You have no cards in your hand by the second turn, your opponent is sitting pretty with powerful monsters and still has four cards in hand. You're topdecking like usual, hoping for that game changing card that never comes. And then your life points get obliterated. What happened? What separates expert players from every day duelists? Even if a normal duelist copies an expert's deck and reads an article about the combos in it and how it should be played, they tend to get roasted in a real duel. It seems as though there's some core mechanic, something invisible, going on in the game world. It's enough to make any normal person dislike the game or even get angry.
It's time to lift the veil on Duel Monsters and expose Duel Theory. You might hear experts trod on about "Card Advantage" or "Field Presence" and the like. What a card's "utility" is and telling you that your field is "over extended". In this Duel Theory series, we will be taking a look at the game from a more mathematical perspective. Rest assured, I won't be busting out the calculus and making you integrate here. This is strictly arithmetic (until we get to deck building). But what is with this strange expert lexicon? Well, one very common set of words you will hear in regard to your cards is "utility", "control", and "aggro".
Utility is when a card allows you to gain something. Maybe it's a monster, maybe it's a card in your hand, whatever it is, it's benefiting you by giving you a card. Not a spell counter, not life points, not a countdown. Cards. Having more cards gives you more options and options lead to victory. So then utility must be cards that give cards - a kind of meta-card. Take a look at Gravekeeper's Spy. Why the hell does it appear in so many non-GK decks? Well the card has a +1 utility that gives you a monster, possibly another Spy that you can Book of Moon and do it all over again. With Spy at your disposal, your opponent might run into its high DEF as a huge wall, letting you keep the Spy on the field and get another GK to boot. You can easily see that his Utility is a +1 because he generally costs nothing and gains you 1 of something. In the case where he is destroyed when flipped, he is a -1 (destroyed by battle) and +1 utility. And that makes him what's called a "floater". These are cards which replace themselves like Card Trooper (destroyed, draw 1 card). Floaters are extremely useful in decks because they allow you to maintain a steady stream of cards to replace the ones you keep losing. Like a river, it will cost your opponent more resources to constantly fight against that flow than if you had dried up sooner.
Being able to maximize the amount of utility you gain from your cards leads you to more control and more aggressive action. You should train yourself to think of cards in terms of +X and -X. Realize that when you play Pot of Greed, it gets removed from your hand, and after activation, sent from the field to the Graveyard and is no longer an option to you. For this reason Pot of Greed starts off as a -1 to your hand (and total number of options) but it does something amazing: it then generates a +2 by drawing from the deck. Thus making it an overall +1. You will notice your total hand size increase by 1 after playing this card, and you will also have gotten rid of Pot--something you can't really use against the opponent--for two new options that you possibly can. For this reason, cards like Pot of Greed usually end up Forbidden. If there were too many of these universal +1 and +2s that speed through the deck, then every deck would need them lest it be a losing deck instantly. To create diversity, Konami chooses to keep cards like this banned. Meaning you will need to come up with other solutions. Allure of Darkness and Solar Recharge are not actually Pot replacements because they count as -1s for themselves, +2s from their effects, but -1s from their costs (rfp a DARK for Allure, and discard a Lightsworn for Recharge).
Reading cards carefully can be the world of difference for what you recognize as good utility and what turns out to be a dud. Magic Jammer is a classic example of something novice duelists tend to think of as good. (Let's ignore the fact that Spell Shield Type 8 is better in every way) The argument from novices goes: I can negate your spells with this card, therefore it's good because I'll wait for a powerful spell. But failing to realize that once activated, it goes to the graveyard (-1) and has a hand cost (-1). It nets you 1 negation, but costs 2 cards to use. Magic Jammer is a terrifying -1 to your options and can cause serious problems for you later. On the other hand, Magic Drain is, at worst a 1:1 (-itself, +negate a spell) and at best a 1:2 (-itself, +opponent plays a spell and discards a spell). We use ratios like 1:1 (one for one) and 1:2 (one for two) to describe how well a card nets you utility. Things like Smashing Ground get rid of themselves to get rid of a monster with high DEF. This is usually referred to as a "One for One". Ironically, the card One for One, is a two-for-one.
Control is the act of harming your opponent's cards. No, not their life points. Not their spell counters. Their cards. Going back to Gravekeeper's, they've often been touted as masters of control decks. Using these types of cards is similar to using negative utility but on your opponent instead. Where Magic Jammer nets you a -1 from the hand, using Gravekeeper's Guard nets your opponent a -1 from the field ideally. Since his DEF is rather high, he generally stays on the field when he bounces the opponent's monster back. For this reason, he is a good +1 control card that is reliable. I bet another card sprang to mind eh? Penguin Soldier. Now at first glance, he seems like a +2 control, and ideally he can be. But more often than not, don't you see your Penguin die after the battle damage and then bounce 2? For this reason, he can only reliably be called a +1 (-1, +2). The field presence itself is very important when dealing with control. If you clear out those two monsters, but lose one of your own, how can you be said to have controlled 2 cards? Your opponent controlled 1 of yours in return!
Smashing Ground, Dimensional Prison, Sakuretsu Armor, and the like are all good examples of +0 control. But what is the use of zero? It seems like adding zero to something means nothing happened to it. And this is the folly of the educational system which does not teach the concept of zero properly. But that is for another article. When you think +0, or plus anything, think of what the components are that made that sum. Smashing Ground is a 1 for 1, we know that. Meaning its components are -1 utility for +1 control on your opponent's monster. When you realize how these cards work mathematically, you can see that these zeroes are actually simplifying the game by making you both lose an equal amount. There's less options in play and less to control now. Take this example, you tribute a monster for Mobius the Frost Monarch right? So you lose 1. Then you gain Mobius, so you gain +1. But then Mobius controls your opponent by activating double Mystical Space typhoon and you get another +2 control. For this reason, Mobius is usually considered a 1:3. Which is absolutely insane. He simplifies the field for only a cost of 1 tribute and then you get a meaty beatstick and instantly 2 MSTs! The Monarch archetype takes tremendous advantage of control in this way.
But what about Mirror Force, Heavy Storm, Dark Hole, and other field clearing cards? Well we definitely know that each one is a -1 once activated. But the destruction is variable. Your opponent might over extend his monster zone and have 4 out on the first turn (*ahemblackwings*). You can take advantage of this by playing your Dark Hole and netting yourself a +3 quickly. Now your opponent has 2 cards in hand, and if you can waste those 2, you will have him topdecking for the foreseeable future in the duel. Massive AoE control like these must be played with essential timing. It's generally looked down upon to Mirror Force a single monster, even if it has high attack. Generally, once the first attack goes through, opponents have no problem summoning additional monsters to go in for the kill. Try to use your area of affect variable control cards for massive damage and get the opponent topdecking quickly. Punish their insolent Roman tactics. Timing is even more crucial with Lightning Vortex. Obviously you never want to activate it on anything less than 2 monsters, but more is ideal. For this reason, Vortex is not Limited in any way. Proper play of Vortex can win you the duel after your other AoE control is exhausted.
Aggro is a nonsensical term used by a lot of expert duelists to refer to monster presence on the field. Even if the term isn't very accurate (it refers to an actual style of play and not a mathematical field standing), I will be using this as the term to refer to monster presence. There's a lot of ways to gain Aggro in the game but it is often the most dangerous play to make and the one I see changing the game the most. Novice gamers often wonder why their OTK failed or summoning a bunch of monsters in one turn made them lose. We just went over variable control cards like Mirror Force, so it should come to no surprise that this loss stems from an inherent flaw in the strategy of swarming while the opponent has options. When you convert your Gravekeeper's Spy utility into Aggro (say with Assailant), you are making a commitment to be on the offensive and go for game quickly. Any duelist that sees this move will not hesitate to Dark Hole, Vortex, or set Mirror Force with protection. Stopping a giant hit on their life points is going to be their main concern and it can be done for relatively low costs to them with high net rewards. Basically, you done fucked up royally.
Most duels are like wars of attrition, using their one free utility (Normal Summon) per turn and free control (attacking to destroy a monster). Without proper planning, obtaining massive Aggro on your side of the field simply sets you up for failure. You might as well have just discarded your hand and said "Go". Anti-OTK is very popular in the world of Duel Monsters. Attacking someone with a clear field and lots of cards in the hand is usually a sure bet on Gorz. Doing battle damage at any time can set you up for Tragoedia. Then he controls your monsters and gets a huge edge on you. Unless you have to work for your massive swarm OTK, then you will probably walk right into a trap. Playing Giant Trunade/Cold Wave when your opponent's back row is close to full means that they had every intention on using it to stop you. Eliminating that threat generally ensures you a nice chunk of life points. Play monsters smart, not often. Many duels I've seen turn into exchanges of little weakling monsters like Sangan just because both people are trying to play heavy control on each other. Think about how much more commonly you see something like this as opposed to someone rushing in with a 3 massive fiend monsters and taking the game by force.
As we close here, I want to mention that some of you idiots out there are getting read to email or comment to me about how all of the utility of these cards change depending on the situation. And I'm here to tell you, save your energy. You will not play every card at the perfect time always forever. Most of the time, you will play cards at a median or average moment for them. The median advantage for Vortex is +0, the median for Mirror Force is +1, and so on. The actual game is not like the show and you will not use those ridiculous situational cards the same way that plot-armored protagonists use them to Deus ex Machina a win.