This was the article that started it all. My first article covered some of the most technical and important information that I wanted to share with the card-flipping world. The statistics in this article are rather complicated, but lead to some of the most important information that a player might want while constructing his or her decklist. How many characters should you run at a certain drop? How often can you hope to draw the cards necessary for your win condition? This article will help you crack the deckbuilding code and offers a fresh perspective on Vs. System and its mathematical nature.

In Vs. System, as in life, there are winners and there are losers. If you do not want to be classified as the latter, then you may want to spend some time in the Kingpin’s School of Hard Knocks. There are a handful of top performers in this game. There are Pro Circuit champions, players with multiple $10K trophies gathering dust on the old shelves, and card flippers who make enough money playing this game that they do little else. Then there are the rest of us—the grinders, the average pro players, the scrubs, the players who make just enough money to buy the next set and take that next trip across the country for tournament play.

We make up the majority of our card-crazy culture but net the least amount of the spotlight. Every once in a while we make a big run on the cash. We blip the proverbial radar. But most of the time we make up the supporting cast, fill the chat boards with questions and critiques, and search for Vs. enlightenment.

This school is for us. It is a collection of bad beats and tournament victories, lessons learned from barely missing Day 2, the mistake caught a turn too late, and the thousand dollar payoffs for months of hard play. A degree from our school won’t make you a champion, it won’t grab you a check for forty thousand dollars, but it might give you a solid chance to pad your pockets on a good weekend.

It’s not going to be remedial. It’s not beginner’s 101, but it’s also not rocket science. The School of Hard Knocks will allow scrappy players to improve and may allow good players to become great. The focus of the school is advanced content. As with all basic “truths,” there is a level of simplicity mixed into a very complicated series of interactions. Discovering those basic fundamentals may allow you to navigate the complexity to a greater degree. In other words, the School will drop a little bit of science and philosophy into your Pro Circuit aspirations.

Your tuition will be your time spent reading and debating the principles, your homework will be the applications in your playtesting and practice, and your degree will come when you make your run at the big money. Like most educational experiences, this will take time, effort, and attendance. If you choose to skip school, sleep through class, or argue with the Kingpin, then somebody will be sitting across from you at the next big event with the academic edge, the preparation, and the play skill to drop the Kingpin’s knowledge and take all of your money.

Deckbuilding for Geniuses: Who cares about the Dummies

I want to serve as both your teacher and consultant. I would like to be the guy to teach you’re the way to “wax on” and “wax off” in the Vs. world, but I will more likely serve as an ally in your quest to avoid scrubbing out at the next PC event. Like any healthy consumer of information, you should ask yourself why I am a credible source. Why would you read my opinions and takes on strategy? I would simply like to throw you through a wall like the Juggernaut and shout, “I am the Kingpin, [edit]!” But that would satisfy few readers.

There are two social bases of power. These are the two types of authority that any teacher/speaker/author might hope to gain. First, there is referent base of power. Referent power might be obtained through the displays of educational degrees, accomplishments, and accolades. I am a member of a successful Vs. team (Team Alternate Win Condition), have made a couple grand playing on the Pro Circuit, was once ranked fourth in the world Constructed standings, and went 9-1 on Day 1 of PC: Atlanta. I am a psychologist in Florida and have played this game since its early days, but if you are smart, you could also look at the flip side. I have scrubbed out of multiple PC events, missed the money by a couple of places a couple of times, and have never won a trophy or had my picture taken while hoisting a sizeable fake check from The Chark.

That is where the second base of power comes into play. Expert power is derived from experience. It is earned through hard work and long hours. Some people speak from the podium, but guys like me have to shout from the crowd. In the end, we are laying the foundation for a championship. We are building a house. Would you rather have your house built by a guy who knows how to build houses, or by a guy who builds houses everyday?

I have had some accomplishments, but I am no Jason Hagar, Mike Jacob, Mike Dalton, or Vidi Wijaya. You will have to trust the lessons presented in the Kingpin’s school of hard knocks because they are lessons learned. I have lived through the bad beats and tough times and worked with some pretty strong players to develop kernels of wisdom. These are not tablets to be handed down from a mountain, but rather advanced play guides written on the “hard” streets of the Pro Circuit.

Advanced Probability: Big Daddy Warbucks

Some players are born with “feel” or “touch,” while other players are seemingly bound to adopting net decks. Unfortunately for the masses, there are only a couple of players that possess that deckbuilding magic. The rest of us are bound to a life of decklist study tweaking and the additions of our own secret tech. Some players don’t even make it that far. I am no Nacho Libre. I am a man of science and I don’t love orphans. Adoption is necessary but not really my thing. If you ever want to move past netdecking and a reliance on other players for your tech, then you are going to have to become a student of the game. You at least have to grasp a rudimentary level of probability; statistics; and how to pack the right mix of characters, locations, equipment, and plot twists into your deck without apocalyptic draws and mad inconsistency.

This is a game of sixty-card decks, drawing, and ratios. In its most simple form (which is where the simple guiding rules are derived), this game is about hitting a curve of semi-exponentially growing characters until one player gives up the endurance ghost. Most decks need to use all of their resource points each turn and a bag of handy tricks to add a check in the win column consistently after a game. This ultimate goal begins with solid, consistent deck construction.

Drop Counts, Character to Plot Twist Ratios, and Drawing

Your first lesson is how to choose the right number of characters, plot twists, locations, and equipment to throw into a deck. Every deck needs a purpose or goal. After you select your goal, you need to put together a puzzle that will assemble match after match to land you the big payoff. Card choice and theme perhaps fall outside the scope of this first class. However, once you identify a strong win condition—the best characters and support cards to pull off the victory—then you have to pray to the gods of probability. Fortunately, the Kingpin will play prophet and shortcut some of the groundwork needed to find favor by producing important basic calculations.

Statistics can be used to make a lot of decisions. We use them all the time. We get a feel for how many of a given card to run, but sometimes our “feel” may be off. Statistics can help hone your feel and actually help change your mind about poor decisions or be the information you need to make more effective decisions. Hopefully, this little write-up will convince you of the importance of making data-based decisions when building decks and will give you more confidence when you put together your own brand new deck.

A “hypergeometric distribution” is used to determine the probability of a certain set of occurrences when extracting elements without replacement (in Vs. System, “extracting without replacement” is drawing cards without putting them back into the deck for the next draw). A bit of research indicated that this type of statistic would be ideal for answering my questions. In Vs. System, we need a way to understand probability when cards are not replaced. To complicate matters, we need a formula that will account for all of the wild things done in Vs. System that wreck simple statistics. We draw, and mulligan, and draw again. Eventually, we manipulate the deck and throw things off of the top and search and do all kinds of confusing things. When we start to answer questions, we will assume a simple version of the game that excludes deck manipulation.

The basic question that needs to be answered after assembling the ingredients for a deck is a question of amount. What ratio of each ingredient is needed to make a product over and over and over? Consistency is essential to victory. In casual play, it may be fun to pack a deck with a delicious combo that only clicks in one out of three games, but on the Pro Circuit, that would end your Day 2 hopes with a 4-6 record.

This game is complex. Your decisions will haunt you. To free up your thinking for those decisions or to make optimal plays, you want to see about the same cards in a similar order game after game. I want to see my curve fall into place, I want access to my power cards and search cards when I need them, and eventually I want the game-ending characters and twists.

I do not want to whiff on turns 4 and 5 with dead equipment and late game characters drowning out my possibilities for victory. So, I must study and practice. The following table is one of the great keys essential for understanding character counts, packing a certain number of plot twists, and using your mulligan condition. It uses the top vertical column to identify the number of a type of card that might be in a deck and the horizontal column to represent turns in a game. The numbers inside the table represent the statistical odds that you would draw at least a single copy of a given card type during the course of the game. If you pack four copies of a card and use the mulligan condition (+), then there is a column for the probability of hitting a certain card type after ditching your initial four-card draw without that card.

+ = with the mulligan

Note: Numbers represent the percentage of time at least one copy of a card will be drawn

If you are a real overachiever or want to learn how to do this type of evaluation for yourself, I have included the formula and syntax at the end of the article.* Using the table above, we find that we have a 35% chance of drawing one card out of our play set by turn 1. If you pack five copies of a give card (Army), then you have a 43% chance of seeing one copy of that card in the first six cards that you draw. When you are looking at generating a curve using multiple character cards, you’ll notice that packing eight 2-drops will give you a 71% chance of seeing a 2-cost character by the second turn. If you mulligan for the 2-drop and have eight copies of a card, then you may expect to see a 2-cost character 85% of the time (note: mulligan conditions may be roughly estimated by looking two turns down the table).

This game has a number of cards that let you search for other cards and knock cards into the KO’d pile. These effects are difficult to simulate in a formula but should be thought of as either increasing the odds of seeing a specific card or thinning the deck count (thus increasing the chance that you draw a single card).

Often, you might want to hit a very specific card in a deck. When TAWC took our Checkmate / Villains United build to PC: San Francisco, we wanted to hit Ahmed Samsarra, White King every time. When we used hitting him or a card that would fetch him as a mulligan condition, we were statistically able to obtain Ahmed 97% of the time. We had four copies of a location that seared for a Checkmate character; four copies of Ahmed; four copies of Connie Webb, Knight; and four copies of Enemy of My Enemy. Statistically, we could, in a slanted way, consider all of those cards potential Ahmeds. After seven players fielded the deck at the PC, we calculated that out of the seventy Day 1 matches, the team only missed Ahmed three times.

In the next couple of articles, we will use this type of statistical approach to decide the optimal curves for Constructed and Sealed Pack decks. We will use a simple model to generate our Vs. guidelines for deckbuilding. In the end, this grouping of lessons will allow you to identify a simple basis for building both curve and off-curve decks in Constructed and Sealed Pack play. Your homework is to look through your current favorite decks and potential decklists and identify the cards that are key to victory. What are your odds of hitting those cards by the desired turn? Do you have overkill at a given drop that may free up card spots for other character drops or tricks?

Class dismissed.

* The formula syntax is a bit complex. For the math geeks among us, a general notation using X! / (Y! * (X-Y)!) can explain what I am about to simplify (if you just went blank, then move to the next paragraph). I prefer to think of the formula like this: X is the specific card or card type in your deck. Y is the total number of cards in the deck. Z is the number of cards you have drawn. N is the number that you are interested in discovering. N = (X, n) * (Y - X, Z - n) / (Y, Z).

For those of you now un-blanking, welcome to the more lucid section of the math instruction. Take that formula and use it in EXCEL. The syntax is HYPGEOMDIST (N, Z, X, Y).