or: Why Patrick Chapin and Sam Black are Right
Back on Magic Cruise 4, Patrick Chapin was one of the featured speakers.
In his talk, he said something that is semi-controversial, which is that there may be more than one correct play in Magic, based on the player.
Recently on the Pro Points podcast, (at about 18:15 in) Sam Black said, 'I think, more than most, that functionally it's valuable to make the right play, and right pick, for you as a player', and I was reminded of how I share his disagreement with the community.
I was stunned and glad to hear this the first time I ran into it, because the Magic community (as Sam mentions) believes that there is only one correct play, ever. And that's not wholly wrong. But it's not wholly correct either. Since models are sometimes correct, and sometimes useful, let me talk about the models that support both of these concepts, and what this might mean more generally.
Level 0: There are lots of plays, and they're close enough
This is the beginner mindset, and it's one that, in a game like Magic that has so many small edges that need to be gained, that people need to move away from.
In the Jon Finkel interview where he laid this out, the way he put it is that people say that plays were 'good plays' when they weren't the most correct play, and they need to stop that. And he's right: a good play is not necessarily the most correct play! Figuring out the relative value and correctness of plays is core to your growth, and ability. I wanted to put this out there because if you are at this level, where you don't really think about which play is truly better than which, or you think that a play that is 'good enough' is fine and doesn't mean you need to improve on it, and you are competitive, you should change your process here. Note that I say you should focus on comparisons, and there's good reason for that. Let's move onto where the Magic community in general, for the moment.
Level 1: There is only one best play
So we've moved on to Level 1: there's
one correct play at every point in a game/match of Magic (or your entire life, by some peoples' reckoning!)
Sometimes, this is actually just true. For example,
Tic-Tac-Toe is a 'solved' game. Solved games usually (perhaps always) have one best (correct) play, or a set of equivalent plays, at all times. But why is this, exactly? It boils down to one major way that you can describe games like this: everyone involved is able to clearly evaluate the value of every possible choice at all times. (It may also be necessary that there are no 'trap' states (like 'shooting the moon' in hearts) that can wildly vary the value of a specific choice.)
The reason I bring that out is that the model of playing a game as complex as Magic actually has more components than the game state. So let's talk about representing Magic as a game for a second.
To represent choosing what to do in a Magic the Gathering game adds two major wrinkles to the simple model of what tic-tac-toe might require. Firstly, it has a significant hidden information component. This means that two different players' knowledge of the game state are different. Secondly, it is too complex a space to solve down to most of the time, so you don't actually know the 'goodness' of a game state, which means that the players' belief in what the goodness of a game state is substitutes for the solved analysis in tic-tac-toe, and that makes a huge difference.
... Actually, this is still too complex. Let's talk about rock-paper-scissors for a second.
Rock-paper-scissors, in concept, is a simple game. Each player chooses one of the three options, and then if they chose different ones, some player wins. If each player is a completely evenly random system, there are no edges to be gained. There are three equivalent best plays at all times.
But people... people are not completely evenly random systems. And so the edges of how people play rock-paper-scissors make it no longer match this abstract model.
This is important: once you bring in modeling the people, the correct decision in a game may no longer be the theoretical one.
'But you're talking about the soul read, that's not fair, that's not realistic to necessarily say there's different decisions based on your opponents' internal models that should be considered correct.' Mmm. Okay. Magic, however, also has the second problem I brought up: it is too complex to solve.
In Marshall Sutcliffe's classic example, If I am playing a game of Magic, and we are in a race where I believe I am winning the race, and my opponent believes they are winning the race, one of us is wrong. Which is to say, our evaluations of the game state, and the ways it could change, differ from each others' significantly.
That sounds a lot like the RPS situation described above, except it's less silly: knowing your and your opponents' valuation functions of the current state, as well as future state, allows you to make more accurate decisions. This is what LSV advises in levels 2 and 3 of his growth of a magic player discussions: realizing your opponent is a real person, and trying to figure out what they are thinking, or rather, what their model is. And their model includes an approximation of what a winning game state looks like.
So imagine there was a supercomputer that could calculate out all of the probabilities, and all of the actual endgame situations, and which had a perfect model of their opponent, so that they could put an objective value on each decision made, there would only ever be one correct decision (or several equivalent correct decisions) for them to make. If there were two such supercomputers playing each other, and they knew it, we would be in a space where all the correct decisions would be known, and executed.
But if they didn't know they were playing a supercomputer, then they'd have to BUILD a model of their opponent. And that means that each of the supercomputer players could try to fool the other as to what their model of the world is. This is what a bluff is, at its core: convincing your opponent that your evaluation of the game state is different from theirs for an important reason that they need to take into account.
None of this is particularly controversial, and people who believe there is one correct play are fine existing with this in their mental structure. Concepts people say which align with this include 'respecting your opponent enough to believe they have a trick here', or 'believing my opponent understands being on level 1, so I can be on level 2' or 'my opponent is a stone idiot, so I'm not going to respect their bluff.' All of these things are things magic players deal with on a regular basis, and they all pull from the above concept, implicitly, in doing so, even while they might still say there's only one correct play.
This might be enough to convince some people there's more than one correct play. But others might still say we're focusing a lot on the opponent. Not all of us are able to do that as well as others, and you can even choose to completely ignore your opponent, playing pure probability and doing quite well. Very fair! So let's focus on ourselves for a moment.
Level 2: There is more than one correct play
Let's say we're a dedicated limited player. We know our combat math, we win more than 50% of our games in Momir basic. And we're playing a game of magic. To maximize our win percentage, it is likely that it will benefit us to create board states which demand good combat math skills. Seems smart? But that by itself breaks the abstraction of Level 1. It's not even particularly controversial.
This is important again: a player's skillset/biases/knowledge/etc. means that the abstract probability analysis of what would give the supercomputer the best chance of winning the game/tournament may not be the one that would give that player the best chance of winning the game/tournament.
This is why I mentioned, above, the idea that comparing the value of plays is the real skill to have. In an operational context, when you are playing a game of magic, a choice might be a 55%er in the abstract, but the 45%er puts us in a world where we are more likely to make game-winning correct decisions than our opponent, and so we should take the 45%er. When good players take Jund into a modern tournament, this is often exactly the kind of choice they are making, and they are quite explicit about it: they want to be almost 50% vs the field, and then rely on their play skill difference, in the game they are choosing to make people play, to carry the day. That logic carries because the model of deciding on what deck to play is very structurally similar to playing Magic: lots of unknown information and probabilities in an iterative problem solving situation. What other players do, and believe, matters a lot, so by focusing on what they can control in their deck choice allows them to fight on a battlefield of their choosing. (Sun Tzu shoutout.)
Similarly, when drafting at the Pro Tour, it might be 'correct' to make a certain pick in an abstract context, but your win percentage may be higher if you make a different pick than that, because it puts you into a better position to navigate a draft, or outplay your opponents, or keep your opponents from outplaying you. When taking all the information into account, it simply isn't true that there is an objectively good choice that everyone should take evenly, and then all wrong choices, when it comes to Magic.
An important addendum: This isn't a paean to results-oriented thinking, this is about taking ALL of the models that are in play into account when deciding what to do.
If you make a play that fails to take into account all of the models, but happens to win you the game, that doesn't mean you made the correct play 'for you'. That means you got lucky. That doesn't change just because we've moved from 'the only model that really matters is the abstract model of how Magic cards interact' to 'modeling the players and the game at the same time'.
(Edit: See my postscript about Jon Finkel down below. Notably, if you are taking into account the players and the game and all the other factors, there is then still only one correct play. That makes the flow of this article a little weird, but I still think teasing out the distinction and why it exists is important.)
How do we use this?
I came at this from a machine learning background, but really, this is a core systems analysis insight, a sociology insight, a marketing insight, put into a specific context: the existing system, and the people involved in the system, and what they believe, and what they are capable of, all actually affect what the best course of action is. You very often can't just look at a system, optimize it in a vacuum, just put it into action, and get the best results. (Machine learning results that are funny and weird are often the result of this sort of raw optimizing, and
often don't solve the problem we thought they would solve.)
This leads to the world where because it's complex, it's tempting to try to figure out an analysis, based on outputs, which lets us know if we're making decisions well enough. This is the world of Key Metrics in businesses: focus on the output, and try to get better output, even if we don't know all the machinery involved. In Magic, this is extremely hard, because every tournament and game is underspecified. It is nobody's weekend to win. You aren't 70% against a deck because you ran a 10 game set. Building up the tools to do the soft analysis with high success is one of the things which separates the best players from the rest.
If I'd solved the question of how to build up those skills, I'd let you know, I promise, but that's a space where I am still trying to figure things out. This is what people who advice 'get feedback from others' and 'play against better players' and such are actually getting at, what they're trying to get you to build up somehow, that soft analysis. But that's the hard part. To get the best results out of your tournaments, though? In the end, you have to make the decision that give you the best outcome, based on the information you have. Analyze it afterwards.
Postscript
Jon Finkel responded fairly quickly to an incidental tag, causing
this twitter thread to exist. One big note to see here is that he thinks that believing there is 'a correct play' means that
of course you take your opponent and your own internal models into account. This post came into being because I, Sam, and Patrick seem to believe that the community, in general, does not see it that way, and so I am trying to tease out how the correct play is different for different situations (but there technically still is only one, given all the information), but if that's what the phrase means to you, then I certainly have no problem with that.
