Shuffling.

That’s right, I’m here to talk about shuffling. Now, I know what you’re thinking: “first Block Constructed, now shuffling? This Giff guy sure is a piece of work, and boring to boot,” but please bear with me. I am of the opinion that many of us don’t sufficiently randomize our decks before or during matches of Magic and I wish to set things straight.

Before I go much further, I want you to do me a favour and watch a quick snippet of video. In this clip Simon Görtzen and Kyle Boggemes are shuffling their decks just before the deciding game of the finals of Pro Tour San Diego 2010. You can stop watching after a couple of minutes, or whenever you get bored, but until you do, I want you to pay special attention to the way Simon is shuffling. He’s the bespectacled ginger in the red sleeves.

What an orgy of inter-mingled playing cards! Quite astounding really. How many times do you think Simon shuffled his deck before presenting it to Kyle to start the game?

If you guessed 22, then you’re right…

Now if you’re not of the YouTube persuasion, or you’re at work, or a funeral, or a place where videos of nerds throwing cardboard about are inappropriate, I’ll clue you in. In 2 Minutes and 32 seconds Simon does the following:

– 2 riffle shuffles;
– 1 pile shuffle (7 Piles);
– 6 riffle shuffles;
– 1 pile shuffle;
– 5 riffle shuffles;
– yet another pile shuffle;
– and finally, 6 more riffle shuffles before presenting his deck to Kyle.

Seems like a lot of shuffling…and it is. But can you blame the guy? There’s $20,000 at stake!

Is it enough shuffling? Too much?

Let’s see what the rules tell us.

From the Comprehensive Magic Rules:

103.1. At the start of a game, each player shuffles his or her deck so that the cards are in a random order.

Well, that’s not a whole lot of help. But it does raise the interesting question, what constitutes a random order? I’ll touch on that in a minute…in the meantime, let’s keep digging for answers. How about the Magic Tournament Rules?

2.3 Pregame Procedures

1. Players may exchange cards in their decks for cards in their sideboards (only after the first or subsequent game of the match).

2. Players shuffle their decks. Steps 1 and 2 may be repeated.

3. Players present their decks to their opponents for additional shuffling. The sideboard (if any) is also presented at this time.

4. Players shuffle their opponents’ decks.

5. Each player draws seven cards. Optionally, these cards may be dealt face down on the table.

6. Each player, in turn order, decides whether to mulligan.

Players may not use more than three minutes to perform steps 1 through 3. Steps 4 through 6 must be performed in a timely manner.\

3 Minutes! There’s a nice guideline. And hey, Simon did all his shuffling in 2 and a half minutes! Sweet! But what about that part of shuffling your opponent’s deck? Do I always have to do that?

Again we go back to the Magic Tournament Rules for some more information:

3.8 Card Shuffling

Decks must be randomized using some form of riffle and/or mash shuffle at the start of every game and whenever an instruction requires it.

A Quick aside “Mash” Shuffling. Mash Shuffling is a technique frequently used by magic players that requires sleeved cards. You split your deck into two halves, put them side by side, and then push the two piles together, allowing the natural separation of card edges created by the sleeves to create gaps for the cards to slide into. Mash shuffling essentially performs the same operation as riffle shuffling.

Back to the rules:

Randomization is defined as bringing the deck to a state where no player can have any information regarding the order or position of cards in any portion of the deck.

Pile shuffling alone is not sufficiently random. Once the deck is randomized, it must be presented to an opponent.

By this action, players state that their decks are legal and randomized. The opponent may then shuffle it additionally.

Cards and sleeves must not be in danger of being damaged during this process. If the opponent does not believe the player made a reasonable effort to randomize his or her deck, the opponent must notify a judge.

Players may request to have a judge shuffle their cards rather than the opponent; this request will be honored only at a judge’s discretion.

If a player has had the opportunity to see any of the card faces of the deck being shuffled, the deck is considered ordered and must be shuffled again.

At Competitive and Professional REL tournaments, players must always shuffle their opponents’ decks. The Head Judge can require this at Regular REL tournaments as well.

So there you have it. At tournaments like PTQs, Grand Prix’s, and of course the Pro Tour, you have to shuffle your opponents’ deck after they have finished shuffling it. We also got another shot of information about what “random” means, but we haven’t quite determined what that means on a practical level. Did Simon shuffle enough?

Luckily for us, weirdo’s in dark rooms have devoted their lives to writing scholarly papers on the subject.

For example, check out Wolfram Mathworld.

Aldous (1983) showed that (3/2)*log2(n) shuffles are sufficient to randomize a large n-card deck, yielding eight to nine shuffles for a deck of 52 cards. When combined with results of Aldous and Diaconis (1986), this analysis suggests that seven riffle shuffles are needed to get close to random (Aldous and Diaconis 1986, Bayer and Diaconis 1992). This is intermediate between too few shuffles and the decreasing effectiveness of too many shuffles.

7 Riffle Shuffles to be close to random, 9 Riffle Shuffles to be considered statistically random! Of course they use the example of a 52 card deck; however the math for a 60 card deck is close enough to go with their conclusion.

So it would appear that Simon did indeed shuffle enough. His 19 Riffle Shuffles guarantee randomness according to those math geeks. It also took less than 3 minutes to do all of it, so according to the tournament rules he didn’t shuffle too much either. I’ve clocked Simon’s riffle shuffles as taking about 4 seconds each, so if he had in fact limited himself to 7 riffle shuffles he would have taken less than 30 seconds!

But what does it all mean? Simon Görtzen’s a super cool dude, and he shuffles like a sonuvabitch, why should I care? You want me to randomize my deck just because “The Man” is telling me to?

Let’s consider the example of a Magic deck that has 60 cards in it and each of those 60 cards is different. 59 of those cards are boring commons like [card]Goblin Piker[/card], [card]Runeclaw Bear[/card], or [card]Barony Vampire[/card], but the 60th card is a [card]Baneslayer Angel[/card].

If you put the [card]Baneslayer Angel[/card] at the very bottom of the deck, set the deck on the table and drew a card off the top, there is a 0% chance that card will be a Baneslayer Angel.

If you put the [card]Baneslayer Angel[/card] at the very bottom of the deck, Riffle Shuffle the deck to the point that it is random (7-9 times according to our friends at Mathworld), and then drew a card off the top, there is a one-in-sixty, or 1.7% chance that card will be a [card]Baneslayer Angel[/card].

By randomizing we give ourselves equal opportunity that the next card we draw is any other specific card in our deck. Obviously in normal constructed Magic you get to adjust the numbers of various cards, as a deck full of an assortment of common creatures and 1 [card]Baneslayer Angel[/card] isn’t exactly a normal way to play magic, but consider a sealed or draft deck with 1 rare bomb like a [card]Hoard-Smelter Dragon[/card] or a [card]Sunblast Angel[/card]. In order to give yourself the best possible shot at drawing that card (without cheating and putting it on top, obviously) during a game, you’re going to want to ensure your deck is randomized.

I hope that I’ve given you some more incentive to properly randomize your decks, a little information on what the rules are surrounding shuffling, and a video example of some excellent shuffling technique.