Wednesday, January 18, 2012

Sufficiently Randomized

Lately I was looking at card drawing probabilities (more on that sometime later), I was stumbling across a closely related topic, that is deck randomization. Looking at it more closely, it occurred to me how different deck randomization techniques (a.k.a. shuffling) are and the theory behind is not trivial (there are quite a number of articles on the topic available on the internet about it).

This is the relevant rule from the VEKN tournament rules regarding sufficiently randomizing one's deck, commonly achieved by shuffling:
3.2. Pre-Game Procedure

The following steps must be performed in order before each game begins.
  • Players shuffle their decks.
  • Players present their decks to their predators for additional shuffling and cutting, if desired.
  • Each player draws seven cards from his or her library and four cards from his or her crypt.
All shuffling must be done so that the faces of the cards cannot be seen. Regardless of the method used to shuffle, players' decks must be sufficiently randomized. ..

But actually means "sufficiently randomized"? There is no fixed formula or procedure in the VtES/VEKN rules how shuffling is done properly, so that your deck is sufficiently randomized. Let's take a brief look at the different, commonly used shuffling techniques:
  • Corgi, Chemmy, Irish or Wash shuffle -- Involves spreading the cards out face down, and sliding them around and over each other with one's hands. Then the cards are moved into one pile so that they begin to intertwine and are then arranged back into a stack.
  • Stripping or overhand -- Small groups of cards are removed from the top of a deck and placed in the opposite hand (or just assembled on the table) in reverse order.
  • Riffle -- Half of the deck is held in each hand with the thumbs inward, then cards are released by the thumbs so that they fall to the table interleaved.
  • Weave shuffles -- Weaving is the procedure of pushing the ends of two halves of a deck against each other in such a way that they naturally intertwine.
  • Pile shuffle -- Cards are dealt out into a number of piles, then the piles are stacked on top of each other.
Several articles (from the MtG community) show that pile shuffling alone is insufficient. Actually some don't even consider pile shuffling shuffling at all, and one can really consider it as non-random reordering of the deck. But at least it helps to make sure, that no two cards stick together or some such thing.

Riffle Shuffling is the best method of making the deck random, but it has to be done often enough. Strictly speaking it's necessary to do 1.5*log2n (where n is the decksize) riffle shuffles to randomize a deck. So 8 to 9 riffle shuffles for a deck of 52 cards make it random for sure. Newer research suggests that seven riffle shuffles are needed to get it close enough to random. But the big drawback is that when you're doing a riffle shuffling you're bending the cards, which can easily damage the cards. So if you're doing this kind of shuffling try to do it more gently and try to prevent excessive bending on cards.

Weave shuffling is actually quite similar to riffle shuffling and can be done quite well when the cards are sleeved, thereby avoiding damaging the cards. Although it has to be done a couple of times more than the more rigorous riffle shuffle.

The wash shuffle is also very good way of randomizing your deck, but it usually takes too much space on the table and too much time before starting the game, so you won't see that very often in a preparation of the trading card game.

So what do I do personally to make sure my deck is randomized properly? Before a game of VtES I usually do the following:
  1. Pile Shuffle in 8-12 stacks once.
  2. Weave Shuffle at least 6-8 times.
  3. Overhand shuffle about 8-10 times.
I don't like riffle shuffles because it might damage the cards, so I prefer the somewhat less "threatening" weave shuffle. All in all, this takes about five minutes to complete.

In the end it's up to you to have a good shuffling procedure (using one or more shuffling techniques) in order to make sure your deck is sufficiently randomized. And in my opinion your opponent (usually your predator in VtES) should always cut your deck (and maybe even shuffle the deck if time permits) before the game begins.



Boris said...

Why does it take more weave than riffle? Because it is more complicated to do a perfect weave than a perfect riffle?

Fun facts: if you start with a pile shuffle in 2 piles, then a perfect riffle, congratulations: you have just reordered your deck in its original state. Same goes if you first pile shuffle a 90 card deck in 9 piles, then 10.

For these reasons I always do some overhand between other shuffles.

Juggernaut1981 said...

I've always been told that for almost all intents and purposes, a deck with duplicate copies of cards would require 13-overhands to be effectively random.

It's what I've always done as part of things like 500, Bridge or Canasta tournaments.

In my own shuffling, I do turn around and distribute it into a number of smaller piles (usually 5 or six) to force apart any clumps that may have happened in a game (e.g. stacks of equipment/allies, groups of combat cards) and then follow it with a good number of weaves and overhands (usually 1 weave, 2 overhands, sample draw cut into the deck, 1 weave, 2 overhands, etc and then hand to predator)

KevinM said...

I'd disagree with your statement about Riffle shuffling, "...bending the cards, which can easily damage the cards."

In fact, given the nature of the design of CCG cards -- not a single ply, but rather a two-ply "card" -- a Weave shuffle is FAR more potentially damaging to non-sleeved cards.

Certainly, if your cards are sleeved, a Weave shuffle is easier, quicker, and less damaging to the sleeves themselves.

extrala said...

@Kevin: Since I almost all the time use sleeves, I can't really tell the effects of weave shuffling of unsleeved cards. But I have some bad experiences where some (bad) card sleeves split after large number of weave shuffles.

@Juggernaut: I don't think that overhand shuffles are good enough for a reasonable randomization, but that may very much depend how you do the actual overhand shuffle.