Author’s Note: The math used in this article was independently verified by my friend Julian, who is currently chasing the solutions for the Millennium Problems for fun.
“Man, all these players do is netdeck, it’s so troll.”
“No, you can’t see my list. It’s mine.”
“There’s only really one deck to play with this set. It’s A B C, GG.”
If you have played card games, including Weiss Schwarz, you may have at one point heard players saying things like this. You may have also noticed that there are is also a social stigma associated with “being unoriginal”, and “netdecking”, or using someone’s deck list.
Let’s begin with a bold statement:
There is nothing wrong with “netdecking”.
Let’s look at one aspect of deck building: the numbers themselves.
The largest single set of Weiss Schwarz to date (Kantai Collection) contains 164 cards.
17 of these 164 cards are CXs.
To give a quick example, if one was to try to make every possible deck with no repeating cards, there are:
(147 choose 42) * (17 choose 8)
2.7636 x 10^41 or
276 duodecillion 360 undecillion 422 decillion 714 nonillion 229 octillion 393 septillion 909 sextillion 640 quintillion 293 quadrillion 583 billion 479 million 5 thousand 200 possible combinations of cards to make a deck, following 8 CX per deck rules, not counting allowing up to 4-of a card.
That’s about 92 nonillion times the number of stars that exist in the Milky Way, which contains 300 billion stars.
Okay, so we have an enormous number. What does it mean?
It means that if you take away qualities from cards, and labeled them only A, B, C, D, etc, we would be playing a game that could be played effectively forever without being solved. Fortunately, we have the help of color, effects, levels, and so on to guide us in the deck building process.
But, this does not mean that the actual process is any easier. Though we might be able to pare down the number in our minds because of truly impossible-to-use builds of decks (e.g. 42 level 3 characters + 8 CXs), eliminating the “absurd” decks from the pool is like trying to drain the Pacific Ocean with an eyedropper. Deck building is not about finding and eliminating the impossible; it’s about discovering the viable.
But then what’s the difference between a deck list that gets posted on Bushiroad’s website and one that I make myself?
It comes down to results. Decks that are freshly crafted versus those that have placed and been posted are separated by their results.
A deck list is only a list in testing until it has been shown to work. And, we know that testing is very important.
In WS, the game as a whole does not move as quickly and visibly as other card games such as Magic: the Gathering. Because there is only one real tournament format (Neo-Standard), the tournament scene moves much more slowly. On top of that, there is only one truly “large” tournament that Bushiroad hosts in its WGP or World Grand Prix; a very small qualified event.
Sometimes a really random or troll deck will just win. What does that say about the legitimacy of deck lists?
Of course, the possibility always exists. And that can be for a number of reasons; a player may have been extraordinarily lucky that day, for example. However, that does not necessarily mean that luck is the be-all-end-all dictator of how a tournament would go. In fact, saying that the game is entirely luck-based is not very mindful of the aspects of the game which do test a player’s skill and game knowledge.
Something that does tend to call into question the majority of all deck lists in WS however, is the size of tournaments that they are involved in. WS tournaments in the Bay Area for example, can have 20+ players, but other areas may struggle to find even 6 players. Compare this with Magic: the Gathering, where large tournaments regularly have hundreds or even thousands of players. WS events with more than 5 Swiss rounds are scarce, but a list that wins a 5-round (with top X) tournament is going to pull more weight than one that wins a 3-round single elimination event. A list that wins multiple 5+ round with top X events is even better. To that end, it’s in a player’s interest to accept every deck list he or she comes across with a grain of salt.
So if luck does play some role in an event, does that mean that a deck list isn’t necessarily the best as it is?
Usually. As stated before, sometimes outliers can win events and put up good results. If the completely “troll” strategy turns out to be viable, it gains the label of “rogue” strategy, which acknowledges its relevance and potential, while still giving it the label of not necessarily being a popular or recommended strategy. However, once a set has been tested extensively, such as Madoka, a “best list” or “best lists” will eventually surface as the best that the set has to offer.
Sometimes, the recipe is meant as a novelty, more than a serious reference.
WS, like any other game with imperfect information, involves at its core a game of risk management, because players have to deal with many unknowns. WS contains the twist of additional unknown information because there are always the top cards of respective decks and those cards’ probabilities of being certain cards. Knowing how to identify and when to bank on certain percentages is one of the “skill gaps” that determines if a player is new, versus if a player is highly experienced.
There are two aspects to using a deck that should be considered when building it, and when testing it: strategy and mechanics.
Being familiar with a set is crucial to building a good deck. In WS, a deck’s overall goal will for the most part, be exactly the same as the next one; get the opponent to level 4. Because other strategies involving forcing a loss condition are much more difficult (and thus much less viable), we don’t see strategies that might involve trying to fulfill one of these alternate loss conditions (e.g. trying to put every card in the opponent’s deck into the resolution zone). With that in mind, the strategic aspect of deck building is allowed more creativity in the effects that it uses to get the opponent to level 4. Contrast this with Magic: the Gathering, where “mill” (or TurboFog), that attempts to make the opponent draw from an empty library instead of reducing the opponent’s life total to 0, has at numerous times been considered a viable strategy even in competitive play. Now, knowing every single card’s effect can be good for constructing a deck, but it doesn’t necessarily translate to using it well.
This is the execution portion of making a deck. When we play a game of WS, even if it is a complete 28 consecutive damage blowout, we gain practice and/or bits of knowledge from simply playing.
It almost seems like a non-point, but our mechanics are indeed tested and improved with every game that we play. You might even notice that there are certain things that are involved with playing the game that get incidentally improved, such as card shuffling.
There are so many decision trees that can be made during a game, but fortunately, the way the game has been designed lets us make some decisions intuitively, such as attacking a character with 3000 power with something that has more than 3000 power. The strategic aspect of this helps us exercise when to attack like this, but the mechanical aspect gives us the why.
Isn’t it the other way around?
Not necessarily. When you attack something, you make the decision based off the advantage that you know would be gained, based on the way the game works. That is, you attack, you make the opponent lose a character and ideally take damage. The strategic portion would be to explore all the possibilities of that attack, including looking at your character’s power against the opponent’s character, if there could be a Backup effect that would make you lose the battle, if there is the chance of a CX being on the top of your or your opponent’s deck, the likelihood that your opponent is using a popular effect from the set he or she is using, and so on.
To go back to the earlier point, playing with a deck that has already been made allows us to focus on practicing playing a deck well, rather than wondering why certain card choices have been made. Often, newer players may find themselves asking “Well, why this card, and why this card?” much to a more experienced player’s chagrin. But, by using a deck, any deck, to just play the game, a player becomes more refined and can then take on the higher strategies that are in the game without being burdened by lack of practice.
So we know how testing is important, and about how many decks there might be with one set, but what about the whole game? How about the number of possibilities of games?
Every game is a statistical impossibility. That is, if you play a game of WS, it is highly unlikely that you will ever see the same game again.
How unlikely is it?
Author’s Note: Credits again to my friend Julian for helping with the math, and providing some very interesting commentary to put things into perspective.
Let’s say we want to try playing WS in Standard format. Counting SPs, RRRs, etc, there are 8659 non-CX cards and 1182 CX cards that are available for a given player to use. Of the 8659 non-CX cards, you can choose 42 (repeating for SPs etc is okay in this case, since it will generally not go over the legality threshold, and even if it does, the number of possibilities will still be so high it will not make a significant difference), and of the 1182 CXs, you can choose 8.
This means that there are:
(8659 choose 42)*(1182 choose 8) =
(1182! * 8659!)/((8! * 1174!)(42! * 8617!))
1.41 × 10^134
(That’s 1.41 x 10^34 googol)
Possible decks allowed with no repeat cards, and each deck containing exactly 8 CX cards. (With repeat cards, the math becomes a lot more difficult, and for the sake of this exercise, we’re going to use the number that is more readily accessible.)
Therefore, there are 1.98 x 10^268 possible games.
After 10^40 years, all galaxies will have either decayed into diffuse matter, or gravitationally attracted into black holes. After googol years, all the black holes will have decayed due to Hawking Radiation. After this time, the universe will be in The Dark Era, where all the matter that remains is lone particles wandering aimlessly as entropy decreases.
Imagine if all 7.2 billion people on Earth suddenly stopped what they were doing and started playing WS, 3.1 billion games at a time. Let’s have them play one quintillion games a second, for good measure.
3.15569 * 10^107 seconds until universe is plunged to blackness * 3100000000 games * 1000000000000000000 games per second
9.782639 * 10^134 games before the universe becomes a void.
You would have to play 9.9 × 10^267 games on average to get a duplicate game.
9.782639 * 10^134 / 9.9 × 10^267 = 9.881454e-134 probability that will happen.
The probability that you will get struck by lightning in any given year is 1/700000.
The probability that you will get struck by lightning in any given second is 2.208983 * 10^-14
So if every person in the world started playing Weiss Schwarz right now with decks where duplicates aren’t allowed, played one quintillion games a second, and played until every black hole in the universe decayed and the universe was plunged into blackness…
The probability that any one of those games would be the same as any other one is less than the probability that all 9 members of the United States Supreme Court are struck by 9 individual bolts of lightning … in the exact same second.
There’s nothing wrong with using someone else’s deck list. Play, and play some more, and have fun with the game!
As always, thank you for reading. If you have any questions or suggestions, please send us a message via Facebook or an email at theninthcx AT gmail DOT com!