Game Theory and the Best Deck

[Elric]

I agree with PucktheCat and AmbivalentDuck here.

Let me use an example that should make it really clear why: let's say that right before the tournament starts, I offer to pay you $100 if you can pick the player who will win the tournament.  All players are assumed to be identical, so each player's chance to win the tournament only depends on the deck he is playing and the rest of the decks at the tournament (and you know all of this).

You might think that the "best answer" to this question is person with the deck that has the highest chance to win the tournament (assuming you know all matchup percentages and can just run through the calculation).  

But now let's suppose that I assert that that "best answer" isn't really the "best answer" at all- it's just the best practical answer.  The real best answer, though, is to know the future and see which players will win the tournament.  Then you simply pick that player.  In theory, this works every time.  

If you complain about this not really being useful, I’d respond as follows:

“How many times do I have to stress the difference between theory and application of theory?  Of course you can't just walk in to a tournament and pick who will win the tournament with certainty.  I have repeatedly said as much.  That doesn't, however, change the theoretical definition of the “best person to pick to win the tournament.�  Application of the theory can only approximate who the “best person to pick to win the tournament� is.  You don't hear scientists say "Well, we can't actually know where an electron is going to be so we'll use this equation that says where it might be." That wouldn't make any sense.  If we want to take this aspect of the game seriously, we have to accept that there is going to be theory; and if there is theory it is not going to match up perfectly with reality.�

Knowing what decks people will play in advance (even though those decks are being chosen in a random fashion) and knowing the results of the matches in a tournament (even though we think that these are also random variables with expected win percentages for each player) are pretty similar forms of divination.  You’re assuming that you know so much that chance no longer exists.  

[Vegeta2711]

Out of curiousity, could anyone explain what exactly your all prattling on about?

I see a ton of sceintfic overanlyzation and big pouty words being thrown about with pretty much zero point. Maybe if you guys played the game once in a while, you would be able to 'answer' your own question instead of just trying to out-theory one another. 

[Klep]

Knowing what decks people will play in advance (even though those decks are being chosen in a random fashion) and knowing the results of the matches in a tournament (even though we think that these are also random variables with expected win percentages for each player) are pretty similar forms of divination.  You’re assuming that you know so much that chance no longer exists. 

I strongly urge you to make sure you understand the difference between the theory of the best deck and the application of that theory before further commenting.

I'm not going to continue repeating myself.

[Elric]

Knowing what decks people will play in advance (even though those decks are being chosen in a random fashion) and knowing the results of the matches in a tournament (even though we think that these are also random variables with expected win percentages for each player) are pretty similar forms of divination.  You’re assuming that you know so much that chance no longer exists. 

I strongly urge you to make sure you understand the difference between the theory of the best deck and the application of that theory before further commenting.

I'm not going to continue repeating myself.

Fine.  We can drop the topic.  From now on, in this thread the "best deck ex ante" or just the "best deck" will be defined as the "best deck given that you do not know the outcome of random processes."  If you start your own thread, feel free to define it however you want there.

[AmbivalentDuck]

Out of curiousity, could anyone explain what exactly your all prattling on about?

We've spent two and a half pages debating semantics, the usefulness of knowing the "best deck" for a tourney, whether or not it's practical to try to predict the "best deck," and whether or not understanding the evolution of metagames is a useful tool for predicting the "best deck." 

Most of the debate exists only because we disagree on whether the "best deck" is the deck that wins or the one most likely to win in theory.  We pretty much agree about what the criterion for the "best deck" is in practice.

The camps, vaguely drawn, are:
-Klep argued against Elric's definition of the "best deck."  Puck sided with Elric.  I've mostly stayed out of that.
-Klep slowly conceded points regarding metagame evolution, but maintained that his theory of the "best deck" excluded evolution as a useful tool in theory.  Which, while debatable enough to be respectable, Puck and I disagree with.  Elric seems to have sided with us.

So, it's mostly three on Klep.  He's not losing so much as we're just disagreeing on definitions and assumptions.  I'd like to believe that our definitions and assumptions are better, but I'm biased. 

If anyone disagrees with my assessment of their positions, I'll correct it immediately.  I'm just trying to sum up a very technical debate that seems like it might be ending.

[PucktheCat]

Duck:  I think that is an accurate summary.

I would add that I am non-math person who found this debate very interesting and informative.  I know people get exasperated with overly arcane debate on fine points, but I think the quality of threads like these is a huge feather in The Mana Drain's cap.

Here is another summary attempting to make clearer the content of the two positions:

Both the best strategy ex ante (i.e., with limited information about the metagame) and the best strategy with perfect information are knowable (in theory) and either one can be defined as the "best deck."  Klep has argued that prior work has used the latter and so the terms meaning is set by usage while Elric and I have taken the position that the plain meaning of the phrase "best deck" better conforms to the former.

Leo

[jpmeyer]

Out of curiousity, could anyone explain what exactly your all prattling on about?

I see a ton of sceintfic overanlyzation and big pouty words being thrown about with pretty much zero point. Maybe if you guys played the game once in a while, you would be able to 'answer' your own question instead of just trying to out-theory one another. 

Sure.

Je devrais, pour ce livre déjà vieux, écrire une nouvelle préface. J’avoue que j’y répugne. Car j’aurais beau faire : je ne manquerais pas de vouloir le justifier pour ce qu’il était et le réinscrire, autant que faire se peut, dans ce qui se passe aujourd’hui. Possible ou non, habile ou pas, ce ne serait pas honnête. Ce ne serait pas conforme surtout à ce que doit être, par rapport à un livre, la réserve de celui qui l’a écrit. Un livre se produit, évènement minuscule, petit objet maniable. Il est pris dès lors dans un jeu incessant de répétitions ; ses doubles, autour de lui et bien loin de lui se mettent à fourmiller ; chaque lecture lui donne, pour un instant, un corps impalpable et unique ; des fragments de lui-même circulent qu’on fait valoir pour lui, qui passent pour le contenir presque tout entier et en lesquels finalement il lui arrive de trouver refuge ; les commentaires le dédoublent, autres discours où il doit enfin paraître lui-même, avouer ce qu’il a refusé de dire, se délivrer de ce que, bruyamment, il feignait d’être. La réédition en un autre temps, en un autre lieu, est encore un de ces doubles : ni tout à fait leurre ni tout à fait identité.

La tentation est grande pour qui écrit le livre de faire la loi à tout ce papillotement de simulacres, à leur prescrire une forme, à les lester d’une identité, à leur imposer une marque qui leur donnerait à tous une certaine valeur constante. « Je suis l’auteur : regardez mon visage ou mon profil ; voici à quoi devront ressembler toutes ces figures redoublées qui vont circuler sous mon nom ; celles qui s’en éloigneront ne vaudront rien ; et c’est à leur degré de ressemblance que vous pourrez juger de la valeur des autres. Je suis le nom, la loi, l’âme, le secret, la balance de tous ces doubles. » Ainsi s’écrit la Préface, acte premier par lequel commence à s’établir la monarchie de l’auteur, déclaration de tyrannie : mon intention doit être votre précepte ; vous plierez votre lecture, vos analyses, vos critiques, à ce que j’ai voulu faire, entendez bien ma modestie : quand je parle des limites de mon entreprise, j’entends borner votre liberté ; et si je proclame mon sentiment d’avoir été inégal à ma tâche, c’est que je ne veux pas vous laisser le privilège d’objecter à mon livre le fantasme d’un autre, tout proche de lui, mais plus beau que ce qu’il est. Je suis le monarque des choses que j’ai dites et je garde sur elles une éminente souveraineté : celle de mon intention et du sens que j’ai voulu leur donner.

Je voudrais qu’un livre, au moins du côté de celui qui l’a écrit, ne soit rien d’autre que les phrases dont il est fait ; qu’il ne se dédouble pas dans ce premier simulacre de lui-même qu’est une préface, et qui prétend donner sa loi à tous ceux qui pourront à l’avenir être formés à partir de lui. Je voudrais que cet objet-événement, presque imperceptible parmi tant d’autres, se recopie, se fragmente, se répète, se simule, se dédouble, disparaisse finalement sans que celui à qui il est arrivé de le produire, puisse jamais revendiquer le droit d’en être le maître, d’imposer ce qu’il voulait dire, ni de dire ce qu’il devait être. Bref, je voudrais qu’un livre ne se donne pas lui-même ce statut de texte auquel la pédagogie ou la critique sauront bien le réduire ; mais qu’il ait la désinvolture de se présenter comme discours : à la fois bataille et arme, stratégie et choc, lutte et trophée ou blessure, conjonctures et vestiges, rencontre irrégulière et scène répétable.

C’est pourquoi à la demande qu’on m’a faite d’écrire pour ce livre réédité une nouvelle préface, je n’ai pu répondre qu’une chose : supprimons donc l’ancienne. Telle sera l’honnêteté. Ne cherchons ni à justifier ce vieux livre ni à le réinscrire aujourd’hui ; la série des évènements auxquels il appartient et qui sont sa vraie loi, est loin d’être close. Quant à la nouveauté, ne feignons pas de la découvrir en lui, comme une réserve secrète, comme une richesse d’abord inaperçue : elle n’a été faite que des choses qui ont été dites sur lui, et des évènements dans lesquels il a été pris.

  - Mais vous venez de faire une préface
  - Du moins est-elle courte.

[Anusien]

Quotes that remind me of this thread:
"Hell is other people." - Jean-Paul Sartre
"Put every great teacher together in a room, and they'd agree about everything; put their disciples in there and they'd argue about everything." - Bruce Lee
Benford's Law of Controversy: Passion is inversely proportional to the amount of real information available.
"Political language— and with variations this is true of all political parties, from Conservatives to Anarchists— is designed to make lies sound truthful and murder respectable, and to give an appearance of solidity to pure wind." - George Orwell
"Convictions are the strongest enemies of Truth." - Friedrich Nietzsche
"All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense." - Principia Discordia

Warble- a CS deck that has 59 cards the same as another CS deck and 1 card different (with the same sideboard) is considered a different deck in this analysis.

This makes your analysis unwieldy at any level of abstraction beyond an 8man constructed event.

If you assume that players are identical, then by definition there is no "best player in the room" in any sense that is independent of deck choice.  In this case, the player who has the deck with the best match win percentage given the rest of the field will have the highest chance to win the tournament.

Strike two.  Good players have shown a long history of winning with inferior results.  Any model that does not take this into account may be self-consistent, but is worthless in terms of Magic applications.  Come on man, when AmbivalentDuck beats you on theory it's time to go home.

The following articles pwn this thread:
Metagames by Ken Krouner
Metaming by Doug Linn
Selecting a Deck for Fun and Profit

Like literally, every statement made in this thread is either a tautology or vacuous.

[AmbivalentDuck]

Quotes that remind me of this thread:
"Hell is other people." - Jean-Paul Sartre
"Put every great teacher together in a room, and they'd agree about everything; put their disciples in there and they'd argue about everything." - Bruce Lee
Benford's Law of Controversy: Passion is inversely proportional to the amount of real information available.
"Political language— and with variations this is true of all political parties, from Conservatives to Anarchists— is designed to make lies sound truthful and murder respectable, and to give an appearance of solidity to pure wind." - George Orwell
"Convictions are the strongest enemies of Truth." - Friedrich Nietzsche
"All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense." - Principia Discordia

Warble- a CS deck that has 59 cards the same as another CS deck and 1 card different (with the same sideboard) is considered a different deck in this analysis.

This makes your analysis unwieldy at any level of abstraction beyond an 8man constructed event.

If you assume that players are identical, then by definition there is no "best player in the room" in any sense that is independent of deck choice.  In this case, the player who has the deck with the best match win percentage given the rest of the field will have the highest chance to win the tournament.

Strike two.  Good players have shown a long history of winning with inferior results.  Any model that does not take this into account may be self-consistent, but is worthless in terms of Magic applications.  Come on man, when AmbivalentDuck beats you on theory it's time to go home.

The following articles pwn this thread:
Metagames by Ken Krouner
Metaming by Doug Linn
Selecting a Deck for Fun and Profit

Like literally, every statement made in this thread is either a tautology or vacuous.

I'd like to say, immediately, that these are great articles for extended and T2.  Solid, grade A, unquestionable.  That said:

Krouner's article is excessively basic, non-predictive, and not useful over-all for innovation.
-Unlike T2, we don't have seated metagames for the simple reason that we never *really* know what the best decks are.  Ignore any disclarity in the word "best," the amount of manpower invested in defining the T2 environment grossly exceeds anything we can consider plausible.  Not only that, our cardpool is much larger leaving literally millions of untested two-card interactions. (6000^2 is a BIG number)  If we take that up to three-card interactions, we're hopelessly lost.  Not only that, you'd fight an uphill battle to say that win percentages between any two top 8 decks in recent major tournaments had a win/loss ratio greater than 60%.  Throw in the fact that people like Smennen can likely pilot tier 2 decks to consistent top 8 finishes, and we have enough unclarity to render this article useless when dealing with T1.

The link to Linn's article is broken.

Flore's article, while very readable, contains most of the weaknesses of Krouner's article and then adds a few.
-We don't have multi-day, multi-format tournaments.  So, there goes the first half of the article.  The next half explains the Nash Equilibrium we were all very happy to concede never actually happens.  While I mention it numerous times, I cite it as a way to predict evolution so you can start working on your deck a month in advance.

To the charge that a large chunk of what we're saying is a tautology, I would instead submit that no single definition is sufficient to encompass either side's position in the debate.  Conversely, I submit that deductive reasoning was applied starting from contested definitions.

To the charge that the remainder consists of vacuous statements, all models necessarily make assumptions.  Unrealistic assumptions don't create a bad models, garbage results define a bad model.  Since none of these models are testable at present (though I'll be happy to create and manage a database of results), it would have been nice to see more attacks on predictive validity.  Unfortunately, that will almost certainly require a new thread.

At the least, my remarks on metagame evolution are neither.  We're evolving towards an equilbrium whether we know what it is or not.  Database analysis could likely tell us where we're going.  It's neither accurate to say that that remark is a tautology, nor that it's vacuous.

[Elric]

Warble- a CS deck that has 59 cards the same as another CS deck and 1 card different (with the same sideboard) is considered a different deck in this analysis.

This makes your analysis unwieldy at any level of abstraction beyond an 8man constructed event.

Here's Mike Flores, from Selecting a Deck for Fun and Profit.  Note that Flores assumes, exactly like I do, that small variations in decks should be treated as discrete decks.

Clearly at equilibrium, the swtich from mono-Black to B/r will yeild significant positive EV. Now here's the part where my brain breaks: edt says that it is a mistake to look at Hoverguard Affinity, B/r Necropotence, and other templated variations on Natural decks as merely variations of core decks. He says that it is instead correct to say that they are discrete decks that represent their own chunks of metagame, even if they are minority percentages.

Your second quote is taken entirely out of context.  Here's the whole thing (plus the Whatever Works quote I was referring to).  Note that I was discussing two different assumptions that you can make- either players are identical or they're not identical; different conclusions will follow from that.  I then used Rich Shay as an example of how it's clear that players are not all identical.  Just cool it, ok?

The best deck is usually the one in the hands of the best player in the room.

When that is the case, that is merely a function of the best player being wise enough to pick the best deck.  As I have stated innumerable times, the identity of the best deck is independent of performance.

No, these are two different things.  To me, it seems clear that forcefieldyou is saying that the person who has the highest chance to win a Magic tournament is usually the person in the room who is the best at playing Magic and that the main reason for this is his skill.  His skill translates into higher win percentages than the rest of the field would have even if they all played the exact same deck as him- it's not necessarily the act of having the exact right deck based on what other decks are at the tournament.  See Whatever Works’ point about Rich Shay for an example of this. 

I feel that way every time I am in the same T1 Tournement as Rich Shay. No matter what the metagame is like... I would take him playing CS over the perfect metagame deck (which unfortunetly is not High Tide... 3 land belcher... UB Fish... or whatever I have ever won with)...

If you assume that players are identical, then by definition there is no "best player in the room" in any sense that is independent of deck choice.  In this case, the player who has the deck with the best match win percentage given the rest of the field will have the highest chance to win the tournament.  I'm not sure where the "independent of performance" part enters into any of this.

Edit: JP- "Madness and Civilization"?  Cute.

[Brutha]

Let me use an example that should make it really clear why: let's say that right before the tournament starts, I offer to pay you $100 if you can pick the player who will win the tournament.  All players are assumed to be identical, so each player's chance to win the tournament only depends on the deck he is playing and the rest of the decks at the tournament (and you know all of this).

Even if all players are identical skill is still important. If everyone know how to play Gifts and nobody knows how to play Grim Long, Gifts will win with a higher percentage than if nobody knows how to play Gifts and everyone knows how to play Grim Long.

You might think that the "best answer" to this question is person with the deck that has the highest chance to win the tournament (assuming you know all matchup percentages and can just run through the calculation). 

But now let's suppose that I assert that that "best answer" isn't really the "best answer" at all- it's just the best practical answer.  The real best answer, though, is to know the future and see which players will win the tournament.  Then you simply pick that player.  In theory, this works every time. 

That is only true if there is only one future. If Schroedingers cat is only alive or dead when someone opens the box, their could also be multiple futures from the start point of a tournement. And random shuffling is based on some electrons that move in our brain so chaos theory should have an effect in there.
So you have to look in who many futures the cat lives and in who many it dies.
You have also to look in who many futures which deck wins.
So you have to remove all random factors and replace them by Fuzzy logic: A coin flip is 50% tails and 50% heads instead of a coin flip can be 100% heads or 100% tails.

[Whatever Works]

Isnt knowing the metagame more important that knowing the best deck? People can argue the best deck all day, but I would rather play the tier 2 deck of my choice in a known metagame over the best deck in the format in a unknown metagame.

To elaborate why:

Lets say that CS is the best deck in the format (this is just in theory)... There is no debate... Its the best deck... Ok, you now know the best deck in the format, and because of this your going to play it at the next tournement... Only its in Europe at a sanctioned event where you dont have time to discover the metagame... You end up going 4-3 losing rounds to R/G Beats... Suicide black with maindeck planer void + chalice... and to some bazaar storm deck you have never seen before...

Know lets just say you have a great understanding of your metagame, and because of your understanding of the metagame you decide to play a UB fish list designed to beat stax (because stax won the tournement the day before), and you do amazing. Is the UB fish list great? NO, but was it designed for a specific known metagame? yes!

Know the best of both worlds is having the best deck, and knowing the metagame. When you have both you should feel great about your chances.

The other value of knowing the best decks in the format (which in my opinion is underlooked) is being able to figure out what you expect to be at the top tables from round 4 on in a tournement. If you know that Oath will be 25% of the metagame, but also believe that 85% of all oath decks will not have a record of 3-1 or better then that is extremely valuable information. Also if you know a specific deck that is perhaps 10% of the metame that will likely dominate an event (unless the deck gets unlucky or paired vs. itself etc.)

Kyle L

[PucktheCat]

Edit:  Deleted a point that Elric made more gracefully than I did.

Brutha:

Even if all players are identical skill is still important. If everyone know how to play Gifts and nobody knows how to play Grim Long, Gifts will win with a higher percentage than if nobody knows how to play Gifts and everyone knows how to play Grim Long.

There are a million caveats that apply to this sort of analysis.  We left out the chance that a player has an upset tummy during the game and can't concentrate, the chance that the road from St. Louis to Chicago will be struck by a meteor so Vroman can't win the next Star City there, and so on.  We reduced the complexity of the problem significantly for analysis.  In fact, that is true by definition:

Analysis
    1. The resolution or breaking up of anything complex into its various simple elements, the opposite process to synthesis; the exact determination of the elements or components of anything complex (with or without their physical separation).

I guess it's not very postmodern of us (JP's post aside), but breaking things down and thoroughly understanding their constituent parts is hardly a prima facia absurd approach to solving a problem.

I agree with your point though, skill definitely matters in real like.  I don't think the theoretical model described by Elric is at all incapable of absorbing this kind of information - skill would just represent a (virtually unknowable) additional factor to include in matchup percentages.  Thus, in addition to treating every single card variation on an archetype as a unique strategy you would have to treat each player/deck combination, even if they were playing the same cards as a unique strategy.  Complex, but theoretically consistent.

I really like your point about randomness too.

This makes your analysis unwieldy at any level of abstraction beyond an 8man constructed event.

I would argue that as a practical matter our analysis is impossible in a 2 person event.  I am far from convinced any of us could agree on the perfect deck to beat a specificly defined opponent deck, known down to the card.  If you add in the possibility of the opponent changing their deck unpredictably, I think there is little possibility we could determine an optimum strategy.

I fairly certain I will never apply any of this to a tournament.  In fact, I usually choose decks far before a tournament and play them a lot to increase my skill, so I often have little metagame information to work with when I make the choice.  I'm taking a Philosophy of Law class in school - will I ever use that in practice?  Probably not.  Will it make me a better lawyer?  Unlikely.  Do I find it enjoyable?  Yes.  I like to think about the larger framework of systems.  I enjoy my other law classes more because I am taking the philosophy course and I enjoy Magic more because of thread like these.  If you don't like them, don't read them.

Leo

[Elric]

Let me use an example that should make it really clear why: let's say that right before the tournament starts, I offer to pay you $100 if you can pick the player who will win the tournament.  All players are assumed to be identical, so each player's chance to win the tournament only depends on the deck he is playing and the rest of the decks at the tournament (and you know all of this).

Even if all players are identical skill is still important. If everyone know how to play Gifts and nobody knows how to play Grim Long, Gifts will win with a higher percentage than if nobody knows how to play Gifts and everyone knows how to play Grim Long.

If players are identical, the effect of skill is captured in knowing how each of the decks match up against each other.  So each player’s individual skill doesn’t matter.  I would assume that if all players had no idea how to play GrimLong (and consequently couldn’t beat anything with it because they couldn’t figure out how to put together a Storm kill), GrimLong wouldn’t be played at all.  

On the other hand, most players are not identical so in order to know how a matchup will play out in a tournament we’d generally have to know the decks being played and the characteristics of the players who are playing those decks.  Likewise you can’t accurately tell which player has the best chance to win the tournament solely by looking at the decklist for each player.  Even if two players in the tournament have the exact same decklist, more skilled player will have a greater chance to win the tournament.

You might think that the "best answer" to this question is person with the deck that has the highest chance to win the tournament (assuming you know all matchup percentages and can just run through the calculation).  

But now let's suppose that I assert that that "best answer" isn't really the "best answer" at all- it's just the best practical answer.  The real best answer, though, is to know the future and see which players will win the tournament.  Then you simply pick that player.  In theory, this works every time.  

That is only true if there is only one future.

This was an argument from contradiction.  I was trying to show why you shouldn’t assume that you can predict the exact outcome of truly random events. Once you know the probability distribution, if that distribution fully describes the outcome then the amount of extra knowledge that you can have, by definition, is zero.  So assuming that you can “cleave the probability distribution� is not only incorrect, but you have no ability to do anything even remotely resembling “cleaving the probability distribution.� 

The "Fuzzy Logic" technique (where even though the coin is going to be entirely heads 50% of the time and entirely tails 50% of the time you treat it as always being 50% heads and 50% tails) is exactly what you should be doing.  Assuming that you know the outcome of a truly random variable beyond the probability distribution is similar to “All ghosts are bodybuilders.  There are no ghosts.�  This is logically true but because there are no ghosts, the first statement doesn’t imply anything at all. 

It's the same thing for "If I know the outcome of truly random future events, then X.  But I can't in any way, shape or form know anything about the outcome of truly random future events beyond the probability distribution, so there's no reason to assume from the first statement that anything like X will ever hold."

Whatever Works- the situation you describe is why, without any probabilistic knowledge or actual knowledge of the decks that you are going to face, it doesn’t make sense to talk about a “best deck� unless that deck is truly a dominant strategy.  If players are identical and a deck is a dominant strategy for one player, it’s a dominant strategy for everyone (you know everyone will choose it).  For this to be the case, a deck needs good matchups against all possible decks but itself (which is a very strong assumption).  

If players aren’t identical, then you can have a situation in which there is generally a small set of  “best decks for Rich Shay� because, for Rich Shay, it is a dominant strategy to play Control Slaver (+- 5 maindeck cards from a standard maindeck and +-10 cards from a standard sideboard) essentially regardless of the metagame.  Note that it probably won’t be a single “best deck� as much as a number of discrete decks that are variations on core deck (to borrow Mike Flores’ wording, above).

[Brutha]

There are a million caveats that apply to this sort of analysis.  We left out the chance that a player has an upset tummy during the game and can't concentrate, the chance that the road from St. Louis to Chicago will be struck by a meteor so Vroman can't win the next Star City there, and so on.  We reduced the complexity of the problem significantly for analysis.  In fact, that is true by definition

You have a theory that may be consistend, but it produces significant wrong results. If you leave the skill out your theory is consist only of some metaphysical assumptions, because skill matters. And skill is no random factor. Skill is certainly predicable, and therefore better analysable than a factor like a meteor that hits Vroman.
That meteor would be a random factor, but skill is not. By the way if a player can't concentrate that is a lack of skill.

If players are identical, the effect of skill is captured in knowing how each of the decks match up against each other.  So each player’s individual skill doesn’t matter.  I would assume that if all players had no idea how to play GrimLong (and consequently couldn’t beat anything with it because they couldn’t figure out how to put together a Storm kill), GrimLong wouldn’t be played at all. 

If I try to get matchup data I propose a thought experiment.
I give 2 team meandeck players a Gifts built and Stax built. They switch the decks after each match. They play 100 matches. Then I would gain a knowledge of the matchup.

On the other hand I take the the same decks to a local shop in which I meet two players who know the magic rules but have never before played T1 in their lives.
They shall also switch the decks after each match and they play also 100 matches.

I would think that the two players in the local shop get a drastically different matchup than the two meandeck players.

Assuming that you know the outcome of a truly random variable beyond the probability distribution is similar to “All ghosts are bodybuilders.  There are no ghosts.â€?  This is logically true but because there are no ghosts, the first statement doesn’t imply anything at all.

Logically you don't know whether it is true or false.
"There are no ghost and therefore all ghost are bodybuilders is true" but “All ghosts are bodybuilders.  There are no ghosts.â€? can be true as well as false because you can conclude a right statement from a false statement.

Quote tags fixed

[Elric]

Assuming that you know the outcome of a truly random variable beyond the probability distribution is similar to “All ghosts are bodybuilders.  There are no ghosts.�  This is logically true but because there are no ghosts, the first statement doesn’t imply anything at all.

Logically you don't know whether it is true or false.

I think you know exactly what I meant, which was: If there are no ghosts, then "all ghosts are bodybuilders" is always a true statement but it doesn't tell you anything more than "there are no ghosts" does alone.

As for matchup data: 100 matches isn't that big of a sample size.  If I told you that Deck A won 56 out of 100 matches against Deck B that statistic by itself isn't enough to conclude with a high degree of confidence that Deck A has a >50% matchup against Deck B.

Also, I have no idea what you are getting at by your thought experiment, unless you are trying to say that skill matters even when player skill is identical across the board.  That's correct, but each player's individual skill doesn't matter, since it's the same as that of every other player.  If all players are identical and you know how a matchup plays out, then you know how it plays out between any two players.