly to the point that you can do an out-shuffle, the top card stays on top, and an in-shuffle, the top card moves to the second position in the deck. You can use the information in the above link to move the top card anywhere you want, given enough shuffles.
In light of all this information, all it takes is seven or more"non-perfect" riffle shuffles to sufficiently shuffle a deck from a mathematical perspective. To prevent the appearance of cheating, a couple of overhand shuffles to move the top and bottom cards should be done. Therefore, when an opponent hands you their deck to cut, seven riffle shuffles and an overhand in the middle should prevent any stacking they may have done. Remember, DCI floor rules allow the deck’s owner to make one cut after you hand them their deck back. One thing we are concerned about with our own decks is the distribution of mana, especially after a game when six or more lands are already together in a pile. Again, seven riffle shuffles with an overhand thrown in for good measure should be enough, but I’m just not comfortable with that. Pile shuffling first breaks up that mana, without doing a true"mana weave" (a no-no). Don’t overdo the pile shuffle however, as it may look like you are trying to put the mana back together which is mathematically probable, given enough pile shuffles. And always keep your cards above the table, face down, and while you should not shuffle slowly, shuffling very quickly may make people think you are trying to hide something.
One final note: DCI has penalty guidelines for"insufficient randomization." But what is"insufficient randomization?" According to Mann, in order for a deck to be randomized, each permutation of cards should have the same probability of occurring, that probability being 1/n!, where n is the number of cards in the deck. The"!" means factorial, and n!=n(n-1)(n-2)...(2)(1). For a standard 60 card deck, there are 60!, or 8,320,987,112,741,390,144,276,341,183,223,364,380,754,172,606,361 ,245,952,449,277,696,409,600,000,000,000,000 possible permutations (order matters) of those sixty cards. A sufficiently randomized, or shuffled, deck would have each one of those permutations equally likely. When Casey McCarrel handed back a deck with the top eleven cards being spells, the probability of that randomly occurring is 0.12% (25 of Brian Hegstad’s 60 card deck was land), or 1.2 times out of every 1,000. If 156 players played six matches on day two, each match lasting on average two and a half games, there would have been at least 2,340 shuffles (not counting mulligans). Therefore, it could be expected that a deck with the first eleven cards being spells would have been seen 2.8 times during day two at U.S. Nationals. (If everyone was playing twenty-five lands, of course. If less land is being played, the number of times this condition would occur would increase).
Therefore, a deck in which certain permutations of cards are more probable is insufficiently randomized no lands in the first seven cards for example. There are two ways to catch a player doing this: The first is to observe the player using shady shuffling techniques, and then check the deck, looking for a pattern that benefits the player. Watching the player shuffle a particular way gives a judge probable cause to look for an advantage. The second way to catch a cheater is to sample a number of shuffles, and see if a particular set of results is more or less prevalent then expected given sufficient randomization. For example, in a sixty-card deck with twenty-four lands, the probability of a no-land, seven-card hand is 2.16%. If you play twelve matches in a day, two and a half games per match, the average number of non-land hands for the thirty shuffles would be .648 less than one. Does this mean that if you draw no lands, your opponent stacked your deck? No, because there is a 34.3% chance in thirty games you will get a one-land hand. Now, if you played the same player thirty times, and got three or more non-land hands, there is enough statistical evidence to suggest that the probability of a non-land hand is greater than 2.16% after your opponent shuffles your deck. (Note: This is for a twenty-four-land deck. The less land you have in the deck, the greater the number of non-land hands you would have to see in order to be suspicious.)
Which brings me to me final point: You can not tell if a player is stacking a deck by looking at one instance of a shuffle. You have to sample randomly from all of the player’s shuffles and then do some type of statistical test. There is not a professional statistician in the world that would testify in court that you could make accurate statements about a population based on just one sample. Applying this to Magic, you could not make a statement that one is"insufficiently randomizing" a deck just be looking at the results of one shuffle you would have to see a pattern over a number of shuffles. I am by no means trying to defend Casey McCarrel, but if this were taken to court, and the penalty was handed out based just on the results of one shuffle and no other proof, I believe the DCI would lose. And that would be bad for everyone.
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