Query: Do you think there is a lack of consensus about Basic Propositions In T1?

[rakso]

I'm fairly certain that Team Paragon was the original T1 team that included members of Shortbus and Meandeck.  The team split mostly due to areas which people came from...namely the northeast consisted of Meandeck and Shortbus is...wherever they are 0_0...

Yeah, Paragons of Vintage split into Paragon A (Short Bus, largely the members near Virginia, plus new recruits), Paragon B (everyone else, from Smeny to Jaypee), and the remaining third who vanished into this oblivion called real life.

Ironically (responding to your initial post), Steve, I am playing in Manila tournaments for once, but do not expect that to last given I am going to begin work about the same time you are.

[rakso]

JD had a good point when he said that we are really more interested in winning an argument than in anything else

As a serious reply, I think there was a drop in the quality of discussion when there was a drop in the number of experienced people writing Type I columns on Star City.

Forum posts are shorter, have a specific context, are often written with just a brief period for thinking, and yes, can degenerate into pissing contests. There are also gaps in topics covered purely by forum discussion. I'd like to think serious discussion began when "primers" were compiled, and that predates Mana Drain's existence.

Yes, some people discuss things with different implicit frameworks, but I always thought the more comprehensive, more thorough articles provided the easiest frames of reference that served as foundations for common discussion. I also thought they allowed (credible) players from lesser known areas to showcase their thought process without getting immediately flamed on a forum.

[vroman]

although Im mentioned in here, I still dont really understand what this thread is about. maybe bc I wasnt seriously playing vintage until 05.

[PucktheCat]

This isn't, of course, to say that Gilded Claw is a good deck. It isn't.

I read your entire post, appreciating and agreeing with the gist of it. What is the point of adding this on? Your post contradicted several of the main arguments used against his deck, and then you reverse and take a random shot at it. Justify your position.

Justify my position?  It's simple.  There are good reasons to argue that the presence or lack of 4-ofs, on its own, isn't a reliable indicator of a deck's quality in Vintage.  But that doesn't make any particular deck good.  Gilded Claw isn't good.  It is a variation on a skeleton that has been around for a while, and I have played against decks like it.  The flaws in its construction are more fundamental than a lot of 1 and 2-ofs.

Leo

[Dozer]

You want an environment, where every deck is an established deck, where every deck follows a certain process, where every deck is composed of the best cards, the optimal build.

The mistake you make is that you assume there's an optimal build. There isn't.

You assume that there is a best deck.

There is no "best" deck. Certain decks don't work in certain metagames. That's all agreed on, and besides the point. The thing is: decks can be mis-constructed. A simplified example would be a Gifts deck that runs 2 Impulse, 3 Brainstorms. That is a clear mistake. If anybody denies that, he is working with different principles than I am. And he has to explain them. Just saying "it's unconventional, and it might be good" is NOT enough. You have to prove this. I am open to innovation and new ideas. But a deckbuilding mistake remains a deckbuilding mistake, not innovation -- unless you convince me it's not a mistake.
People right now often don't take the time to explain why they deviate from the established paths, but instead bash those who say they should have stuck to the established path as "not open for new ideas". Often though, they cannot clearly point out the advantages of their path over the established one, whereas the "old guard" always can argue their side well.

Maybe, just maybe, a deck is good in one locale, and bad in another?

Very true, but a mis-built deck will always be worse than a well-built one, wherever it is played. Even if the misbuilt one wins the tournament. That is the nature of Vintage. A Gifts deck with 2 Impulse and 3 Brainstorms can win tournaments, but it still has a glaring mistake in it. We need to realize across the board that the winning decks are not necessarily the best-built ones. That's also where some flame-wars come from: If anyone critizes a winning deck, he always, *always* gets the reply "but it won". The reply "I accept your success, but I think you could have built your deck better" is almost never accepted, but instantly dismissed as envy, ridiculing, disrespect or whatever. But it still can be true.

Dozer

/edit re: Best deck. Klep's right, but there still is no best deck in a vaccum. There is always a best deck for any given situation, but there is no "best deck, period".

[Klep]

Just to set something straight, there is in fact always a 'best deck.'  The best deck for a tournament is the deck that has the greatest probability of winning the tournament.  Such a deck always exists.  There is no guarantee that someone will be playing the best deck, nor is there a guarantee that if someone is playing the best deck, that that person will win the tournament.  It may even be (and quite likely is, most of the time) infeasible to determine what the best deck actually is.  Nevertheless, it is a certainty that it does exist, whether you know what it is or not.

[rakso]

Just to set something straight, there is in fact always a 'best deck.'  The best deck for a tournament is the deck that has the greatest probability of winning the tournament.  Such a deck always exists. 

With the decrease in writing and now coverage, though, I'd like to think it gets harder and harder to even identify the actual best deck in a tournament, especially when there's an upset when the Top 8 finishes.

[ROLAND]

Why are we all speaking at each other instead of to each other?  Why is there such a disensus when it comes to basic propositions in this format?  What's going on?  How can we improve this?

The problem is that we all spend large quantities of money on the cards we use to build decks. This causes us to become emotionally attached to our cards because in many cases we put in long hours of work to pay for them. 

When someone says "This deck sucks, or that deck is washed up!" We take offense to it because now we have to invest more time and money into another deck. 

The other problem is the lack of sportsmanship among the type 1 players. (This is based on my experiences in my own area. So don't flip out.)  Some of the players in my area get pissed off when my nether void deck stomps the current hot deck in type one.  (I'm not saying nether void is better than any deck in the current metagame, it's not) They simply can't accept this fact, and start to complain and make excuses.

As far as best decks go, you can get all logical an calculate the percentages, etc.  You can playtest until your blue in the face, but if you and your deck can't perform when the time comes it really doesn't matter what you play.

The debate isn't whether or not your deck is better, it's your play skill. It's knowledge of the field and most importantly your ability to guess what you opponent will do next. And the ability to guess consistently in order to win.  Not to mention the 9 million other factors you have to take into consideration.

The fact is we need to be mature enough to step back and say " This isn't personal this is about Magic!" We need to realize this is about finding the best solution to the current metagame, and focus on that.   We need to be open to everyone's ideas and not jump down their throats when they suggest something off the wall.

Furthermore, You win some, you loose some. On any given day anybody could win the tournament. No matter how much preparation is involved, it's all in the cards. If the luck of the draw isn't on your side, then you probably won't win. Accept that fact maturely and move onto the next game.

Just some thoughts,

Roland

[Elric]

Just to set something straight, there is in fact always a 'best deck.'  The best deck for a tournament is the deck that has the greatest probability of winning the tournament.  Such a deck always exists.  There is no guarantee that someone will be playing the best deck, nor is there a guarantee that if someone is playing the best deck, that that person will win the tournament.  It may even be (and quite likely is, most of the time) infeasible to determine what the best deck actually is.  Nevertheless, it is a certainty that it does exist, whether you know what it is or not.

If you believe magic follows mixed strategy equilibrium (a concept from game theory) then there may be a best deck once you see what decks people at a tournament are playing but no best deck beforehand.

Imagine that you have three choices of decks to play: Rock, which wins 80% of its matches against Scissors (and 40% against Scissors); Scissors, which wins 70% of its matches against Paper (and 20% against Rock); and Paper, which wins 60% of its matches against Rock (and 30% against paper).  Each deck is 50/50 against itself and no other factors matter (this is of course unrealistic). 

Then in advance all you can say is that optimal play is to play Rock 1/6th of the time, Scissors 1/3 of the time and Paper ½ of the time (I think this is a fairly surprising result—that Paper, which would be the worst deck if each were played in equal percentage, is the most played deck in equilibrium).  The day of the tournament it’s highly unlikely that even if everyone uses this plan there will be exactly this percentage of decks, in which case one of these three decks will be the “best deck� on that day.  However, if the tournament were to be played over, people should make random choices according to the same rule as before- the revealed "best deck" is just the result of chance. 

[PucktheCat]

Elric: Thank you for making the point I was trying to make, but doing it much better than I did.

I think there is no doubt that the equilibrium concept you describe applies to most metagames that we refer to as "healthy."  I would further submit that it has substantial applicability at the level of individual card choices within established archetypes, especially with metagame slots and sideboards.  Think about Solemn Simulacrum in Uba Stax.  That card is awesome if you see Stax all day, and merely average to below average in most other matchups.  By changing a few cards like that in a deck you can reposition it within the metagame.  That kind of variation can have similar effects to actually switching archetypes, on a more incremetal scale.

Leo

[Klep]

If you believe magic follows mixed strategy equilibrium (a concept from game theory) then there may be a best deck once you see what decks people at a tournament are playing but no best deck beforehand.

Actually the decks in the tournament are the single most important factor as to what the best deck is, and this is why figuring out which deck is the best deck is so hard.  It requires prescience (the best deck before the tournament is the same as the best deck during the tournament).  Without knowing ahead of time exactly what decks everyone will be playing, you can never be 100% certain which deck is best; all you can do is make an educated guess.  That's the whole point of metagaming.  To determine, based on your best information about what people will be playing, what deck you should play.  By doing that you are looking for the best deck.  It is a game, but for a single tournament, you can't play a mixed strategy.  I once thought of writing an article in which I did game theoretic analysis of the metagame to help guide players in selecting a deck to play, but I swiftly realized it was far too complex to really attempt.

[AmbivalentDuck]

The main reason for the lack of consensus is the increase in overall power.

-As an honest question: how insane did a hand in Keeper need to be for a bad player to absolutely roll a good one?  Now something to compare that with: a bad player playing Belcher with two maindeck copies of Grey Ogre because they "roxor against Fish."  He's got a decent shot of winning against any hand that doesn't include Force of Will.

-A proposition: Tempo is the key change.  Back a while ago I posted a widely flamed deck involving some Extracts.  A first turn Extract can do evil things against half of the last SCG top 8.  As decks become more focused, "random" cards like Extract, Nezumi Shortfang, and Kataki shine.  Disruption and speed are better than ever before, that's most of why pure aggro is dead. When's the last time pure Workshop Aggro got a T8 showing?  So much the worse for Stompy.  Food Chain only sticks around because of the combo kill and utility of Gempalm Incinerator and Goblin Vandal.

-An observation: The power level of the format has increased unilaterally.  Vintage accumulates power.  Every time Wizards print a less disuptable kill (storm), a new accelerator (Chrome Mox), a new mana fixer (the Fetches), or a new draw engine (Dark Confidant), the game turns on its head.  And not only are our kills better, our disruption is better.  For any deck you can name, I can name a card (in some cases a pair) that you CANNOT win through.

Arcane Lab
Moat
Planar Void
Aether Flash
True Believer
Null Rod

And the list goes on.  The game has gotten more swingy and more defined by huge swings in tempo. That means an intelligent "n00b" (a mediocre extended player) can easily beat Smennen three to four games out of ten with the right list.

-My point:  It's hard to find a Nash equilibrium when the "best choice" can get randomly owned by n00bs playing last year's Belcher build.  So while Klep is VERY right in theory, it will never happen in practice.  Also as the power level rises, some sacred cows start losing their sheen.  How many times have we heard Randy Bueler call Mana Drain the worst card in a deck?  Humans may be argumentative by nature, but they're also creatures of habit.  How long did Oscar Tan hold onto the deck after Psychatog was clearly better?  I'm not poking at anyone, I'm just saying that it would be very nice if we had a machine to pop our decks into that would clearly output "This deck wins 51.2% of the time against the last SCG T8."  But we don't.  New cards continue to be undertested that could revolutionize the format, though most will not even if tested.  At the same time, mediocre cards win a large enough percentage of the time through sheer randomness that it's harder than ever to *know* what's good objectively.

-A "solution:" Transparency in innovation and rapid, logged testing to *PROVE* which "Basic Propositions" still hold true.  Set up a small javascript program here on TMD to collect *all* game results that people are willing to submit.  Weigh out individual player skill by keeping track of individual win records and rank decks.  Why will this work?  Any newly submitted deck will start out with a 50% record, putting it near the top of the list.  Losing 4-5 times will be more than sufficient to bump it down.  I have 20 minutes a day to prove that bad decks are bad.  If they involve Grey Ogre, the mods can delete them just as quickly as they'd lock a Grey Ogre post now.  If an idiot starts spamming ficititious results, ban his IP just as if he started spamming the boards.  Delete decks with a record lower than 45% after a week of testing.  This should take no more than 3MB of server space and I'd be happy to write it over Xmas.  Also that people play bad decks at tournaments all the time: it's called "sealed deck."  Tuning bad decks doesn't reduce your playskill, it helps you to better understand how to make a bad deck better.

For those who have Paragons A and Paragons B, feel free not to take part in such a thing.  But I think this would be a great way to eliminate disagreements over "Basic Propositions" by creating numerical fact that "n00bs" can be referenced to. 

[Klep]

-My point:  It's hard to find a Nash equilibrium when the "best choice" can get randomly owned by n00bs playing last year's Belcher build.  So while Klep is VERY right in theory, it will never happen in practice.

Two things.

You aren't looking for a Nash Equilibrium when selecting a deck, because a Nash Equilibrium won't necessarily give you your maximum potential payoff.  It's entirely possible, in fact, that the "metagame game" doesn't even have a Nash Equilibrium (EDIT: in pure strategies, obviously).

The other thing is that Magic is a highly non-deterministic game due to all of the random factors that come into deciding who wins a game.  Thus, the definition of the "best deck" does not specify that the best deck will win, only that it has the highest probability of doing so.  Things like being a terrible player and/or having awful luck are therefore accounted for in the definition.  If by some chance you happen to stumble upon the best deck for a tournament, it's still entirely possible that you will scrub out; just less likely than if you had another deck.

[rakso]

Disruption and speed are better than ever before, that's most of why pure aggro is dead. When's the last time pure Workshop Aggro got a T8 showing? 

Over dinner, Smeny elaborated on his basic proposition that Type I is just about who resolves Yawgmoth's Will first. So I said, that creates four corollaries:

Combo: Strives to resolve Will before the opponent can do anything.

Control: Strives to stop the opponent from doing anything relevant before it resolves Will.

Aggro-Control: Strives to stop the opponent from resolving Will before it wins.

Aggro: Sucks.

[jpmeyer]

"I can tell that it's bad just by looking at it" is shorthand for "When I look at the list, I see numerous aspects to it which completely go against standard deckbuilding and/or theory practices and I can't understand why those fundamental rules were broken."  So if we use that Gilded Claw list, I could take something like the fact that it runs two Metalworkers and get confused, since it seems like the kind of card that you would run either four of or zero of since its utility decreases greatly after the first few turns unless the deck is running Stroke of Genius or something.  Or, if the whole point of Metalworker is to Intuition for Metalworker/Staff/Crusher, I could see running the singleton, but if that's the case it looks like there is a needlessly wasted slot.

There's also that the one Mind's Eye.  I can see that you could Tinker or Intuition/Welder for it, but I can't see when you'd Tinker for it over something like Mindslaver or Sundering Titan (or the Darksteel Colossus which I can't figure out why it's not in the deck) or why you'd put it in your Intuition pile when you could do something like Crucible/Strip/Trinisphere or Metalworker/Staff/Crusher.

I should also point out that these are the impressions given by the card choices and thus that decisions like these need to be throughly explained not just in terms of why you made the choice to build the deck in this way but also as to why this way is better than the commonly accepted way.  Without that second explanation, you get the inevitable "I can see that it's bad" and "Just test it!"  Breaking rules requires attention to be drawn to the rule-breaking process or else it is simply assumed to be a mistake.

[AmbivalentDuck]

-My point:  It's hard to find a Nash equilibrium when the "best choice" can get randomly owned by n00bs playing last year's Belcher build.  So while Klep is VERY right in theory, it will never happen in practice.

Two things.

You aren't looking for a Nash Equilibrium when selecting a deck, because a Nash Equilibrium won't necessarily give you your maximum potential payoff.  It's entirely possible, in fact, that the "metagame game" doesn't even have a Nash Equilibrium (EDIT: in pure strategies, obviously).

The other thing is that Magic is a highly non-deterministic game due to all of the random factors that come into deciding who wins a game.  Thus, the definition of the "best deck" does not specify that the best deck will win, only that it has the highest probability of doing so.  Things like being a terrible player and/or having awful luck are therefore accounted for in the definition.  If by some chance you happen to stumble upon the best deck for a tournament, it's still entirely possible that you will scrub out; just less likely than if you had another deck.

The presence or lack of determinism doesn't effect the (dis)presence of a Nash equilibrium.  Not that I think we could ever find it if one did exist...evolution takes millions of years, Wizards releases a new set 3-4 times a year.  All I'm saying is that the "optimum" meta is harder to find because of the amount of randomness.  You have to play more games to find the real odds.  As far as the highest potential payoff...the Nash equilbrium directly dictates ratios such that every deck has an equal chance. (EDIT: Clarity)

[Klep]

The presence or lack of determinism doesn't effect the (dis)presence of a Nash equilibrium.  Not that I think we could ever find it if one did exist...evolution takes millions of years, Wizards releases a new set 3-4 times a year.  All I'm saying is that the "optimum" meta is harder to find because of the amount of randomness.  You have to play more games to find the real odds.  As far as the highest potential payoff...the Nash equilbrium directly dictates ratios such that every deck has an equal chance. (EDIT: Clarity)

First, I would encourage you to read my post again, and to take special notice of the fact that I made two distinct points.  Neither point suggests that a Nash Equilibrium's existence is affected by the determinism of the game, nor do I assert that there is definitely not a Nash Equilibrium.  I merely conjectured that a lack of one is possible.

Secondly, it is clear that you do not really understand the concept of a Nash Equilibrium.  An NE does not in any way guarantee the highest possible payoff for any one player, nor does it guarantee that all players have an "equal chance" of "winning" the game.  It merely guarantees that if a game is at a Nash Equilibrium, no one player can improve his payoff by changing his strategy.  Players at an NE may have different payoffs, and they may have payoffs which are lower than their optimal payoff.  Finding the best deck is not the same as finding a Nash Equilibrium because the strategies (decks) other players choose may result in your best choice not being a Nash Equilibrium.

[Dante]

The main reason for the lack of consensus is the increase in overall power.

-As an honest question: how insane did a hand in Keeper need to be for a bad player to absolutely roll a good one?  Now something to compare that with: a bad player playing Belcher with two maindeck copies of Grey Ogre because they "roxor against Fish."  He's got a decent shot of winning against any hand that doesn't include Force of Will.

-A proposition: Tempo is the key change.  Back a while ago I posted a widely flamed deck involving some Extracts.  A first turn Extract can do evil things against half of the last SCG top 8.  As decks become more focused, "random" cards like Extract, Nezumi Shortfang, and Kataki shine.  Disruption and speed are better than ever before, that's most of why pure aggro is dead. When's the last time pure Workshop Aggro got a T8 showing?  So much the worse for Stompy.  Food Chain only sticks around because of the combo kill and utility of Gempalm Incinerator and Goblin Vandal.

-An observation: The power level of the format has increased unilaterally.  Vintage accumulates power.  Every time Wizards print a less disuptable kill (storm), a new accelerator (Chrome Mox), a new mana fixer (the Fetches), or a new draw engine (Dark Confidant), the game turns on its head.  And not only are our kills better, our disruption is better.  For any deck you can name, I can name a card (in some cases a pair) that you CANNOT win through.

Arcane Lab
Moat
Planar Void
Aether Flash
True Believer
Null Rod

And the list goes on.  The game has gotten more swingy and more defined by huge swings in tempo. That means an intelligent "n00b" (a mediocre extended player) can easily beat Smennen three to four games out of ten with the right list.

-My point:  It's hard to find a Nash equilibrium when the "best choice" can get randomly owned by n00bs playing last year's Belcher build.  So while Klep is VERY right in theory, it will never happen in practice.  Also as the power level rises, some sacred cows start losing their sheen.  How many times have we heard Randy Bueler call Mana Drain the worst card in a deck?  Humans may be argumentative by nature, but they're also creatures of habit.  How long did Oscar Tan hold onto the deck after Psychatog was clearly better?  I'm not poking at anyone, I'm just saying that it would be very nice if we had a machine to pop our decks into that would clearly output "This deck wins 51.2% of the time against the last SCG T8."  But we don't.  New cards continue to be undertested that could revolutionize the format, though most will not even if tested.  At the same time, mediocre cards win a large enough percentage of the time through sheer randomness that it's harder than ever to *know* what's good objectively.

-A "solution:" Transparency in innovation and rapid, logged testing to *PROVE* which "Basic Propositions" still hold true.  Set up a small javascript program here on TMD to collect *all* game results that people are willing to submit.  Weigh out individual player skill by keeping track of individual win records and rank decks.  Why will this work?  Any newly submitted deck will start out with a 50% record, putting it near the top of the list.  Losing 4-5 times will be more than sufficient to bump it down.  I have 20 minutes a day to prove that bad decks are bad.  If they involve Grey Ogre, the mods can delete them just as quickly as they'd lock a Grey Ogre post now.  If an idiot starts spamming ficititious results, ban his IP just as if he started spamming the boards.  Delete decks with a record lower than 45% after a week of testing.  This should take no more than 3MB of server space and I'd be happy to write it over Xmas.  Also that people play bad decks at tournaments all the time: it's called "sealed deck."  Tuning bad decks doesn't reduce your playskill, it helps you to better understand how to make a bad deck better.

For those who have Paragons A and Paragons B, feel free not to take part in such a thing.  But I think this would be a great way to eliminate disagreements over "Basic Propositions" by creating numerical fact that "n00bs" can be referenced to. 

Don't take this the wrong way, but frankly, I call "bullshit" on this post.  Let me explain - I don't mean in that it's stupid and has no merit and is full of s--t, but merely that some of your assertions are incorrect and the rest is confusing and could be explained more clearly.

Not sure what your point in the first "section" about the bad player playing Belcher with 2 Grey Ogres in it and rolling good players.  If it was that Vintage is made up of powerful decks that even noobs can mis-tweak and still win, that's nothing new.

As for your next paragraph about tempo and Extract, let's break it down-

SCG Chicago Top 8:

Uba Stax - not affected
Stax - not affected
UW Fish - not affected
Grim Long - majorly affected, only 1 win condition
Oath x2 - still has 1 big creature
Belcher - not affected
Gifts - partially affected, a good player can go off either way (colossus or tendrils), let's call this 1/2 affected.

So out of the top 8, only 1.5 decks are affected by Extract.  In fact, you have to go down to the 24th place deck (Gifts with only 1 Tendrils as a win condition) to find the next deck that really cares about 1 Extract, even first turn.  Extract isn't tempo, it's just a waste of a turn, at least vs the top part of the last SCG field.

Again, your point in the "observation" paragraph is not clear.  It's a list of hosers, most of which, even if you get them out vs the deck you're trying to "hose", you can still lose.  For example, Null Rod vs Belcher (welder or naturalize) or anything vs Long (bounce), Planar Void (not good vs anything), etc.  Decks have been winning through hate that was supposed to "destroy" that particular deck for awhile now - or was that your point?

I think the whole point of your post has do with randomness really skewing the validity of results and not having enough points in the data set to truly be statistically relevant.  If that's it, please head down that path.  If not, please correct me.

The whole Nash equilibrium business is just academic posturing - if we're really going to talk Nash, there are some conditions that need to be met, and also, it's almost  impossible to prove anything with something like a Magic deck because of the HUGE number of actions (i.e. decisions).  It's not as simple as your math examples where you can keep the price fixed, lower it, or raise it or some other simple 2- or 3-action game.  Not that higher-level academic thought isn't worthwhile, I just think you guys need to come back and relate it to Magic each post a long the way a little more.  Maybe it's just me, feel free to let me know.

Bill

[jpmeyer]

The whole Nash equilibrium business is just academic posturing - if we're really going to talk Nash, there are some conditions that need to be met, and also, it's almost  impossible to prove anything with something like a Magic deck because of the HUGE number of actions (i.e. decisions).  It's not as simple as your math examples where you can keep the price fixed, lower it, or raise it or some other simple 2- or 3-action game.  Not that higher-level academic thought isn't worthwhile, I just think you guys need to come back and relate it to Magic each post a long the way a little more.  Maybe it's just me, feel free to let me know.

Bill

As was discussed in #tmd earlier:

<jpmeyer> game theory is the sort of thing that people only talk about when they are trying to sound really, really hardcore
<jpmeyer> nobody ever uses game theory without political intent
<jpmeyer> i will apply game theory to this problem to show both how to win, but more importantly, to show how gigantic my cock is
<jpmeyer> and how tiny yours is

[Godot]

In fact, you have to go down to the 24th place deck (Gifts with only 1 Tendrils as a win condition) to find the next deck that really cares about 1 Extract, even first turn.  Extract isn't tempo, it's just a waste of a turn, at least vs the top part of the last SCG field.

Actually the deck still has two win conditions since it runs Burning Wish--a single Extract does absolutely nothing.  Hate to nitpick, but I had to point that out.

[Elric]

If you believe magic follows mixed strategy equilibrium (a concept from game theory) then there may be a best deck once you see what decks people at a tournament are playing but no best deck beforehand.

Actually the decks in the tournament are the single most important factor as to what the best deck is, and this is why figuring out which deck is the best deck is so hard.  It requires prescience (the best deck before the tournament is the same as the best deck during the tournament).  Without knowing ahead of time exactly what decks everyone will be playing, you can never be 100% certain which deck is best; all you can do is make an educated guess.  That's the whole point of metagaming.  To determine, based on your best information about what people will be playing, what deck you should play.  By doing that you are looking for the best deck.  It is a game, but for a single tournament, you can't play a mixed strategy.  I once thought of writing an article in which I did game theoretic analysis of the metagame to help guide players in selecting a deck to play, but I swiftly realized it was far too complex to really attempt.

The idea of mixed strategy equilibrium is that everyone will be going through the same process of trying to find the optimal deck to play.  The way players choose which deck to play is what could be a Nash equilibrium, not the specific metagame that results from one set of these choices.  If you look at the specific rock-paper-scissors metagame I used as an example and only know that everyone else is playing the equilibrium strategy (Rock 1/6th of the time, Scissors 1/3 of the time and Paper ½ of the time) then there is no best deck for you to play. 

Let’s say you know the outcome of everyone else’s decisions and know that even though people were choosing (Rock 1/6th of the time, Scissors 1/3 of the time and Paper ½ of the time) that the actual distribution of decks at the tournament (due to random chance) is going to be 10% Rock, 30% Scissors, 60% Paper.  In this case the best deck to play is clearly Scissors.  However, given that you can’t tell this before the tournament, there is no best deck beforehand. 

Magic won’t actually follow mixed strategy equilibrium for a number of reasons (play skill matters, lots and lots of required information isn’t known, etc.) but as a general way to think about things I think this provides useful insights. 

Here’s my take on the Ambivalent Duck-Klep exchange:
In order to have a well defined Nash equilibrium you’d have to know decks’ match win percentages against each other.  Since matchup percentages are never very close to 100% due to “type 1 brokenness� the variance of testing results is high and you’re never going to statistically figure out what an equilibrium would look like before Wizards releases a new set that shakes it up. 

A specific tournament’s metagame doesn’t need to be a Nash equilibrium for the concept to apply.  It’s almost certainly impossible for a 100 person tournament to have no best deck after deck choices are revealed, but that doesn’t mean that there was a best deck in advance since everyone has to choose the deck he or she is playing simultaneously.  In other words, once you see the decks at a tournament everyone can do better by changing strategies but no one could do better by changing how they select decks in advance.

Klep is correct when he says that the best deck is only the “best� in a probabilistic sense.  In the case when all players have the same set of deck choices and the same resulting payoffs, a Nash equilibrium will guarantee that for each player the expected payoff to playing each deck is to win 50% of his matches.

Edit: typos

[Vegeta2711]

I believe I can sum this up for everyone not involved in the equilibrium thingie with no further complaints or posts needed.

ENGLISH, MOTHERFUCKER! DO-YOU-SPEAK-IT?

[Klep]

The idea of mixed strategy equilibrium is that everyone will be going through the same process of trying to find the optimal deck to play.  The way players choose which deck to play is what could be a Nash equilibrium, not the specific metagame that results from one set of these choices.  If you look at the specific rock-paper-scissors metagame I used as an example and only know that everyone else is playing the equilibrium strategy (Rock 1/6th of the time, Scissors 1/3 of the time and Paper ½ of the time) then there is no best deck for you to play. 

You can't really play a mixed strategy in deciding your deck for a single tournament, and ultimately that's what you're doing every time.  You can't have a deck that is, say, Control Slaver 50% of the time, Stax 25% of the time, Gifts 15% of the time, and Belcher 10% of the time (at least, not without savage cheats).  Thus, the "metagame game" is decided in pure strategies and there may not be a Nash Equilibrium.  What I was trying to tell Ambivalent Duck is that though it's possible you may find an NE as part of looking for the best deck, that isn't what you are looking for.

Let’s say you know the outcome of everyone else’s decisions and know that even though people were choosing (Rock 1/6th of the time, Scissors 1/3 of the time and Paper ½ of the time) that the actual distribution of decks at the tournament (due to random chance) is going to be 10% Rock, 30% Scissors, 60% Paper.  In this case the best deck to play is clearly Scissors.  However, given that you can’t tell this before the tournament, there is no best deck beforehand.

No, there is a best deck beforehand, you just don't know what it is.  Like I said, knowing the best deck requires prescience, which is why figuring out what it is is so hard.

A specific tournament’s metagame doesn’t need to be a Nash equilibrium for the concept to apply.  It’s almost certainly impossible for a 100 person tournament to have no best deck after deck choices are revealed, but that doesn’t mean that there was a best deck in advance since everyone has to choose the deck he or she is playing simultaneously.  In other words, once you see the decks at a tournament everyone can do better by changing strategies but no one could do better by changing how they select decks in advance.

How many times do I have to repeat this: there is always a best deck. Always. The only question is whether you know what it is, not whether it exists.  Once all other players have chosen their deck, the best deck before the tournament is the same as the best deck after the tournament.  It is only your foresight (or lack thereof) which might tell you that they are different.  The identity of the best deck is actually independent of the tournament results.

Klep is correct when he says that the best deck is only the “bestâ€? in a probabilistic sense.  In the case when all players have the same set of deck choices and the same resulting payoffs, a Nash equilibrium will guarantee that for each player the expected payoff to playing each deck is to win 50% of his matches.

A Nash Equilibrium guarantees no such thing.  An NE could exist such that player A will win 70% of the time, player B will win 30% of the time, player C will win 40% of the time, etc..  There is nothing about a Nash Equilibrium which demands all players have the same payoff. Now if all players are playing the same deck, they may all have a 50% chance of winning a match (assuming equal skill), but that is not a function of an NE, but merely what happens when you take all non-random variables out of the equation.


EDIT: Actually on topic: I think this recent debate has shown us what the problem is, with regards to the original thread topic.  Concepts that the old guard intuitively understand are not known to or misunderstood by the new players entering the format.  If I ask JP, for example, what the best deck is, he knows what I'm talking about whereas this thread has made clear that many new players don't fully grasp it.  I think this problem stems from the fact that so many fundamental theory articles have already been written (Everything is a Time Walk, Who's the Beatdown, etc.).  The old guard was learning to play Magic when they were being written, and so took the lessons therein to heart.  New players coming in now are standing on the shoulders of giants with regards to theory, but haven't bothered to check that their footing is sure by reading up on what has come before.

Also, JP, I clearly have an enourmous penis.

[Elric]

Klep- You can’t play 50% Gifts, 10% Belcher, 40% Stax but that doesn’t matter.  It’s a mixed strategy equilibrium of choosing pure strategies (the way each player decides which deck to play is the mixed strategy, the decks themselves are pure strategies).  If your opponents are choosing their decks with the correct mixed probability all you know in advance is that you can't pick a best deck without seeing their choices.

If there’s no way to figure out what it is beforehand, then it might as well not exist.  It’s really irrelevant whether or not a best deck exists beforehand if there’s no way to figure it out (mixed strategy equilibrium assumes simultaneous choices so if you're assuming mixed strategy equilibrium by definition you can't see opponent's choices in advance). 

This is like saying in Rock-Paper-Scissors, if your opponent is playing each strategy with equal probability the “best strategy� is to play whatever beats what your opponent is going to play.  While this would be true if you could do it, you can’t do it so it doesn’t mean anything. 

You also missed the point when I said “In the case when all players have the same set of deck choices and the same resulting payoffs, a Nash equilibrium will guarantee that for each player the expected payoff to playing each deck is to win 50% of his matches.�

Each deck that is played is expected to win 50% of its matches in this situation- period.  If these conditions are satisfied, each player would be using the same strategy for choosing decks which implies that they have the same win percentage.  That isn’t to say that this situation describes reality- this will never be the case in general because the assumptions aren’t satisfied- all players don’t have the same information, the same set of deck choices, and the same resulting payoffs. 

As for this recent debate implying that new members don’t understand concepts that the old guard intuitively understood: are you trying to say that I don’t understand what a best deck is?  If so, you can say that straight up instead of referring to the halcyon days of your youth.  I read all of those articles when they were being written.   

[Klep]

Klep- You can’t play 50% Gifts, 10% Belcher, 40% Stax but that doesn’t matter.  It’s a mixed strategy equilibrium of choosing pure strategies (the way each player decides which deck to play is the mixed strategy, the decks themselves are pure strategies).  If your opponents are choosing their decks with the correct mixed probability all you know in advance is that you can't pick a best deck without seeing their choices.

Right, you can't play a mixed strategy, so it's best to look at the game in terms of pure strategies, with each player  individually choosing a pure strategy.

If there’s no way to figure out what it is beforehand, then it might as well not exist.  It’s really irrelevant whether or not a best deck exists beforehand if there’s no way to figure it out (mixed strategy equilibrium assumes simultaneous choices so if you're assuming mixed strategy equilibrium by definition you can't see opponent's choices in advance). 

But it does exist, and the fact that it exists is of great foundational importance, and it is this point that I think new players are missing.  The fact that there is always a best deck means that you can metagame.  It's very simple, but critical.  If there is no best deck, then there is no point in planning ahead what you should play, because every deck has as good a shot as any other.  The existence of the best deck means that by planning ahead and trying to figure out what other people will be playing, you can make a deck choice that has the greatest possible chance of winning the tournament.

This is like saying in Rock-Paper-Scissors, if your opponent is playing each strategy with equal probability the “best strategyâ€? is to play whatever beats what your opponent is going to play.  While this would be true if you could do it, you can’t do it so it doesn’t mean anything. 

It means exactly what you just said.  The best strategy is to play whatever beats what your opponent is going to play.  If you can make an educated guess as to what your opponent is going to play and choose your own play accordingly, it greatly increases your chances of winning.

You also missed the point when I said “In the case when all players have the same set of deck choices and the same resulting payoffs, a Nash equilibrium will guarantee that for each player the expected payoff to playing each deck is to win 50% of his matches.�

  Ah, I missed where you said they all have the same strategies and resulting payoffs.  In that case yes they would all have a 50% chance of winning there if they all chose the same deck.  This could only happen if all players chose the same deck and were of equal skill (eliminating all non-random factors).  The concept of a Nash Equilibrium does not guarantee this, and it's entirely probable that not all players have the same deck choices and payoffs.  I, for example, could not play Uba Stax, and so do not have the same set of strategy choices as Vroman. In more competetive play, a good example would be a GP Rich Shay played in last year where he dropped after round 5 because he only wanted to bump his rating high enough to qualify for Nats.  His payoffs were clearly different from people who entered the GP with the intent to win it.
  I don't think this situation would be a Nash Equilibrium in most cases however, because if N-1 players choose to play deck A, then the Nth player could choose the deck that walks all over deck A and have a better payoff.  The only situation where this is an NE is in a degenerate metagame where there is no deck that can beat the best deck, and the best deck is widely recognized.  Bannings would swiftly ensue.

I recommend taking further discussion of game theory to pm, because i'd like to see this thread back on track.

[AmbivalentDuck]

{Snip}
Not sure what your point in the first "section" about the bad player playing Belcher with 2 Grey Ogres in it and rolling good players.  If it was that Vintage is made up of powerful decks that even noobs can mis-tweak and still win, that's nothing new.

My point was that throwing two Grey Ogres into Belcher doesn't decrease its chances of winning enough to be obvious statistically without many games.  I don't think this was *as* true in past years.

As for your next paragraph about tempo and Extract, let's break it down-

SCG Chicago Top 8:

Uba Stax - not affected
Stax - not affected
UW Fish - not affected
Grim Long - majorly affected, only 1 win condition
Oath x2 - still has 1 big creature
Belcher - not affected
Gifts - partially affected, a good player can go off either way (colossus or tendrils), let's call this 1/2 affected.

So out of the top 8, only 1.5 decks are affected by Extract.  In fact, you have to go down to the 24th place deck (Gifts with only 1 Tendrils as a win condition) to find the next deck that really cares about 1 Extract, even first turn.  Extract isn't tempo, it's just a waste of a turn, at least vs the top part of the last SCG field.

It's a horrible topic to get into on this board, but I'd be happy to clarify "evil things" in PM.  One thing we can all agree on: Extract as an effect is much better now than it would have been 7 years ago.

Again, your point in the "observation" paragraph is not clear.  It's a list of hosers, most of which, even if you get them out vs the deck you're trying to "hose", you can still lose.  For example, Null Rod vs Belcher (welder or naturalize) or anything vs Long (bounce), Planar Void (not good vs anything), etc.  Decks have been winning through hate that was supposed to "destroy" that particular deck for awhile now - or was that your point?

I think the whole point of your post has do with randomness really skewing the validity of results and not having enough points in the data set to truly be statistically relevant.  If that's it, please head down that path.  If not, please correct me.

Correct, the ability to win through increasingly potent hate was my point.  The random hosers that are available are *much* better than they were while simultaneously being less playable because of how broad the field is and how likely it is that your opponent will simply win before they can come down.  Better examples would include Ivory Mask, Aether Flash, Moat, and (in some cases) Choke.  Despite the fact that these are wrecking balls against whole archetypes, they see little to no play.  The paradigm is to simply win better: my brokenness is better than your brokenness.  The problem is that we're both so broken that who's better takes a while to figure out.

The whole Nash equilibrium business is just academic posturing - if we're really going to talk Nash, there are some conditions that need to be met, and also, it's almost  impossible to prove anything with something like a Magic deck because of the HUGE number of actions (i.e. decisions).  It's not as simple as your math examples where you can keep the price fixed, lower it, or raise it or some other simple 2- or 3-action game.  Not that higher-level academic thought isn't worthwhile, I just think you guys need to come back and relate it to Magic each post a long the way a little more.  Maybe it's just me, feel free to let me know.

Bill

With payout being limited to the top 1-2 in a "small" tournament and the top 8 in a "large" tournament, I *can* push an argument that requires too many assumptions to be useful that a Nash Equilibrium involves reasonably equal chances of victory for the participants.  The problem is, tweaking 3-4 cards dramatically changes matchups.  Predicting a Nash Equilibrium is therefore impossible without gobs of time and no additional cardsets, if there even is one.  The debate is academic, but if Magic stagnated for a half a millennium while getting into top 8's was necessary for survival I would feel safe predicting that a stable "best deck" would emerge and a metagame involving that deck would reach a Nash equilibrium. 

The key here is the metagame, not the"best deck."  All players, n00bs and pros alike, benefit from ability to predict the meta and that's where a Nash equilibrium comes in.  IF a numerically based online meta were to emerge, infinite proxy tournaments became the norm, and everyone cared about nothing but winning, the online meta might be a good enough predictor that a stable meta could emerge.  Notice the two large ifs.

Which takes us back to basic propositions and what's not "clicking."  Until we figure out what a real "ideal" and fully advanced meta should look like with the cards we have available, we don't know what's still true.  Without clear data about "right and wrong," there are two ways to be wrong about basic propositions:
-It was never true.
-It's no longer true. (Synonymous with it *should* no longer be true)

We all agree that a lot of the traditional wisdom about mana bases went out the window with the fetchlands.  We all agree that the printing of the Judgment wish cycle affected the traditional wisdom about sideboards.  I think we can all agree that we're not omniscient and we're missing similar cards that should be changing our traditional wisdom.  The question is what a basic proposition is and what kind of card is necessary to break it.  Or conversely, whether traditional wisdom gets broken while "basic propositions" cannot be.  I'm just trying to clarify this, so we can talk about the same lines in the sand.

Broken Mana Well
0
Artifact
You may pay 1 life instead of paying the mana cost of spells you play.

Okay, obviously this would be pre-banned.  But, it would throw most of our "basic propositions" into disarray.  The question is what traditional wisdom actually constitutes a basic proposition and what it takes to break one.  That's an open question.  I don't think that any card, even the one above, should be able to break a basic proportion (as long as no resource is made truly free).  That definition dictates that unless we come up with a grand theory of card advantage, tempo, and everything else, there should be a lack of consensus. The only way of getting consensus requires numerical results because analytical results will never happen.  Assuming that "analytical" intuition is acceptable is ridiculous.

Encapsulated: There is a lack of consensus because not only is it unclear as to what traditional wisdom remains true, it's difficult to test and prove without a LARGE pool of empirical results.  Placing that burden on naysayers is ridiculous. I'd like to play in the most advanced format I can.  To do that, we need numbers. To get numbers we need ease in discovering them.  Once we have a common statistical reference, we'll all be on the same page.

[Elric]

But it does exist, and the fact that it exists is of great foundational importance, and it is this point that I think new players are missing.  The fact that there is always a best deck means that you can metagame.  It's very simple, but critical.  If there is no best deck, then there is no point in planning ahead what you should play, because every deck has as good a shot as any other.  The existence of the best deck means that by planning ahead and trying to figure out what other people will be playing, you can make a deck choice that has the greatest possible chance of winning the tournament.

You're just wrong that there's a way to find a best deck in advance if the situation is really mixed strategy equilibrium.  You'd have to be literally psychic to tell what deck I'm going to play if I really choose randomly in advance, just like you'd have to be psychic to know what I'm going to play in Rock-Paper-Scissors if I'm using a random number generator to determine my actions. 

If your opponents are really choosing decks randomly (with a given probability to pick each deck) (and in mixed strategy equilibrium they are doing exactly this) then once you know the chance that they will pick each deck you have no better ability to figure out what deck they are playing than you have a chance to call a Mana Crypt flip correct.  The answer “the best strategy for Mana Crypt is to call the coin the way it’s going to end up� doesn’t mean anything.

Here's the thing: magic doesn’t follow mixed strategy equilibrium.  There are a large number of people who in the short term are going to play a particular deck no matter what (personal preference, card availability, play skill, etc.).  If half of the field is going to play Cheap deck because they don’t own any expensive cards and Cheap deck should only be 20% of an equilibrium metagame you can obviously do better by playing something that beats Cheap deck.

People don’t all have the same information- everyone else may think they’re in a metagame in a rough equilibrium but if you create a new Tarpan deck that they don’t know about there will be no opportunity for the metagame to adjust before you wreak havoc with the Tarpans.

Furthermore, if you play a particular Complicated deck much better than most people do the deck may be rare because most players can’t win a game with it.  Then the metagame won’t react to be better against Complicated because almost no one can play it.  If you’re one of the few people who can play it well, you’re going to do better than you would if the deck were easy to play (and the metagame subsequently adjusted for it).

If you’re much, much better at Since1994 deck than every other deck you shouldn’t worry about trying to change to a new deck based on the metagame.  You should put in clearly superior cards, make a few changes (especially to the sideboard) based on the metagame, and then just play the deck.

I’d like to also add that people might simply disagree about the respective payoffs for different decks.  If I think deck A is clearly superior in every way to deck B and if you think the reverse then I’m going to devote sideboard slots in my deck to A over B and you’re going to do the reverse. 

Here’s a point that should be interesting: if my decklist is known, it’s “good� and I plan to play it in future tournaments it’s to my advantage to make everyone think that my deck is terrible.  If I plan to play a Different deck (and it beats my Current deck) then I should try to convince everyone that my current deck is strictly better than a deck in the existing metagame that has a better matchup against Different deck than my Current deck.

So the next time you look at a list and think it’s terrible, be warned: if the person who played that decklist has a “good deck� and wants to win with it again, they’re hoping you’ll think that way.  Most people have too much ego to try this strategy, but you never know…

Edit: typos

[jpmeyer]

Ii just realized that another reason why "just test it out!!!!" doesn't work as a defense for a deck is because the person who is being told to "just test it" will probably play in a way to minimize and/or avoid the "nonstandard" card choices.

Uba Stax is a GREAT example of this.  If you are a Workshop n00b and someone says "just test it!", you will think that the deck looks horrible because of the cards like Null Rod and the lack of cards like Tangle Wire and will let it alone.  If you actually know Workshop decks though, you'll try it since you know that Null Rod doesn't actually do anything AGAINST Stax and provides a nice way to lock out your opponent's mana.  At the same time, you would also know that Tangle Wire was always the weakest lock component in the deck.  Null Rod only looks counterintuitive because people back in the day looked at the card and saw that it hosed artifacts, saw that Stax played artifacts, and therefore thought it would be a good card.

Here’s a point that should be interesting: if my decklist is known, it’s “goodâ€? and I plan to play it in future tournaments it’s to my advantage to make everyone think that my deck is terrible.  If I plan to play a Different deck (and it beats my Current deck) then I should try to convince everyone that my current deck is strictly better than a deck in the existing metagame that has a better matchup against Different deck than my Current deck.

So the next time you look at a list and think it’s terrible, be warned: if the person who played that decklist has a “good deckâ€? and wants to win with it again, they’re hoping you’ll think that way.  Most people have too much ego to try this strategy, but you never know…

The problem here being that if the deck gives reason to look good, people won't think that it's bad, and if the deck isn't good, people won't think that it's good.  So if you post a deck on TMD that doesn't have some strong tournament success promoting it, flies in the face of common deckbuilding practices/theory, and doesn't show evidence that you are conciously breaking these conventions (which shows that you aren't aware that your deck is bad), your deck is not actually good and thus it doesn't matter if people are unprepared for it.

[Jacob Orlove]

Broken Mana Well
0
Artifact
You may pay 1 life instead of paying the mana cost of spells you play.

Okay, obviously this would be pre-banned.  But, it would throw most of our "basic propositions" into disarray.  The question is what traditional wisdom actually constitutes a basic proposition and what it takes to break one.  That's an open question.  I don't think that any card, even the one above, should be able to break a basic proportion (as long as no resource is made truly free).  That definition dictates that unless we come up with a grand theory of card advantage, tempo, and everything else, there should be a lack of consensus. The only way of getting consensus requires numerical results because analytical results will never happen.  Assuming that "analytical" intuition is acceptable is ridiculous.

Since this thread is already sidetrack city, I might as well explain what the theoretical impact of that card is (see Putting it all Together for the framework I'm using). First of all, it's clearly a Tempo card, because it effectively generates mana. Now, what effect does it have on your four turn-limited resources? It makes land drops much worse, since you no longer need lands for mana. It makes draw steps much better, since the cards you see can all be cast immediately. Attacks and untaps are only indirectly affected, because this shortens the game (making attacks weaker) and places the emphasis on casting spells, rather than utilizing permanents (making untaps weaker). Essentially, decks that could reliably get this card out would seek almost exclusively to draw more cards, because every card you draw is an immediate Tempo gain.

I don't see how this card violates any kind of basic understanding. Sure, it makes otherwise powerful Moxes irrelevant, because extra land drops have near-zero value, but it doesn't change the theoretical framework I proposed.

[Klep]

You're just wrong that there's a way to find a best deck in advance if the situation is really mixed strategy equilibrium.  You'd have to be literally psychic to tell what deck I'm going to play if I really choose randomly in advance, just like you'd have to be psychic to know what I'm going to play in Rock-Paper-Scissors if I'm using a random number generator to determine my actions. 

Yes, and I've been saying knowing the best deck ahead of time requires prescience this whole time.  That doesn't mean it does not exist, nor does it negate the theoretical importance of its existence; just as my not knowing what tomorrow entails does not mean tomorrow does not exist, nor negate the importance of its existence.

What knowing the existence of the best deck means, as I have stated, is that it is worth your time to metagame, and to select the best deck you can find to play in a tournament based on your best guess of what people will be playing.  In this fashion you are attempting to make a deck choice that is as close to the best deck as you are capable of getting.  If the best deck did not exist, such an excersize would be pointless, because all decks would be equally good (ignoring, of course, the remote possibility that some small subset of decks, say 2, are equally good).