Incoherence and Innovation

[Machinus]

Please don't post before reading this:

http://www.themanadrain.com/forums/viewtopic.php?t=16967



I have a few comments, but cannot reply in the original thread.


First, I think Phil and Steve present arguments which have some interesting implications. Obviously, more innovation will occur at times when the card pool has increased, such as right after mirrodin. But what does this have to do with testing? Let us not immediately decide on one point of view. Let us merely say that if we were able to adequately test the subtypes of each archetype against each other, we would eventually discover that the number viable decktypes would significantly decrease - while it may be true in fact that there would be only one deck left in each group, this conclusion is not necessary for my argument. The reduced metagame would consist of decks which were the most powerful, etc. Ok, so this can't happen - how then can we make intelligent use of the information that does exist, such as tournament rankings? Here is where we need to define what "innovation" really means.

New deck archetypes rarely arise solely from innovation itself. Frequently, however, they come about because new cards are created which allow for new strategies or viable counter-strategies to be created around them. Witness GAT and Slavery. But how much of these decks is really new? Saucemaster states, roughly, that once some principles are discovered and defined about the system (in this case, the Type 1 environment), they become part of the basic rules of that system. I believe there is a great deal that "new" decks draw upon that is not innovation, but methods which are understood to be a part of the basic structure of the system. How did these methods work their way into the underlying rules? I believe this answer is simple - cards which have existed longer have received more coincidental testing and analysis by players, and therefore older strategies (cards) are more familiar and better understood. Take a look at a match between two of the best decks in the format, and then consider how many of the plays and interactions in that game could have happened two, or four years before. I think there is a great deal that is not in fact new, that over time the best cards and strongest strategies have themselves become a part of the rules of magic, and that there is LESS ROOM for innovation because of them. If you go underground, mox sapphire, and drain your opponent's first spell, there is no way to tell if you are playing in 2004, 2001, or 1997. There is a very real and very powerful set of conditions which have been applied, by players, to the basic rules of magic, which must also be considered when attempting to construct a succesful deck in any subsequent environment.

Second, some of the theoretical analysis seems to be getting out of hand. You cannot simply take two strings of sixty cards each, and compute the "score" of an arbitraty number of matchups between them. I hate to rehash the card advantage discussions, but there was an analogy made to some sports method of computing win percentages where each player is given a number and the numbers are simply added up - and then the magic player went on to say that magic is more complex than that, that you can't just give a card a number and say that's how much it is worth, etc. This is really true. If you do any kind of experiment or discussion about viability or metagame strength, and you leave out player skill, your results are going to be invariably wrong. To echo PTW: A better player will win more with the same deck; therefore it stands to reason that a better player with a "worse" deck could beat an opponent with a "better" deck. Talking about decks versus each other is inherently flawed and very limited in its usefulness, because I am sure that the discrepancy in player skill affects all the data we have to work with - top 8s, team playtesting, everything.

Lastly, attempting to discern the value of metagame strength vs. absolute strength of a deck (assuming all players are equal) does depend somewhat on the format, but I believe that it does not take a very diverse card pool to assure that metagame becomes the dominant factor. There are certainly enough powerful cards in Type 1 to reduce the effectiveness of absolute strength of a deck. You could enter a tournament with suicide black, and not even be that great of a player, but still win if every other deck in the tournament was a deck that lost to sui (what is that deck?). But even if you are playing the best deck in the format with the highest concentration of synergy and power, you can still play RGHate and lose. Of course you aren't going to play suicide, and you won't face lots of hate decks, but what it comes down to is choosing between the top three or four decks on power level, and then making a metagame call between them - but the metagame has more influence. The reason that absolute strength is more appealing is because metagame is impossible to predict; there really is no way to know what people are going to play, and what color your first round opponent's creatures are going to be when they start smashing you on the second turn.

[Ephraim]

The problem that was danced around in the initial thread was why there are competing variants of any particular deck. People spoke at length about why there is no best deck, why sub-optimal decks appear in the first place, and how the metagame evolves. Other people argued that this does not adequately explain the posed problem. However, I believe that it does.

Magic is an incredibly complicated differential system. With a powerful enough computer, you could almost certainly model a Magic metagame of an arbitrary number of players with an arbitrary variance of access to cards. With periodic disturbances (restrictions and new sets), it is very likely that the system would never resolve into a point solution (a static metagame) or even a cyclic solution (a metagame that repeats itself.) Without such disturbances, such solutions are at least possible. What I believe you would find, however, with successive trials, is that a small change in the system's initial conditions would have a profound effect on the results. The decks that appear could be completely different or similar decks would appear with notable variations. This is precisely what happens in real life. Because of geographical distances, local metagames are like simulations with different initial conditions. The GAT decks appearing in Europe, for example, are likely to be different from those appearing in North America.

As you focus in on smaller and smaller regions, the system becomes less and less stable. Because successively smaller regions have fewer players than larger regions, a small region developing even a semi-stable solution between disturbances is less likely than a large region doing so. Furthermore, the same reliance on initial conditions applies here as well. The conditions in my county may be different from those in a neighbouring county. The variance is probably very small, but because the system is chaotic (in the mathematical sense), this variation will produce a relatively large change.

To conclude, a series of similarly chaotic systems with varying initial conditions will produce different results. Because the Type 1 playing field is not absolutely uniform throughout the world or even throughout a particular country or state and because it is just such a chaotic system, variations, which may never stablize, are bound to appear.

[monstre]

I'd like to suggest that even if the metagame wasn't a factor, I don't believe an optimal deck could be found. The fact that such a deck might exist doesn't imply that we can ever identify it. Consider the amount of playtesting required to choose between two decks with a single card difference. Contemplate the number of such decisions involved in making a deck. Repeat for any number of decks. All this testing should be carried out by perfect players to eliminate playing skill as a factor. If this is reality we're talking about, there's no way we can come close to achieving this. You know, given a computer with infinite memory, you could write a program that plays chess perfectly, so you might want to consider why no one is proposing to solve chess anytime soon...

Analyzing tournament results and testing decks to the best of our ability is all well and good, but let's not pretend that we know what the best decks are in any objective sense. Looking back, it's easy to find a time when a dominant deck existed in the card pool but had yet to be found (like necropotence and pre-errata mirror universe). This trend suggests that there are still better decks out there that we aren't aware of.

[combo_dude]

This playtesting point is an important one.  Perfect play is vital for "true" playtesting (in so far as knowing what the result should be for certain) - but it's hard to come by.  In addition, there is the random element to Magic - namely, that every turn you draw a card. Whether this is from a deck of 50, 30, or 2 cards left, there IS always this random element. Even modelling the 2-cards-left point with Pascal's Triangle (i.e. over a total of 1000 tries, which card will be drawn) allows for so much variation from the 500/500 split that it's impossible, even with "infinite" memory, to calculate. This in turn implies that the random element is impossible to eliminate, and only grows with every card introduced; as a result, Magic is too random to 'solve'. Deck construction is there to give the maximum chance of drawing the best cards in the right situation - but as nothing can know in advance what this situation, it is impossible to predict and this is what makes Magic a game that is impossible to solve. This extra variation is a metagame, which I think will be like this statistical variation: deck A with X possible (and realistic) variations will NEVER reach 100% versions of deck A. Obviously this deck construction is not entirely random like the statistical situation described, but we do not have the computer power (see above - and my next point) to solve it, and as soon as a human element is introduced, a capacity for error comes with it.

In short, I don't think a perfect mathematical model of Magic is possible.

monstre: with your point about chess, nobody is proposing to solve chess because it's too complex. There are more possible 40-move games of chess than atoms in the visible universe. That's a lot of games.

Anyway, if a computer COULD do all these calculations, there are more practical uses - breaking the RSA algorithm used for internet encryption, for example, which is breakable by sheer power - than solving games. I'm not sure that even if chess WAS solvable we would want to solve it (thereby ruining the challenge to humans), but that's a different issue.

[Machinus]

Monstre's point about chess is more important and more relevant than I think we realize. The initial conditions of chess are invariable - sixteen pieces on each side. There is no information hidden from either player, and there is minimal player interaction with the board - only one piece can move each turn. In the early game, there is usually only one or two places a piece can move; this increases later on, but still remains a pretty small number of possibilities. Chess is far less complex than magic, much easier to model, and is impossible to "solve."

This doesn't stop the existence of chess strategy though. Chess is a well understood game, and has been popular for a very long time, so we see that the solution is not necessary. Kasparov still manages to harass IBM's best offerings (accepting a draw from IBM at the last standoff, what a dick) even though he does not have access to the solutions guide to chess. In the same way, Kai does not need to know all the right answers to tell the difference between a lesser play and greater one. This is where our examination of fundamental theory comes in, because even if we DID know the complete solution set to Magic, it would still probably be more efficient and mush less time consuming to just analyze plays according to these basic rules and make game play and deckbuilding decisions based on them.

[Saucemaster]

Monstre's point about chess is more important and more relevant than I think we realize. The initial conditions of chess are invariable - sixteen pieces on each side. There is no information hidden from either player, and there is minimal player interaction with the board - only one piece can move each turn. In the early game, there is usually only one or two places a piece can move; this increases later on, but still remains a pretty small number of possibilities. Chess is far less complex than magic, much easier to model, and is impossible to "solve."

Wait, no.  This is just wrong.  I mean, like, actually wrong.  Chess is possible to solve, we just haven't done so yet because it requires vast, vast, vast resources and computing power, and even if we do have the computing power--and I don't know whether we do--it's kind of a waste of the resources at the moment.  combo_dude is right on the nose w/r/t this.  On reading monstre's post, though, I think that Machinus misunderstood him.  Monstre conceded that Chess has a knowable solution, but was arguing that the process of finding is too labor-intensive to be worthwhile.  Which is true.

However, combo_dude, I don't see why a perfect mathematical model of Magic would be impossible.  It would be based on statistics and probability, and it would require awe-inspiring amounts of computational power, but it should be just as theoretically possible as a mathematical model of Poker, for example.  Though, again, it would require vastly, vastly more computational power because the "deck" wouldn't be defined in advance--though the possible contents of the deck (the cards legal in the format, and in what quantities) would be.

[Machinus]

I meant "impossible" in that we don't have the power to figure out all possible games, not in the sense that it is theoretically un-computable. Chess is effectively unsolvabe because it is too complicated to calculate. My point was that even though chess is far simpler than magic, we still don't have nearly the computational resources to analyze it completely. I bring this up because I want to suggest that perhaphs it is not worthwhile to try to analyze magic completely from a win probability standpoint.

[Dante]

[quote="Saucemaster
However, combo_dude, I don't see why a perfect mathematical model of Magic would be impossible.  It would be based on statistics and probability, and it would require awe-inspiring amounts of computational power, but it should be just as theoretically possible as a mathematical model of Poker, for example.  Though, again, it would require vastly, vastly more computational power because the "deck" wouldn't be defined in advance--though the possible contents of the deck (the cards legal in the format, and in what quantities) would be.[/quote]

The problem is that Chess is a game of total knowledge, not partial knowledge like Magic and Poker.  What I mean by "total knowledge" is that all the information about all future moves are available to both opponents (and observers).  Thus a reasonable powerful computer can compute, based on all possible outcomes, the top strategy and particular move.

Magic and Poker have incomplete information, where even if you not only knew your own hand, but your opponent's hand, any forumla or strategy could/would be susceptible to totally change after each card is drawn, as opposed to Chess, where every specific move can be calculated EXACLTY since there is no hidden information.  

This is why Chess computer programs can play to a Master-level and beyond, whereas Poker programs are mediocre (at best) that can't really hold up to live players (and I've tried a lot of them).

Bill

[monstre]

Wait, no.  This is just wrong.  I mean, like, actually wrong.  Chess is possible to solve, we just haven't done so yet because it requires vast, vast, vast resources and computing power, and even if we do have the computing power--and I don't know whether we do--it's kind of a waste of the resources at the moment.  combo_dude is right on the nose w/r/t this.  On reading monstre's post, though, I think that Machinus misunderstood him.  Monstre conceded that Chess has a knowable solution, but was arguing that the process of finding is too labor-intensive to be worthwhile.  Which is true.

I can assure you we don't have the "vast, vast, vast resources and computing power" necessary for this. As combo_dude pointed out, there are more possibilities to consider than there are atoms in the universe. I have a program that can crack RSA encryption too given enough time (say, a billion years), but the existence of these solutions is purely academic. If you add the constraint that your chess program has to fit in this universe, then chess can no longer be solved in such a naive way. Wether there is a better way to go about this is an open problem (settle this and get rich!). As it stands, a final solution to chess or magic is not only unknown, it is unknowable.

[Machinus]

This is what I was referring to; it is effectively impossible to solve chess, which serves to provide us with a benchmark for seeking solutions to magic - and it shows us that if we want to discover something valuable, we should look elsewhere.

[hellswarm]

MOST UNREADABLE POST EVER -jpmeyer[/b]

[Kowal]

I've taken the liberty of making your post readable.  Please try to do so yourself in the future.

Then, settle this and get rich...

Haha, no one thinks outside the box anymore?

A complete list of probabilities is easy to obtain.  Take that complete list of all combinations and remove all the impermissable results.

Then choose a random number of people from that compilation.  That way only acceptable choices remain and thus don't need to be checked.

But given the way it's worded, it seems horribly tedious to make a list once, then check if it doesn't repeat until it's solved.  That's way too much time.

Now if you take another look at Magic, and give specific archetypes (like combo for example) it is theoretically possible to determine an exact probability and likelihood that your deck will not fizzle when going off.   For example, to give you knowledge of what you can do with your opening hand and mana, and feasable "draw X cards" and "grab 1 of X  things you need" to draw X many more cards and win that turn.  This is computable in most combo players' heads.  Yes, there is still a chance that a card that allows you to gain more cards isn't going to appear, but if you have already drawn X of 60 cards you still have a chance of doing something else with the cards you've already drawn.

Add in the fact your opponent can do things to you during the seach for those X cards and/or stop you completly, and that's where it becomes incalculable.

Despite this cleaning up, it still doesn't make much sense.  It appears you've learned a couple new things to make your posts better.

Grammar
Syntax
Spelling
Word choice (we appreciate the esoteric words to provide a little more variety in your post, but please try to use them correctly...  And make certain that they are in fact actual words)
And please, make your posts make sense.

[Dante]

If you add the constraint that your chess program has to fit in this universe, then chess can no longer be solved in such a naive way.

Except that there are computers who can beat the top grandmasters in the world at chess.  This is not true at all for poker or magic.

[monstre]

If you add the constraint that your chess program has to fit in this universe, then chess can no longer be solved in such a naive way.

Except that there are computers who can beat the top grandmasters in the world at chess.  This is not true at all for poker or magic.

Yes, I hear there are chess programs out there that are very hard to beat (I don't play myself). It should be noted that they use heuristics much like you and I, so they are only approximations of an optimal solution. There will always be some distance between the programs we have and a perfect solution. This is what I meant when I said that chess or magic can't be solved, but maybe "close enough" would be a more useful metric, if a little fuzzy.

[Saucemaster]

I can assure you we don't have the "vast, vast, vast resources and computing power" necessary for this. As combo_dude pointed out, there are more possibilities to consider than there are atoms in the universe. I have a program that can crack RSA encryption too given enough time (say, a billion years), but the existence of these solutions is purely academic. If you add the constraint that your chess program has to fit in this universe, then chess can no longer be solved in such a naive way. Wether there is a better way to go about this is an open problem (settle this and get rich!). As it stands, a final solution to chess or magic is not only unknown, it is unknowable.

This has gone way off topic, but again, such a solution is *knowable*, just incredibly impractical.  From a philosophical and logical standpoint, there is a very important difference between claiming that something is actually unknowable (say, simultaneously knowing the exact position and momentum of subatomic particle, yes?) and something that is simply unknown, even if it is likely to remain unknown forever.

Anyway, personally I've somewhat lost sight of my original point by now.  In practice I will agree with Milton that perception is the single most important factor in metagame coherence and that politics is the greatest influence on that perception.

[hellswarm]

figured as much..

oh well... im not goign to bother attepting to explain that again..and how i can releate it to magic...

[Machinus]

The point I'm making is that there is that there is a small set of synergies and card alliances that basically make up Type One at the moment.

This is what I was getting at in my first point. The majority of card interactions in Type 1 are in fact, NOT innovative, but are shared with many other decks, and most of them are not new synergies.

[AIcOPed]

I love magic chess and math, so this thread is for me.

Chess can not be solved! this is a fact. This is because even if you could fit the "memory"of a chess game on the smallest known particle, and packed the known universe as densly as possible w/ this particle, you would have at most 10 to the 125th power of particles. there are an estimated 10 to the 75,000th(this number can be found in the book sizeasaurus among others) power of possible chess games using united states chess federation rules. This means that you can not even look at all of the chess games in some form of memory bank.

Some of you are thinking what about storing some and dissmissing them once they are found to be "weak". the problem is this. even if you still could store 1 game on a particle and could use this densly packed universe filled w/ chess games and you could do this 10 to the 100th power of times a second, it would take you more than 10 to the 750th power of seconds(35 million seconds in a year) which is liking living through the length of the universe of time more than 10 to the 700th power of times. remember this is not 700 times but 10 to the 700th power of times.

By the way, magic is virtually infinitely more complex than chess. This is a fact that anyone should be able to see, based on chess having 6 different piece types (king, queen, pawn, knight, bishop, rook) and 16 pieces for each player.

Let me make some assumptions: ignoring land every player must use exactly 4 of any card in his deck (obviously less options than possible). this means that assuming they have 24 lands, they have 9 different cards in their deck. more "pieces" to play with and more different "pieces" to use in any given game, means all other factors being equal magic is more complex.

I realize all other factors are not equal. in a chess game white can open w/ 20 different moves and black can respond w/ 20 different moves. most of these are blunders akin to taking a mulligan and then doing nothing while your opponent crushes you.

 I believe there are 7 accepted first moves for white by the gm's (e4,d4,g3,b3,c4,knf3,knc3)
and black has typically about 3 or four responses for each move of whites.
this is more interaction/choice than typically will happen in a normal game of magic, so advantage chess, but since most chess masters are playing by the book until move 15 or 20 they are not even doing anything different/innovative until after that. w/ magic you can be innovative before reaching the table (aka do not netdeck and inst6ead find something new) in chess the most innovative move ever (as agreed upon by most chess masters was when bobby fischer made an opening move he had not made since the beginning of his pro career.) it is the only first opening move to ever get an exclamation point.

In magic, how many type one turns get exclamation marks? a ton (yes, I do mean 2000 lbs of exclamation marks)

I think the metagame will eventually settle only if new cards are stopped being made. Then and only then would some form of true rock-paper-scissors exist.