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Returning from Nationals, many players have been talking about the various examples of card shuffling shenanigans that they saw there. As a level II DCI judge, I also have been hearing about a good deal of confusion from judges all across the world on the subject of card shuffling, fair and unfair. Players want to know when their opponents are failing to randomize their deck properly. Judges want to know how to tell whether players are doing the right thing. As the issue heats up on both sides of the game, it all really boils down to shuffling cards. The time has come for the fine art of card shuffling to be recognized as the all-important factor that is really is in the game of Magic. Competitive Magic players spend hours and hours developing the best possible deck, only to shuffle the deck improperly game after game, wondering what went wrong with the deck. Let's start with the basics. The rules require that players randomize the order of their cards by means of the general term "shuffle" before each game. The generally accepted idea, from DCI judges, is that a properly shuffled deck should contain no discernable pattern of any kind among the cards in the deck. Most judges extend this lack of pattern to include the idea that the player shuffling the deck should not have any knowledge of where any particular cards are in the shuffled deck. Upon reading this, you may be suddenly aware that "properly shuffled" and "properly randomized" are terms that do not seem to be clearly defined. Not surprisingly, players and judges also can't agree with how to get a deck to a randomized state. Let's start with our friend the riffle shuffle. A riffle shuffle is defined as cutting the deck into two parts, possibly uneven in size, and then raggedly interleaving the two parts. According to this definition, the kind of "mashing together" of two cut halves of a deck in sleeves would count as a riffle shuffle. I certainly agree with this. Whichever way a riffle shuffle is performed, it is optimal to have the interleaving of the two deck halves as completely even as possible. This means that an optimal riffle shuffle, when complete, would result in a card order of one card from the first half of the deck, then one card from the second half of the cut deck, and so on. If you look closely at your own riffle shuffle habits, don't be surprised if you find that you aren't getting the optimal riffle shuffle. Most people aren't. A perfect riffle shuffle is difficult to achieve, frankly, with the quality of card stock used for Magic cards. Placing the cards in plastic sleeves is another obstacle to correct riffle shuffling. According to statisticians, six or seven riffle shuffles in succession is more than enough to bring a deck of fifty-two cards to a state very close to mathematical randomness. In my experience as a poker player, I have seen as few as four riffle shuffles provide very good levels of randomization in fifty-two card decks. Six or seven riffle shuffles for a sixty card deck, and possibly as few as four to five shuffles for a forty card deck is probably sufficient.

What about mana weaving?

If a proper method of randomization is used, it will not matter what order the cards are in before shuffling is performed. In other words, if you can properly shuffle a deck in six or seven riffle shuffles, your deck can be in any order before shuffling and you will still end up with a randomized deck.
This means that it doesn't matter if you just finished a game with most of your land in one big clump. It doesn't matter if you mana weave before you shuffle or not. If you shuffle correctly, it will not matter if your deck was completely sorted before shuffling. Recently, a math-wiz on the DCI judges list noted that decks should be "re-meaned" before shuffling. That is, he believed that decks SHOULD be mana weaved before the deck was shuffled in order to produce a result deck with the best average land distribution throughout the deck. The problem with this idea, and this error exists in the minds of most players that like to mana weave their decks, is the notion that a shuffled deck should have some kind of "even distribution". If a deck that has been shuffled has any kind of "even distribution", then the shuffle has failed. Even mana distribution in a Magic deck does not meet the criteria of random. Of course, if your opponent wants to mana weave, don't worry about it, as long as you see a high quality shuffle take place after the mana weaving is complete.

Shuffle more, whine less

In the end, players need to shuffle their decks more and complain less. When your opponent presents his deck to you, shuffle that deck to your satisfaction. Ask your opponent to shuffle your deck as well. More shuffling is good. There is no reason to worry about pile shuffling either. If a deck has been properly shuffled, then there is no pile shuffle that will hurt the randomness of that deck. Pile shufffling is where a deck is dealt out (face down!) into some number of piles using a pattern, or, more randomly, without using a pattern. Pile shuffling is a perfectly acceptable form of randomization, although less efficient than riffle shuffling in general.

Cheating and shuffling

Yes, cheating is a problem in competitive Magic. Cheating, or perceived cheating, is probably the reason that players get so worried about the other player's shuffle. Yes, a player could possibly cheat when he shuffles his deck. He could be some kind of magician or card shark and deceptively move cards around in his deck (or yours) to affect the outcome of deck shuffles or card draws. Players can gain knowledge when they pile shuffle cards that have marked sleeves. Cheating injects an artificial factor into the game of Magic that is neither welcomed or allowed by the rules. If you think that a player is cheating in a match in any manner, it is your responsibility to report the behavior to your judges or whatever staff is running the tournament. Proper shuffling cannot remove the possibility of a player cheating. Proper shuffling can, however, make game play between two honest competitors as fair as possible.

Some homework for the competitive Magic player

Okay, so you want to make sure you are shuffling your deck the best way possible, and you also want to make sure that your opponent is doing the same? Then do some homework. The following links were provided to the DCI judges recently. These links have to do with proper deck randomization, and come from sources outside of the game of Magic. Check out these links and, by all means, improve your shuffling skills.

http://www.sciencenews.org/20001014/mathtrek.asp

http://www.pubs.royalsoc.ac.uk/proc_maths/abstracts/2002.htm.

http://mathworld.wolfram.com/Shuffle.html.

I found the information at the above links to be helpful, and I hope you will too. I would personally be very happy if players would quit saying they have incredible luck drawing cards, or that they have no luck drawing cards in certain kinds of decks. Instead of devolving the game of Magic into some kind of wacky pseudo-religious experience, they should instead focus on making sure their cards are randomly shuffled each game. It simply is the way the game is intended to be played. I'll certainly be working harder on my own shuffling skills, which will be good news for you when we play in a tournament and I shuffle your deck!

Jeff Zandi
Texas Guildmages
Level II DCI Judge
Zanman@thoughtcastle.com