Category: Thinking It Through


“I play collectible card games, like Magic or YuGioh or Pokemon.” This is the statement I usually have to admit when I start that awkward conversation with people not in the life. At this point, their puzzled looks typically grow in confusion… except the time I explained my hobby to my fraternity members. “Oh Magic,” they said, “I’ve played that before.” To be fair, my fraternity was Gamma Iota Sigma, the insurance and risk management frat. Had they been the Alpha Betas this would be a different story.

So how did they know about Magic? Well, under the umbrella of insurance there is a degree called actuarial science. These are the guys and gals that figure out the probability of damages happening in an insurance case, the probability of certain dollar amounts of damages, and how the company should price premiums for the insured. Needless to say, they folks are kind of smart and love their probs.

In a world of imperfect information, probability analysis is the best we have to make educated guesses. Evaluating a board state or predicting what cards your opponent might have in hand aren’t much different than figuring out the likelihood that a 16-year-old boy might crash his parents’ car. Actuaries play trading card games because the hobby rewards people with these skills. Lucky for us common folk, you don’t have to be a master of statistics to win at cards; however, it helps to know some tricks to improve your deck building and play skill.

Hypergeometric Distribution

This is, by and far, the most important function you can use as a card player when running stats on your deck. You can read about this theory in detail here. But let’s say you’re like me: it would take reading the opening paragraph of that article five times before you (maybe) gained a clue about what was going on. In that case, here are three quick and dirty points you need to know about Hypergeometric Distribution:

  • It measures successes over a finite number of draws from a finite pool of resources , where the pool of resources is not replenished after each draw.
  • The outcome of each draw can only be categorized as success or failure.
  • The probability of success is different for each draw.

Why Do We Need This?

If you want to figure out if Bottle of Wishes is the first shield in the row, you don’t need all this fancy math crap. You can just do three divided by forty—full playset of Bottles, divided by total cards in the deck (in this case the minimum) —and you would discover the odds are 7.5%. But that only measures the first shield. What if you want to know the odds of Bottle of Wishes being any of the five shields? This is where we need hypergeometric distribution.

Math is Hard

Computers do math well, so let them do the work. You could go back to the Wikipedia article and try your hand at the formulas there, or you can open a blank document in MS Excel and use the function HYPGEODIST (or HYPGEO.DIST in earlier versions of MS Excel). The function requires the following information (translated into card language):

  • Sample_s = how many successes you want (how many copies of a particular card you want to see)
  • Number_s = how many successes exist in the total population (how many copies of the card exist in your deck)
  • Population_s = how many draws from the population (how many cards you will draw from your deck to hit the particular card)
  • Number_pop = total population (total size of your deck)
  • Cumulative = TRUE (if the function ask for this you want cumulative calculations)

So if you run three copies of Bottle of Wishes in a forty-card deck, punch the following into the function:

  • Sample_s = 0
  • Number_s = 3
  • Population_s = 5
  • Number_pop = 40

Why use these numbers? Well, 3 is how many copies are in the deck and 5 is how many shield blasts you put out at the beginning of the game. You pull the shields from your starting deck without any other cards removed, so use your total deck size as the Number_pop (40 if you play the minimum). But 0? Yes, this doesn’t tell you want you want. It gives you the probability of not having this card in your shields; however, if you take this result and subtract it from one, then you will have the probability of at least one copy of Bottle of Wishes in your shields. In the above example, the odds of Bottle of Wishes as a shield is 33.76%.

Remember that Sample_s is how many copies you are solving for. If you put in 1, then the function will produce the odds of having exactly one copy of the card. This isn’t really helpful. Sure knowing the chance of one Bottle of Wishes is great, but having more than one is definitely a success as well. When you solve for 0 the function produces the chance of no copies; therefore, the other value that will make up 100% is the chance of having at least one copy ( % of zero copies + % of any amount of copies = 100%).

Note that this holds true for any shield blast you run three copies of in a forty card deck. So there is a 33.76% chance of Terror Pit, Stormspark Blast, etc. if you run full playsets in a deck where the deck total is at the bare minimum (testing per card in these examples are independent from other cards or factors). For exact results of one copy, two copies, or three copies of a blast in your shields, just change the Sample_s to the desired result.

Do You Accept the Challenge?

You can use this function for a seemingly infinite number of card game applications. For example, on your turn one going second, the odds of a shield-blasted Bottle of Wishes hitting the second Bottle of Wishes which will hit the third Bottle of Wishes in a forty-card deck is 0.013369%. Did you know how I got that answer?[1] Try some of the following problems and post your results in the comments below.

  • What are the odds of having at least two shield blasts in a forty-card deck when you run 18 spells with Shield Blast?
  • If you go second, what are the chances of hitting Andromeda on a turn five hard-casted Bottle of Wishes?
  • In a deck that runs 12 Light Cards, what are the odds that you will draw Keeper of Laws by turn four and have Light unlocked to play it?

As people comment, I will confirm if anyone posts the correct answers and jump in to help where I can.

[1] This requires the rule of the Probability of A and B, assuming A and B are independent events. For quick reference, when you want to know the chance of two independent events happening together (example: rolling a result of 3 on a die and flipping tails on a coin), you take the product of probability of each individual event; therefore, in the example the answer would equal the probability of rolling 3 multiplied by the probability of flipping tails.


Tournament Etiquette: Sloppy Resources

Thinking it Through

Thinking it Through

Random Guy: “Hey man, can you spread out your resources please?”

Every so often I need to ask this question, usually after my opponent taps all his resources to cast a couple things or one big thing. Most of the time, my opponent has no problem and fans out his resources.

Some Dude: “Why?”

When I need to explain, my polite reply is, “I just want to know what you’ve resourced this game so far.” If some dude needs more explanation, I tell him it’s because it helps me calculate what’s left in his deck and what he might have in hand – let’s not forget that resources are public information to begin with. I shouldn’t have to state that, and if I do, I start to feel paranoid: he shouldn’t have a problem with this request because it’s illegal to hide public information.

If your opponent constantly keeps his resources in sloppy piles, stacked up in one or a couple piles, or has to be constantly reminded to fan them out, then something fishy may be going on. There are a lot of tricks a shady player can do with these types of game states that you need to protect yourself from.

Do You Know How Counting Works?

One trick is the cheater sneaking a giant creature into play a turn early. Let’s say the cheater plays Andromeda when he only has eight resources, which the cheater might try when he has been stacking his resources the whole time and is on the draw. On the draw is key here because you could forget that fact and think he was on the play —going to 9 resources yourself will help with the psychology of accepting the false game state.

Another trick is the cheater resources quickly, and then takes forever to enter his main phase plays. If he’s trying to pull a fast one here, I guarantee one of two things might happen:

  1. He will try and play a second resource
  2. He will under drop over his resources

You can protect yourself from the first scenario by paying attention to what the cheater resourced, and calling out when he tries to resource again. He won’t disagree with you. Unless he’s a highly, highly skilled—and possibly desperate—cheater, he will probably apologize and take back the second resource play. When he finishes his plays for the turn, ask him to spread out his resources. If he played more than possible, then he must rewind the last play to repair the game state.

How to Prove You’re Honest

Except for Kivu, no cards interact with your resources. Until someone plays that card and activates his effect, this is how I suggest tournament players present their resources:

  • Upside Down
  • Turn Order
  • Never Tapped or Piled

Upside Down

This is literally the most convenient way you can present your resource row to your opponent. He can just look if he has a question about what a card is or does.

An upside down resource row also keeps it in the opposite direction as your hand. This will help you repair the game state if you accidentally drop a card , as well as show your opponent that you have no intention of Hans’ing[1] him.

Turn Order

This ensures the integrity of the game. If for some reason players disagree and need to rebuild the game state, this provides an effortless way to track the turns.

Never Tapped or Piled

Well, never say never. Tapped, in most situations, is fine if your opponent can see all of your resources still. I gravitate away from tapping because it can easily break up the Turn Order principle, which does add a lot of value to tracking. Piled, however, is always questionable.

Like most players, I need to count out my resources when I underdrop in a turn. I recommend separating your resources in sections. Let’s say you’re thinking about playing Terror Pit and a Nix with your ten resources. I find the best approach is just separating the first three resources in your line, to create a short line of three and a long line of seven. This keeps the first two principles in order, but still allows you to visually count out what you have available.

Don’t Cheat

Duh. But in all seriousness, take it as another disclaimer. My pointers on how to play in high-level events are to protect you from the crappy 1% that will take advantage of you. As always, the shady player sitting across from you could be telling the truth about their nervousness or inexperience playing in high-level tournaments. Just keep in mind that might be an act to hide malicious intentions.

[1] Hans Joachim Hoeh is a seasoned TCG player who has notable success in VS System, Spoils, and the WOW TCG; however, he is infamous for the cheat he performed in the top 8 of a VS System ProTour, now known as Hans’ing. The cheat involved switching a card in his hand with a facedown resource. Luckily the cheat was caught during the match, leading to a disqualification and a ban from the game.

Thinking it Through

Thinking it Through

Etiquette begins the minute you sit down and set up at the table. There are the small things such as introducing yourself to your opponent and asking how their experience has been, and there are more important things to be mindful of, such as keeping drinks off the table and making sure your playmat doesn’t creep into another player’s space. These conventions are out of politeness. The practice of sharing is a necessity for an honest game.

The Die Roll

When deciding who will go first, always share the die or dice. If a player doesn’t do this, it’s grounds to call a judge. I’m sorry if it’s your lucky die and if anyone else touches your die then it will lose its magic—I need to touch it. Cheaters will use weighted dice to make sure they always have the option. If you happen to have a lucky die that is honest but you don’t want to share, then leave it at home. It unfortunately won’t fly in a tournament setting.

This is pretty common knowledge. I would also wager that it’s common knowledge that players use a highest result when determining the winner of the die roll Many players announce this before rolling. Props to them for great communication, and I recommend that everyone does the same; however, in the event that someone doesn’t declare, the default is clearly a high roll. Don’t be the guy that tries to snake your opponent for not saying high or low and you rolled the worse result. If your opponent is a seasoned tournament player, he will just call a judge and both of you might end up with a communication violation or an unclear game state warning, or as I like to call it: “Failure to agree on reality.”

Don’t be that guy. Assume your opponent meant high roll.

“But this is the Only Way I Know How to Shuffle”

Don’t be this guy either. When each player presents their deck to their opponent, he or she has the right to shuffle instead of just cut. Always shuffle. It’s just good common practice to ensure an honest game; however, if you do shuffle your opponent’s deck there are some key ways of doing it to make sure you don’t come off as a cheater.

  1.  Keep the deck off to the side. Shuffling off to your side ensures that neither your opponent nor you can see where cards are being shuffled into the deck. If one of you could, that would destroy the integrity of shuffling in the first place.
  2.  Keep the deck above the table. Obviously shuffling under the table is a huge “no-no,” but even shuffling a deck not above the table is questionable. It could lead your opponent to think you might drop-kick** him. Worse, you could be an honest player and accidentally drop a card on the ground. If neither of you notice but a judge does, you receive a game loss immediately.
  3. Keep your eyes on your opponent. This serves two purposes. It shows your opponent that you are honest and aren’t trying to peek at their deck. It can also protect you by making sure your opponent isn’t sneaking peaks at your deck.

Time and time again I’ve heard people try and tell me that they can’t shuffle without looking at the deck. This might be true, but this is a competitive tournament. First place is free airfare, and last time I won WotC paid for a ticket costing $850. We’re playing for serious, so please respect the context in which we’re playing. I’ll trust you on your kitchen table or the local card shop to not cheat me, but at a KMC, I have to be skeptical to protect my interests.

If you honestly can’t shuffle without looking at the deck, then start practicing at home before playing in a high-level competitive event. It’s a skill that you just need to acquire if you want to perform on that stage.

I Choose You, Randomly Selected Card

With the advent of cards like Spire Puppet, players can start discarding cards from their opponent at random. For many games, there is a generally accepted way of handling this action across all high-level tournament play:

  • The opponent shuffles his hand then lays out the cards, face down, in a row on the table.
  • The player who played Spire Puppet assigns numerical values to the face down numbers.
    • Example: If the opponent has three cards in hand and you have a six-sided die, then two numbers can be assigned to each card.
    • Example: If the opponent has five cards in hand and you have a six-sided die, then they’re numbered 1 through 5 and the player rerolls on a six.
  • The opponent rolls a die to determine the result.

Why does this matter? The opponent shuffling his hand ensures that no one knows the order of the cards in his hand. This information could be somewhat public before playing Spire Puppet if the turn before you casted Mesmerize. Rolling a die—the same common die used to start the match—prevents you from feeling for a specific type of card. Foil cards are noticeably different. Even if you can’t feel for foils, just watching your opponent’s reaction as you hover your hand over each card can provide information. Either way, the randomness is decreased and invites other factors into the action that shouldn’t exist. The above practices are the fairest and safest way to produce a random discard for all parties involved. If someone has a problem with it, a judge will be called. It’s not that I don’t trust you; I just can’t afford to trust you. As Khaled Saad says, “If you give your trust to a person who does not deserve it, you actually give him the power to destroy you.”


**Drop Kicking is when a player sabotages his opponent by tricking the judge into thinking he never presented a legal deck. It starts with the player shuffling his opponent’s deck over his lap instead of the table. When his opponent isn’t paying attention, he purposely drops a card by his foot then kicks it over to his opponent. After this move is executed, he will pile shuffle his opponent’s deck and count how many cards it has (it will now count 39 instead of 40). The cheater then calls a judge. Eventually, the table will discover the missing card on the other player’s side, resulting in a game loss for that player for not presenting a legal deck.***


In no way am I promoting the use of the drop kicking technique. It’s cheating. Period. In no way do I condone drop kicking, or any other method of cheating. The explanation is meant to serve to purposes.

  1. To define the term so the audience would not feel lost
  2. To protect honest players from cheaters

Intentional Draws: The Lesser of Two Evils

Thinking it Through

Thinking it Through

Fact: Intentional draws are lame. The 1% takes full advantage of their power position and coasts into the Top 8. Instead of the top players actually knocking each other off, they agree to help each other secure playoff positions by avoiding any losers. Without anyone winning a game, they all remain “winners.”

Let’s say you’re Eric Spoelstra (head coach of the Miami Heat). Your team is up 20 points with two minutes left to play. Not only is your team locked for the playoffs, but they can’t lose the first seated position. Assuming he isn’t on the verge of breaking any records, would you play or bench Lebron? How would you feel if the NBA had a rule that forced your top paid/performing athlete to play so many minutes? What if in those forced minutes King James incurred an injury?


Fact: Not allowing draws creates Machiavellian paths to victory.

In the WOW TCG the policy was after each player exhausted their extra turns in time (or  completed their remaining turns after time was called) a winner would be declared as the person who had taken the least amount of damage.  This wreaked havoc on the game. Clearly going last in extra turns was imperative, and tournament players did unscrupulous – but legal – things to ensure they had the last turn. One such tactic was abusing the one-minute time limit on shuffling.

When I played in the 2008 WOW Nationals, it was game three and my opponent ended his turn. I saw there was a minute left on the clock and said, “End of Turn, activate Preparing for War for three.” I went through the motions of shuffling three cards from my yard into my deck, exhausting the full minute I’m allowed. The clock beeps and time is called. I presented my deck to him for a shuffle and cut, which he did, then finally declared that I was done activating effects at the end of his turn. Since it was still his turn, it counted as one of his two extra turns in time. I would have lost the game and the match if he’d had one more turn.

No, my actions were not the “nicest”, but we’re not playing on my kitchen table with chips and soda. It was Nationals, and each round had the potential to cost or earn you thousands of dollars. There are always some people at these events that will always do what it takes. By no means do I mean to encourage a player who wants to keep casual at a tournament to change his play style, temperament, or even ethics; however, that player is naïve if he thinks that people at a high-level event aren’t going to use every legal means necessary to win. Some people travel well over four hours for a KMC, and it’s not with the intention of just hanging out.

Fact: Intentional draws are a necessary evil.

Could you imagine a world where quarterbacks couldn’t take a knee to run the clock out? Outside of the shot clock and back court count, how would you change the policy in basketball to force a maximum amount of time a single player could dribble? Is it even possible?

Yu-Gi-Oh! allows for draws, but its tournament policy forbids intentional draws. The problem: the resources necessary to police this don’t justify the policy. As a scorekeeper for large events (Regionals and YCSs), I see this happen all the time. Judges watch players to prevent intentional drawing. Each player can legally choose not to play a removal spell, or forget to attack, or take the allotted time to shuffle – so how do judges identify a legit attempt to orchestrate an intentional draw. Worst of all, while these judges police this policy, they are not handling real problems: rule questions, collecting slips, and watching for bribery.

Fact: Incentives can minimize the lameness

In recent years, WotC has introduced a policy that really improves the lame factor of intentional draws. In Kaijudo specifically, they made it so a draw doesn’t improve a player’s rating, so that player has to play to win if he wants to improve his rating. The best incentive applies to Kaijudo and MtG: standings determining the die roll in the playoffs. Instead of rolling a die to see who goes first, the higher seeded player gets to choose who goes first in Kaijudo and MtG playoffs. There is a significant incentive to play it out), because going first in the playoffs can be such a huge advantage.

Taking the risk to play versus draw depends on your deck and the decks that you might play against in the top 8. This will require studying people’s tie breakers and scoping out what they’re playing on a case-by-case basis. But if you’re curious how the math works out on when the undefeated can draw in, use the following model:

q/2R ≤ 8 – t

q = Players who are X-1

t = Players who are X-0

R = rounds left in the event

At the end of the day intentional draws will always be lame. But I would rather have the ability to draw than pay a higher entry fee or have prizes cut because of increased expenses to have staff watch players to prevent intentional draws. Or deal with the situations that arise when a winner must be declared in time after extra turns. If you still disagree with draws, let me share one final reason for intentional draws: since anything can happen in the playoffs, I take solace in the fact that the top 8 players who go X-0-2 and X-1 almost always achieved the same win streak to get there.

Introduction to Column and Author Brian Durkin

“I’d say my coaching style is centered around fundamentals, with an emphasis on fun. And a second emphasis on … mental.” – Chris Pratt as Andy Dwyer (Parks & Recreation, Season 3 Episode 1: “Rainy Day”)

The shutdown is over. My column Thinking it Through will return here at Kaijudo 24/7. You can expect new content at least biweekly. But what should you expect?

Round One Feature Match at WOW TCG Nationals 2008

Round One Feature Match at WOW TCG Nationals 2008

As the above quote from Andy suggests, this column will focus on fundamentals. My previous writings under this title have included appropriating classic Magic: the Gathering articles and strategy for the Kaijudo community. You can certainly expect more of that. A quarterback can memorize every play in his coach’s book, but he’s no good if he can’t throw a perfect spiral. Piloting a deck starts with knowing how to play the game well first. But who am I to talk about this stuff? What authority do I have in this area?


For those that might not know me in the community already, I won the Madisonville, KY KMC. It was the first weekend of KMCs in the first season that WotC offered this new, higher level of organized play.  I had a great day that day in Kentucky, but to be fair most of my matches were won based on my expertise on playing card games. I started playing MtG in 4th grade. Since then, I’ve owned and played over 25 collectible card games, several of which included pro-level success. My notable accomplishments outside of Kaijudo include:

Day Two - 15th and Final Round of Swiss: Second Draft Pod. Brian Durkin faces off against Joe Gayda for Top 8 of Nationals 2008

Day Two – 15th and Final Round of Swiss: Second Draft Pod. Brian Durkin faces off against Joe Gayda for Top 8 of Nationals 2008

Alex Shvartsman, event TO, shaking hands with Brian Durkin after his Philly DMF win (2007)

Alex Shvartsman, event TO, shaking hands with Brian Durkin after his Philly DMF win (2007)

  • Call of Cthulhu
    • Competed in the first World Championship
    • Former #1 Ranked Player in the World
  • VS System
    • Top 8-ed and won several PCQs
    • Played in 2 Proc Circuit Invitationals (PC: Indy 2006 & PC: Los Angeles)
    • Won DMF Dream Machine Championship Philadelphia 2007
    • Placed 9th at nationals 2008

After the WOW TCG, I took several years off from cards to focus on other things in my life, and came back to the scene with Kaijudo. Like always remembering how to ride a bike, I owe a large part of my success in Kaijudo to the fact that I haven’t forgotten core, macro-level strategies.

What is Macro-Level Strategy?

These are the tools that transcend a specific match-up or deck list and improve the player’s overall skill level. Ever notice how someone at your local card shop seems to pilot any type of deck and perform well? That’s because that guy can throw a perfect spiral. He might not know all the plays in the playbook (specific interactions within the deck itself), but he’s going to know the following:

  • When to attack shields versus attacking creatures, or whether he should attack at all
  • Why it’s more advantageous to play it out versus accepting an intentional draw
  • What to play as a resource, or whether he should play a resource
  • How to be a good teammate and a respectful opponent
  • Who commands the rapport at the table

The above list is just a quick list of some of the topics a player with good macro-level skills will possess. The name Macro-Level Strategy comes from Macroeconomics: the part of economics concerned with large-scale or general economic factors. Instead of concerning ourselves with a particular deck list (or smaller markets/businesses in microeconomics), we want to hone in on the factors that will affect the system at large.

Darkmoon Faire Philadelphia Finals: Brian Durkin vs. Erik Topham

Darkmoon Faire Philadelphia Finals: Brian Durkin vs. Erik Topham

Why Does this Matter?

Deck X might have a 90% win rate against Deck Y, but when Player A pilots Deck X that could drop to 50% because Player A is making wrong resource choices or attack decisions. Or maybe Player A usually pilots Deck X correctly; however, when battling Player B, his win percentage drops because he doesn’t notice Player B scoping out his deck while he shuffles, because Player B’s teammates scouted out Player A’s deck in the last round, or because Player B creates a rapport that he uses against Player A.

The situations where Player B gains an edge over Player A – legal or illegal – all have to do with concepts outside of actual deck choices and card inclusions. I want to show the tricks of unscrupulous players in hopes that it will protect you from them. I want to teach you how to communicate with your opponent, using proper etiquette, but still develop your advantage. I hope that I can help you improve how to mentally approach a game while still having fun learning about it.