Feedback Thread: Design Space Implications for Magic Theory

[Spiderman]

Comment on the front page article here!

 

[Oversoul]

Well, I think that the Manaleak article correctly identifies that problem. Games like Poker and Bridge have detailed book-length treatises on theory, and Magic, which is more complex (not saying that as a point for or against it, but merely as a fact), is lacking in that department. A major culprit is that so much of the focus in competitive gameplay is on Standard, which changes too quickly for theory discussions to take root.

There is some good theory writing out there, though. I've taken my own crack at the field as well, not that it amounts to much. For example, this is my kind of theory article. But I'm a filthy casual, so my attempts at theory have been colored by that.

That "Transcension" deck, raises the question: If a given decklist falls outside the bounds of what a given theory can describe, is that a deficiency in the theory or is it merely describing a boundary on the scope of the theory? If, hypothetically, I craft a robust theory that seems to work well for, say, Standard (ew), but someone builds an elaborate, non-competitive deck like Transcension and it seems to "break" the theory, what does that tell us? On the one hand, I'm reminded that plenty of theories in science really only work within a certain frame of reference and, if applied to extreme cases, start to wilt at the edges. I have a chemistry background, and while I'm not much of a theory person there, I did learn the basics for things like molecular orbital theory, crystal field theory, VSEPR, etc. Those theories tend to work marvelously for the cases where they were originally developed and for most applicable chemistry, but they have their limits, and if we start getting extreme, like trying to force neon to form compounds, the theories stop prettily describing all of the details and become more of a murky "well, it kind of still works." But on the other hand, we know that sometimes it has happened that someone, somewhere broke the metagame before anyone else, and if we rely on a theory that doesn't really work, we might miss out on important insights.

So far, my inclination is that just about everything in Magic theory must be taken with a grain of salt.

 

[Psarketos]

I think that 'competitive' is a major component of difficulty in crafting a broad theory for many reasons, including how you delimit the term without a specific temporal context (part of why 'single instantiation of Standard format' does so much work in my view). In Poker one player cannot choose to draw the game, that game state has to arise out of both player choices over the course of the game and is dependent upon the cards they have in hand. How does the ability to choose to draw affect the concept of competitive? Perhaps more relevantly, Poker theory is based on probabilities: 2/7 off suit can beat pocket aces after the flop in Hold'Em, as an example, even if the flop contains no cards that directly affect either hand. The useful information Poker theory gives us about that matchup, outside player behaviors such as bluffing, is the likelihood that 2/7 off suit can win if both players stay in the game to the end.

A theory of Magic that provided similar probability assessments would be orders of magnitude more computationally intensive given that there are, conservatively, over 9000 different Modern legal cards that might exist in a deck brought into competition, and the calculations involved are not limited to > = < values per card but somehow need to be evaluated by unique sets of cards using a far more interactively broad metric.

Computational difficulties being one facet of the problem, another that remains even if they were solved would be discerning an objective meaning for competitive. This might be solved with something like "wins more than 1 in 2 games on average against every deck it might possibly face in a particular format," which would be easy if you had the computational side solved for "every deck it might possibly face in a particular format" already. Yet a theory would need to be true for subsets within its claimed domain as well, which leads to a different problem we can demonstrate practically.

I go to my local game store and create two tournaments for Magic: the Gathering. The first is a Modern legal game with the additional, tournament specific rule that decks may contain no cards that are not instants or sorceries. Winner gets a large gift card to the store! Can a theory that works for 'competitive' at the World Championship Modern tables answer what deck I should bring to win the competition for that gift card? So that tournament went over well with the local players, everyone had fun and the gift card was won, now I am hosting a new tournament next week. It is Legacy legal, with one rules twist - decks may contain no cards that can deal damage, whether directly or via a power value in an attack phase. Can a Legacy solving theory tell me, out of the much smaller set of cards it now has to account for, which decks will be competitive?

My belief is that the mathematics of Chess and Poker, while still very difficult, are in the kind of range that human intuition can look at and feel reasonably confident using in a way that 'competitive' is equivalent to "I win the game or specific set of games." While I do feel that my Standard limitation may put Magic into that same general reach, it seems increasingly true to me that the difficulties of both understanding and shared definition become intractable at the larger scale of other existing formats.

 

[Oversoul]

I think that 'competitive' is a major component of difficulty in crafting a broad theory for many reasons, including how you delimit the term without a specific temporal context (part of why 'single instantiation of Standard format' does so much work in my view). In Poker one player cannot choose to draw the game, that game state has to arise out of both player choices over the course of the game and is dependent upon the cards they have in hand. How does the ability to choose to draw affect the concept of competitive? Perhaps more relevantly, Poker theory is based on probabilities: 2/7 off suit can beat pocket aces after the flop in Hold'Em, as an example, even if the flop contains no cards that directly affect either hand. The useful information Poker theory gives us about that matchup, outside player behaviors such as bluffing, is the likelihood that 2/7 off suit can win if both players stay in the game to the end.

A theory of Magic that provided similar probability assessments would be orders of magnitude more computationally intensive given that there are, conservatively, over 9000 different Modern legal cards that might exist in a deck brought into competition, and the calculations involved are not limited to > = < values per card but somehow need to be evaluated by unique sets of cards using a far more interactively broad metric.

Computational difficulties being one facet of the problem, another that remains even if they were solved would be discerning an objective meaning for competitive. This might be solved with something like "wins more than 1 in 2 games on average against every deck it might possibly face in a particular format," which would be easy if you had the computational side solved for "every deck it might possibly face in a particular format" already. Yet a theory would need to be true for subsets within its claimed domain as well, which leads to a different problem we can demonstrate practically.

Speaking very broadly, yes it's true that Magic is more complex than Poker or Bridge (I picked them because they're card games with extensive bodies of literature concerning strategy, but this goes for lots of other games as well), but there are a lot of things that we can shortcut. In your example of Modern as a format, there are certain known decks that tend to be played often and these decks are capable of certain things. Affinity, Tron, PiF Storm, Grixis Suicide, Burn, Scapeshift, Merfolk, Lantern Control, etc. Now, if the goal of a deck is to be competitive, setting aside the exact criteria for competitiveness, it's certainly going to have to hold its own in that field. One might not have a good average matchup against all of those popular decks, but being unable to beat too many of them necessarily means that one cannot compete.

The simplest metric would be an estimated match win-rate, but that is tedious and not really helpful because it doesn't tell us anything about why a deck is or isn't competitive, about what to look for. We can break it down further by looking at pre-board and post-board games, which still doesn't tell us enough. We could even throw in other metrics like how many turns the games ran, how much damage different cards dealt, and so on, but that still doesn't tell us enough. Well then, how much is enough? It takes more than that stuff I named, but I don't think it takes a full computational assessment of every possible card choice in terms of some scalar value (and I'm not sure how much that would even help anyway).

What we need to be able to do is find out how to beat those decks, and there are only so many ways to do it. You can outrace your opponent, killing the other deck faster than it can kill you. You can disrupt your opponent so that the other deck becomes slower than yours, then outrace your opponent. You can use sufficient disruption to nullify your opponent's attempts to outrace you. And that's pretty much it. You have to be faster, slow things down and take control, or hybridize them by slowing your opponent down while being fast yourself. Aggro, control, or aggro-control. We can attempt to categorize things further and stipulate nuances within categories, but there do not seem to be any other options that don't fall into one of those three. Combo is just putting cards together to do one of those three things: usually either a direct kill (which is clearly an attempt at racing) or a lockdown (which is clearly an attempt at slowing things down). So let's say that I want to build a Modern combo deck and I'm looking at the matchup against Affinity. Or perhaps "Affinity" as current lists under that umbrella often contain no actual Affinity cards, but that's another topic. Anyway, it's a highly aggressive deck that dumps cheap artifacts from its hand and attempts to use beatdown with evasive creatures to kill opponents before they can mount defenses. Understanding that, our hypothetical combo deck can either use a combo that can be executed so quickly that it outraces Affinity (difficult to do), or it can use general disruption that happens to give it an advantage in the race against Affinity (also difficult to do), or it can run sideboard artifact hate and hope for a strong post-board matchup (possible, but that does put constraints on the sideboard for other matchups), or it can write this off as a bad matchup and focus on beating other opponents (dangerous, but potentially an option if the metagame isn't already too weak against Affinity). Those would seem to be the only approaches to the matchup, and for each of them, only a very limited set of cards are options at all. Presumably our deck has its core combo and support cards for the combo, as well as a mana base, so it has limited slots to use for any one of these approaches or any combination of them. This is still very complex! But our search is narrowed. A lot.

 

[Psarketos]

Oversoul, your responses were excellent enough that I wrote an article in response Submitted just now, attempting to broadly address your points regarding competitiveness, known decks, popularity, and their relationship to the sort of theory I have been going on about. To give a brief overview of what I submitted, there are a lot of cases where I would want to know what theory says about decks that have never shown up in a tournament. It would be easy to simply find a decks statistical average win / loss vs, as an example, the top 10 tournament appearance decks in a format.

That will not predict for me, as an example, which deck is going to win between MetaEsper and Transcension on average. More importantly, it won't tell me why those matchups are different, or what causes it to be the case, in specific deck building terms, that whichever deck between MetaEsper and Transcension wins more does so. You allude to this yourself, but it is the heart of where I am going with my theory focus - we can make theories about what are called "Tier 1" tournament showing decks, and those theories can give us excellent insights for playing in those matchups and any similar looking environments in the future, however there are huge swaths of game interactions we are collectively missing if we only focus on that concept of 'competitive.'

I understand why most of the community is looking for the 'best' deck for their abilities and play style - for me, the 'best' deck is the one that showcases some eccentricity of the game itself while still capable of winning in certain cases, rather than anything involving win rates in a tournament setting, and that is an area that I feel we are both lacking as a community and could use more support for (like your idea to create a rogues gallery of odd decks, and the general mission of the CPA as it has existed over its history, and potentially the creation of a new format with a little more focus on comprehensibility and coherence that Wizards design has shown over the past 5 years or so).