Strictly Better/Worse, Hyperbole, and Magic: My Stoic Rebuttal

So, last night, @zbeg was firing off corner case after corner case about how no card is strictly better than another. This carried on to this morning, as people caught up to the conversation. Many people had varying points, but ultimately, the confusion arises from two main things.

1) People are not defining "Strictly Better/Worse" correctly. (@modogodot provided a definition he claims WotC R&D uses, and later I'll get into why I disagree. Even if THEY use it, doesn't mean they are correct in what it actually means.  EDIT: Since then @mtgaaron did infact use a similar definition to @modogodot, which @modogodot confirmed he agrees with)

2)Magic Players love hyperbole. This doesn't have much to do with this conversation, but is typically how these sorts of things come up. One person uses the phrase in hyperbole, gets shot down, and then mass hysteria ensues.

Onward, Ho!

Game theory, from an academic standpoint, is one of my strengths. This debate, really is, an academic one. It's a debate over how to define the term, not how it impacts game development/design, or actual game play or strategy. Many people are saying, but it's only useful if we define it like this...! We don't define academic terms for their usefulness. "Strictly Better" was not defined for the purposes of MTG, and if it just so happens that you don't find any value in using that term, as its defined, then we probably just shouldn't. If @modogodot (and others) choose to create a different definition, to describe only Magic The Gathering, that's their perogative, but it's never going to be the globally accepted definition of what the term means, and will always continue to create confusion when used.
I (and others including @marshallLRcast) suggested sticking to the term "better". Which is much safer, and easier to debate with out academic minutia. But, here we are, and since I'm particular about my academics, I'm going to set the record straight.

Strictly Better, is a common replacement, for "Strictly Dominant Strategy".
In game theory, the general premise of study is that both players select a strategy before the game begins, then the game happens, and both players execute said strategy, and then there is a result, where each player receives a payoff/outcome from the result of the game. A common example you may already be familiar with is The Prisoner's Dilemma. While that example is not a zero-sum game, like MTG, a much simpler example is Rock-Paper-Scissors is indeed a zero-sum game. Before the game begins, each player mentally selects what they will choose, and after 1-2-3-Shoot, they display their strategy using hand symbols. In this case there is only 3 outcomes: Win(+1), Lose(-1), and Draw(0). There is no Strictly Dominant Strategy in this game, as there is no single choice (or mixture of choices) that is always better than any other. (There is an optimal mixed strategy, that provides the best EXPECTED outcome, but is not strictly best, i'd be happy to write more about mixed strategies if people are interested.)

I digress. Here, we're trying to define "strictly better" as it applies to one MtG card, over another. What the term means in this context is: Card A is better than Card B to be included in a deck, because to combat every given STRATEGY (or card choice etc) the opponent may select, Card A provides an equal or better outcome, never worse.

My example will be: Stoic Rebuttal is strictly better than Cancel.
How much better? Not much really, in most decks not at all, but that's now what we're getting at here.

Common (incorrect) counter-arguments:
Mindslaver-
"My opponent has Mindslaver, when they activate it against me, the cheaper counter may give them the opportunity to counter my own spell when they otherwise wouldn't have."
This is a description of a game state, not a strategy. Stoic Rebuttal is still strictly better at beating the strategy your opponent is playing. If your deck can indeed take advantage of the discounted cost, you're better off at preventing the Mindslaver from resolving, which is far more relevant to how that card will impact the match, as compared to what will happen when the opponent needs to cast it out of your hand. Ultimately, once they've activated Mindslaver on you, they've won the game. So what you have in your hand, and what they do with it, isn't really relevant to what's the best strategy.  Even if you did know that all of your opponents on a given day were running Mindslaver, would you choose cancel over stoic? Absolutely not. Maybe if in your deck its literally impossible to Metalcraft, then you would be indifferent between the two cards, but you certainly aren't saying that Cancel is better.

Meddling Mage-
"My opponent cast a meddling mage, naming Stoic Rebuttal! I bet you wish you had a cancel now!?" No, I wish i had a lightning bolt to kill the damned Meddling Mage. That's what makes Meddling Mage good, once they know what IS in the opponents deck, they have the dynamic decision to prevent you from playing it. Unfortunately, NEITHER Cancel, nor Stoic Rebuttal can be defended from that. Maybe you trick your opponent once, by running an inferior card, but it certainly isn't increasing your overall outcome (this is covered in the "equilibrium" part of the link i provided above. In fact they're probably just playing poorly, if they chose to name a card with Meddling Mage, that isn't even in your deck.

Defining Payoffs/Outcomes-
Outcomes, in the case of MTG are your win% against a given strategy over time. Because MtG is a game that contains variance, we must rely on the law of large numbers to assign payoffs to any given card choice. Cancel would never provide a higher win% against any given strategy than Stoic Rebuttal would, but Stoic Rebuttal COULD provide a higher win% against many strategies, if the deck was built to take advantage of its inherent "betterness".

Why we shouldn't be in a vacuum:
Sometime between when I began this post, and now, @mtgaaron Head of MTG R&D chimed in, and explained that he uses "Strictly Better" to compare two cards in a vacuum, and if Card A is better in every way than Card B then it is Strictly so. It's good to know that my Stoic Rebuttal example still fits his definition, but I don't agree with his definition.

Magic is not a vacuum, and neither is the metagame for any given format. This is really the issue here, we don't want to be isolating individual cards as reasons why one card could be better than another, but rather, strategies that an opponent may select before the game begins.
For example, Counterbalance, is of course a card, while it also is the namesake card of an entire Legacy archetype. While, the existance of the card creates the existence of the archetype, its a fine line that says its the archetype that makes it relevant to the discussion. The Counterbalance player (or rather, deck designer) has taken a look at the metagame and said, "I've noticed that in Legacy, most decks run cards that have low casting costs, and run from 0 to about 5. There's a much higher density of those cards in the 1-3 range. I'm selecting a strategy that gives me a strong ability to consistently counter every spell they cast, using other abilities that can manipulate the top card of my library." Here, my example of Stoic Rebuttal vs Cancel still stands, because they both have the same CMC of 3, even though Stoic Rebuttal may actually cost less. There are CERTAINLY times when selecting one card choice over another has been impacted by the existence of this deck, infact I read an article about it this week, and i'll find it and update it here. The fact that making such a card choice is actually better to defeat one strategy, is no trivial fact, it is what we are precisely defining.

Another such example is Chalice of the Void, in mono-brown vintage archetypes. This is the reason why blue players keep both Hurkyl's recall and Rebuild in their 75. While the difference in CMC is not the only reason why one card is not strictly better than another, it is the reason its selected in this case.It is simply another illustration why 2 cards with the same/similar functional ability at different CMC's cannot be considered strictly better in formats where archetypes that can limit the types of CMC's their opponents can play, are available to be chosen.

Many are saying, that without the vacuum, nothing valuable can said.

That may, or may not be true, and I tend to disagree. Each person is going to find different types of information valuable. But lots of valuable things can be said about comparing cards both inside and outside of the vacuum. Basically, if you don't like my definition (see: textbook), then we should simply be using a different term. Just because the definition some have chosen may be more "valuable" to you, doesn't make it correct.  I'm going to once more go back to my good ol' ... "Just say better, and then describe quantitatively and qualitatively, how it is better. Using the term strictly better, is rarely correct, and when it is, it probably isn't even describing what you'd like it to."

Hopefully the comments section below will allow the debate to continue in a format that doesn't stop us at 140 characters (after we @ all the interested parties).

Looking forward to the flames!