When I started playing RCQs last year, I struggled a lot with false tempo decks like Jeskai Creativity in Pioneer. They always seemed to have the combo when I didn't have an answer but if I played around it I just lost to their fair plan. But when I played the decks, my opponents were always able to answer my combo and then beat my fair plan.

(In case you’re unfamiliar with the term „false tempo“, here’s a great article by Gerry Thompson explaining the concept: https://articles.starcitygames.com/articles/the-false-tempo-archetype/)

This year, some of my best tournament results came from playing false tempo decks, especially Dimir Reanimator in Legacy. In this article I want to talk about a view of the game I developed that helped me not only understand false tempo decks, but Magic as a whole a lot better.

Chapter 1: Definition/Explanation

In this chapter, I will try to explain what a constrained optimization problem is and how it applies to a game of Magic: The Gathering.

1.1 What is a constrained optimization problem?

In mathematics, an optimization problem describes the problem/process of finding the best solution (either a maximum or a minimum value) for a specific quantity (the objective function) under certain conditions or limitations (the constraints).

1.2 Magic as an optimization problem

In a game of magic, whenever we have a decision, we want to make the optimal choice. If you were to goldfish your deck, the optimal choice is pretty obvious most of the time. It’s the one that gives you the highest chance of winning as fast and consistent as possible. However, in a real game of magic there are a lot of conditions to your choices.

1.3 Unconstrained optimization

Goldfishing your deck is essentially an unconstrained optimization problem. There is something to optimize (killing your opponent as fast and consistently as possible ), and nothing constraining your options.

1.4 Constrained Optimization

Some people add rules to their goldfishing so they can somewhat replicate a real game. For example, when goldfishing ruby storm, you might add the rule that you have to win by turn 4, because most decks in modern can kill you by then. Or you might add the rule that your opponent destroys your first cost reducer, emulating an interactive match. Those are the simplest versions of constraints. You still try to optimize the same problem (killing your opponent fast and consistent), but under certain conditions . Maybe you have to try to combo off even though it’s very uncertain it will work because your constraint is that you will die next turn, maybe you have to keep a weaker hand because it has multiple cost reducers.

As you can see, these conditions change what the optimal line of play is.

1.5 Hidden Information and Constraints

Now with only a few conditions, it’s still pretty easy to deduce what the correct choice for most decisions is. But imagine a game where you have to goldfish a deck, but under an unknown constraint chosen by a second person. It would be impossible to consistently make optimal choices.

The same is true for a real game of magic. If you don’t understand what constraints your opponent is putting on you, you will likely make a lot of suboptimal decisions.

Imagine the same game, but now the second person is putting 6 constraints on you, but only 3 of them are actually real. In a real game, your opponent will often represent multiple constraints, but not all of them will be real. E.g. when you‘re playing against UB Reanimator in Legacy, your opponent will represent the constraint "you need to be able to answer Entomb + Reanimate " but also "you have to be able to answer Tamiyo, Inquisitive Student // Tamiyo, Seasoned Scholar + Brainstorm " and "you need to be able to answer interaction + Orcish Bowmasters /Murktide Regent " etc. However, not all of these constraints will actually apply in any given game. Since constraining yourself unnecessarily leads to suboptimal decisions, it is important to get as much information from your opponent to deduce which constraints are actually real.

1.6 Lifting/Ignoring Constraints

If you look at the goldfish example again, but this time you are goldfishing Storm under the constraint "your opponent has 3 boardwipes". Since you barely have any creatures and most boardwipes cost 4+ mana, you can essentially ignore this constraint. However, if the constraint was "Your opponent starts with Leyline of Sanctity in play, you can't ignore the constraint because your primary wincondition is Grapeshot . However, this obviously doesn't mean you can't win the game anymore. You can lift this constraint by using Wish to either get enchantment removal from your sideboard or trying to win with Empty the Warrens . Some decks, like classical UW Control are very good at lifting constraints, usually at the loss of being able to present strong constraints of their own. Decks that can present strong constraints of their own, like most combo decks, can usually ignore a lot of constraints, but struggle more with those they can't ignore.

Chapter 2: Characteristics of Constraints

In this chapter, i will attempt to give a better definition of constraints to help you understand them better.

2.1 Strength

The strength of a constraint describes how powerful its impact will be if you ignore it.

Example: Entomb + Reanimate in Legacy UB Reanimator creates a strong constraint, while Delver of Secrets // Insectile Aberration and Dragon's Rage Channeler only create a weaker constraint

2.2 Robustness

The robustness of a constraint describes how easy it is for you to disable/disrupt the constraint. Since this changes a lot based on matchup (e.g. Spell combo doesnt necessarily care about the constraint the removal suite of a control deck generates) the robustness is generally talked about in the context of a given meta, similar to the strength of course.

Example: Pioneer Rakdos Midrange genenerates more robust constraints than UR Phoenix, since its more difficult to hate out.

2.3 Consistency

The consistency of a constraint describes how often the constraint will actually be "real", i.e. how often you would get punished if you didn't respect it.

Example: Standard MonoRed aggro creates a lot of consistent constraints ("You need to be able to answer a 1 drop, 2 drop, 3 drop, etc.)

2.4 Amount

Imagine the game from 1.5 again, but while this time you know the constraints the second person is putting on you, they can pick 20 different constraints. While you have a better chance of making correct decisions this time, it will be a lot more difficult than if you had only 2 or 3 constraints.

Again the same is true for a real game of magic. The more constraints your opponent can put on you, the more difficult it will be for you to make optimal decisions. This means you should aim to put as many constraints as possible on your opponent.

Chapter 3: What can we gain from this?

Now that you (hopefully) know what constrained optimization is, how it applies to mtg and what type of constraints there are, i will try to explain how we can use this type of view on the game.

3.1 Matchup information

If you want to better understand how a certain matchup will play out, look at all constraints both decks present. First, eliminate all constraints that the other deck can easily lift/ignore. Then, look if there are any constraints that are particularly strong. If there are, look at how consistent they are and if there are ways the other deck can lift them. Generally speaking, a matchup will revolve around the strongest constraints in it.

Example: If you look at UR Vivi vs Dimir midrange in standard, Dimir's strongest constraint is "don't get snowballed by Kaito/Curiosity". However, this constraint can be lifted relatively consistently by Vivi, since the deck plays a lot of good cheap creatures and removal, which makes it difficult for the Dimir deck to snowball. The Vivi deck has 3 strong constraints. "Have an answer to Vivi Ornitier + Agatha's Soul Cauldron ", "Be able to handle Proft's Eidetic Memory + creatures" and "Be able to go over/under the lategame provided by Quantum Riddler and Winternight Stories ". Dimir runs a lot of removal and cards like Azure Beastbinder which allow it to answer the first 2 constraints very well, but it can't go over the Vivi players lategame. This means it would have to go under by snowballing with Kaito/Curiosity, which as we discussed it can't do consistently enough. We can conclude that the matchup is favored for Vivi and revolves around the dimir player trying to snowball and the Vivi player trying to prevent him from doing so.

3.2 Deckbuilding

If you want to tune/build a deck for a certain meta, you first have to understand what type of constraints are popular in the meta/which ones work well against the meta. This works similar to 3.1, but going over each deck. If you can identify which strong constraints are presented in the meta and which constraints the meta decks are weak to, you can then begin looking for decks that can either ignore/lift the presented constraints or present the strong constraints against the meta itself (or ideally both). Generally speaking a deck will only either be very good at lifting constraints or will be able to present a powerful constraint itself. If you can find a deck that‘s very good at doing both (or the constraints it creates are extremely powerfull) its usually the best deck in the meta.

Example: Current standard is very dominated by UR Vivi, so for a deck to be good in the current meta it has to be able to answer Vivis constraints/present stronger constraints of its own. Since its very difficult to answer all of Vivis constraints (if you can deal with both the combo and profts plan, you still have to be able to beat the value provided by Quantum Riddler and Winternight Stories ) we should look at creating a stronger constraint. This has already happened in the meta with UG Aggro and UG Omniscience , two decks that aren't really good at lifting constraints but instead present their opponent with a/multiple very strong constraints. However, these decks struggle to gain metashare since while they are able to beat Vivi, they lose to decks that are good at lifting constraints like Dimir Midrange.

3.3 Decisionmaking

This is probably the most important but also most difficult part, since here we actually have the decisions we want to optimize, but as discussed in 1.5, we often don't know exactly under which constraints to optimize. Essentially there are two parts to each decision making process. We first have to figure out to the best of our abilities what constraints our opponent is actually putting on us, and then make the optimal choice given those constraints. To make the optimal choice you will also have to figure out which constraints your opponent can likely lift and which he can't. Going into detail about how to do all this is far beyond the scope of the article (and there is already a lot of good content about reads/bluffs and decisionmaking out there), but as a general idea try to think about how the game plays in theory (3.1) and how your opponents play actually matches that. If your Dimir opponent gets an attack through while having 3 open mana and doesn't ninjutsu Kaito, Bane of Nightmares its very unlikely he actually has it in hand.

Now making the optimal decision does not only mean lifting your opponents constraints, but also constraining your opponent as much as possible/making it harder for them to lift your constraints. This brings us back to false tempo decks. While it is applicable/important to every deck, I think this concept is most important to understand when playing false tempo decks. A false tempo deck generally presents a very strong constraint (usually a combo) that‘s not very robust, and a second weaker, but more robust constraint (usually a fair plan). Usually the second constraint alone is weaker than the constraints your opponent puts on you, and your opponent will have the tools to answer the first constraint (especially postboard), so how is this a viable strategy?

Example: You are plaing UR Vivi against UW Control and are on the draw. Its your second turn, you only played a Spirebluff Canal t1. Your opponent has 2 open mana. This is your hand, whats the play?

Playing the Cauldron seems intuitive, since it enables the turn 3 combo. However, it is very likely our opponent will have an answer to the cauldron (No More Lies , Pinnacle Starcage , Seam Rip ). If our opponent can answer our cauldron, they will be less constrained in their future plays because they know we are now less likely to combo off. So now they can e.g. tap out for an Overlord of the Mistmoors on t4 or an Elspeth, Storm Slayer on t5. Since they present stronger constraints than our second constraint and have somewhat lifted our first constraint, we will likely lose. However, if we hold off on actually commiting to the combo and instead present them with mainly our second constraint by playing profts into scholar etc., they will be forced to use a lot of their answers and/or eventually tap out for a threat or boardwipe of their own, which can open up a window for us to combo. In other words, they don't know if our stronger constraint is actually present. they have to decide between trying to lift our second constraint (and losing if we have the combo) or trying to lift our first constraint (and losing if our second constraint gets too strong).

As i said, this doesn't only apply to false tempo decks. Generally speaking, if we understand what constraint our deck puts onto our opponent, and which ways our opponent has to lift our constraints, we can then look for ways to make it more difficult for them to lift them or punish our opponent for trying to do so if we don't actually have the cards to enforce that constraint.

What to take away from this article:

To summarize the article in one sententence: In Magic, you want to figure out which constraints your opponent is putting on you and then make the optimal decision given these constraints, while trying to make it more difficult for your opponent to lift the constraints you are putting on him.

As i said in the beginning, i wanted to use this article to show you a way to think about the game that has helped me improve a lot. I hope it can also help you understand matchups better, make difficult decisions during games or at least give you another lense to view the game through.