Unified Theory: Some Kind of Summary
Will Price | January 27, 2010 | 11:03 pmBased on the comments on the podcasts and tweets I have seen, it looks like people are really missing the point of this Unified Theory thing. The goal of this post is to try and crystalize the ideas from our (myself, mike j, and others) discussions (both recorded and not) to the best of my abilities.
For as long as I have played Magic, there has always been language to try and quantify the events and outcomes of a game. This is understandable since the hobby of Magic is, in many ways, a science. All sciences require an established language through which discovery and collaboration can occur. In Magic, the most commonly used unit (up until now, at least) is “the Card.” It is very easy to describe some events using the Card e.g. playing spells that draw you cards and/or make your opponent discard cards. Most game events that literally involve cards work great. Attempts to describe more nuanced events in the language of Cards has always been tricky. If I attack you for 1, is that worth a Card? Is it worth a fraction of a Card? What fraction is it worth? How many Cards is it a Stone Rain worth on turn 2? What about turn 12? How many Cards is Dredge 6 worth?
The problem with the Card, as a unit, is that it does not have an easily applicable size (or even a well defined size, for that matter). It is too large of a unit to describe many of the events that take place over the course of a game.
I think what we are talking about with the Unified Theory is a new way of measuring game events. This is not a new theory, because its not changing anything about the game yet. The rules and tactics stay the same. What changes is the way we look at them. Thomas Kuhn wrote a book about this called the Structure of Scientific Revolutions (Read it!). What we have on our hands right now is a paradigm shift in magic.
What this Mana “theory” provides us with is a metric for measuring game events in a way that is magnitudes more precise than was available previously. Its not different from Card Advantage, its just more precise. It is an improvement, and over time it should completely replace the previous paradigm. Our job is to convince the community that what we have is better than the existing paradigm/standard of measurement.
What makes the Mana Theory a “Unified Theory” is that we can account for many many more game events, if not all game events, with much greater precision. The unit of Mana (not going to get into the “different colors of mana have different values” discussion here) is sufficiently small that, possibly, we can describe all game events with this system. What makes it the Unified theory is not that it replaces Tempo, Card Advantage, the Philosophy of Fire, or any other theory… It just gives us a better common language for discussion.
I want to take a moment here to say that I don’t blame anyone for missing the point based on the Victory Bacon podcast. None of this was explicitly said, and it was at best loosely implied by a few passing remarks. We spent most of the podcast focusing one application of the theory (Card evaluation), and not the theory itself. I think that card evaluation discussions are the easiest way to illustrate the value of the new system, but not the most valuable use of it.
On that note, the discussion of card values on twitter I think is distracting from the magnitude of this system, to the point where it has become confused with the theory itself. Essentially, it is not important to come to a consensus about what a card is absolutely worth. The game of Magic is dynamic and subject to many different frames of reference. As we have said, card value change based on format and game state. Basically, everyone is right when they say “Card A is worth X mana,” so its not really something to be wasting too much time on outside of a framed theory discussion.
So while card values change, what isn’t changing is the way we are measuring it. Thats the take-away here.
Assuming the new paradigm takes hold, there are two tasks at hand:
1. Apply the new system to what we already know. (This is what we are doing now)
2. Develop new theories that could not/did not exist under previous systems (easier said than done)
Hopefully this has been a bit easier to follow than the Podcast. As you can probably tell, we don’t script anything or even necessarily go into the process with a plan for what we are going to talk about. Usually that isn’t an issue (except when BDM and Flores go off on Basketball), but sometimes the big ideas get lost in the noise. As usual, I invite discussion in the comments (or @ me or mike on Twitter).
~WillPoP
What you and Mike have developed isn’t a theoretical construct but an engineering tool. The difference is important. I feel I can work with this tool which is good.
My biggest problem with this tool is that it is very benchmark driven. The benchmark value for a creature with 3 toughness is largely a variable of whether lightning bolt is available or if your opponents have to settle for shock. Further, the setting of proper benchmarks is extremely experience dependent. Those with large quantities of good experience will set better benchmarks than those whose experience is more limited and/or of a lower quality.
Still the tool is a useful addition to our tool box.
MSTEric
TAB ENTER ENTER
The GUToM is more of a system, and should be used to make formulas based on the information available.
Given the information I’ve been able to gather across the different mediums, I think the card evaluation should be based on ‘value variance’ as well as ‘effective cost’.
There are 4 ways I can see to evaluate a card:
1. Super Micro - How does the card evaluate alone in a vacuum.
2. Micro - How does the card evaluate in a given game/match.
3. Macro - How does the card evaluate in a given tournament meta
4. Super Macro - How does the card evaluate in the given format environment
Cards like Tormod’s Crypt have a high value variance. This affects the effective cost of the ability. In contrast, a more basic card like Isamaru, or Elite Vanguard isn’t going to have such a wild variance. I think a higher variance negatively impacts the effective cost of a card in the super micro just because it’s harder to establish a fair value to the card.
Card evaluation is the groundwork for individual game measurement, which I think is the basis for the theory. The downside is the theory seems to be a far more retrospective way to look at the game. Applying it to deck construction is going to be far more difficult.
Agree with Poster above!
This isn’t a failing, but as a designer I find another assumption inherent to all these conversations that is worth pointing out. I’ve always assumed that Wizards is designing these cards with entirely different models (like fun factor, longevity, and broad appeal) in mind. What your section of the community is doing is ignoring the inherent value of a card outside of a competitive framework. The best example I can give off the top of my head is a card like Doubling Season, where the monetary value stays stable ($12 - $14) over time regardless of standard format changes. This puts into the same monetary value as Dark Confidant, except Doubling Season ignores all three of the known models to some extent and yet its applications are exceedingly broad and it will always find itself in various decks. Ultimately the ” theory of everything” is more like a “theory of everything competitive” I only say this because I think that part of the reason these discussions feel like they are missing something is that.. well they are. A card that is exceedingly effective in one-on-one will draw political ire in a multiplayer event. If you’re truly intending to approach evaluation with a holistic viewpoint, then you need models for these other cases as well.
Until your “theory” is more coherently defined, there’s no way anybody else can even comment on it or its validity.
Thus far, as near as I can tell, you’re not actually making statements, just tautologies. Your “theory” is purely retrospective–”They won because they got the most value out of their mana. I know they got the most value because they brought their opponent’s life total to 0 first.”
Here are good places to start:
- State your theory, with definitions as appropriate.
- Is your theory positive? That is, does it make predictions?
- Is your theory falsifiable? That is, what could we observe that would render the theory demonstrably false?
- Under what circumstances does your theory fail? That is, what are the exceptions to the rules?
- Is a doom blade worth more when it kills a Baneslayer Angel than when it kills a goblin token? Based on your disagreements over the coffee table, I can’t even tell. I thought a grizzly bears was worth “W” or whatever, but if they have an elvish warrior does that mean it’s worth less?
Bring this out of the haze of bong smoke Either put it in words–reasonably coherently, reasonably thoroughly, on (digital) paper–or quit talking about how revolutionary you’re being.
@david You’re right that the theory isn’t finished yet. It’s just now beginning to be grasped.
You’re not quite getting it. Doom Blade is worth 1B, always. If the Baneslayer didn’t get the chance to do anything, their 3WW actually netted them 0. If you’re using the rest of your mana effectively, that doom blade put you 3 mana ahead of your opponent. And yes, killing a goblin token with it is a loss of 1. It’s easy to see that doom blading a goblin token is a situation that should really never arise.
While ‘David’s comment is, in my opinion, a little strong in its tone, I do find value in the ‘good places to start’ that he suggests - I have found the effort to quantify relative value very interesting and I think the podcast was engaging and thought provoking - what I’d like to see now is refinement of the ‘theory’ so that it may be accessible and testable by the wider MTG community.
If your work does hold up to such scrutiny you will have done us all a great service and you will have answered your critics in the most eloquent way possible - and if there are holes, then the exploration and dialogue can continue.
I believe that much of the hyperbole and self-gratification that at times grated on your detractors is driven by the excitement of feeling that you are on the cusp of discovering a paradigm shifting model for a game that you’ve already invested much time and energy into - that’s laudable and understandable but in the absence of clarity and audience-focused delivery (given the nature of the podcasting platform as a broadcast medium) it can be misread. I’d like to thank you for your efforts and look forward to where you go from here with this line of work.
It seems to me that based on this theory the best way to win a game of magic is to disrupt an opponent’s ability to use their resources (mana) as *early* as possible, thereby negating as much future value as possible, while simultaneously (or as close to simultaneously as one can) doing the bare minimum that is necessary offensively to win - but doing so as quickly as possible. I feel that the games where I have dominated my opponent were not due to landing the most undercosted threats and racing their inferior board position, but by beating down with a V.Clique/Ruinblaster/Sculler and them not being able to play anything, or by the time they were able to, I was so far ahead on effective use of resources that they simply did not have time to come back. Like being up 20 points going into the 4th quarter in a game of basketball when your team has been dominating the boards all game, I’ll take the odds of winning that one anytime! So, maybe unifying theory is pointing more towards a particular archtype?
Think for a moment of the 5 color cascade deck with Roil and Spreading Seas as two drops…that deck wins every game if it gets safely to turn 4, what if the opponent could not do anything before turn 4?
First, please note that “Becker” above is not me.
Fishysua: How is this tool good?
Mike/other magic physicists: I find all of these attempts (not just here, but several others that have been doing the same thing on other sites) to pin down some grand unified theory of magic (i) silly, (ii) self indulgent, and (iii) mostly useless. These give me faint echoes of Jordie Tait’s implied card advantage debacle, where basically you take a situation or a play and apply this giant complex mathy theory to it, and then you look and see if it makes sense to make the play without the theory, given the game state, and if so, do that. So don’t do A, do complicated B. THEN do A. If A and B agree, great, but if not, take action A. Since A wins whatever B is, why not just do A in the first place? No GUToM required. Shrug.
A card’s value is only as good or bad as the situation allows it to be. Lets use the “Doom Blade a Goblin Token” example:
They are attacking. You are at 1. You have no other possible play. Obviously you Blade it, but why? The value of that goblin NOT hitting is the potential sum total of your deck’s mana expenditure. If it connects, you are unable to continue using mana since you’re god damned dead.
You have a 7/1 (with no trample because its terrible and you’re terrible), and they have a 1/1 goblin token and nothing else. It might be correct to ace the token there, because you’re denying them the option to make a trade AND getting 7 damage to their head.
The point is, while any good player will see those situations and say ‘duh’, we have the framework to QUANTIFY the “duh”. The point is not to evaluate a card’s value in a vaccuum. It helps to have an idea of what “good” cards in certain roles “should” cost, but its more important to derive values situationally.
What’s the value of a bolt when the other guy is at 3?
What’s the value of a White Knight against a Mono Black deck?
What’s the value of Doom Blade against a Mono Black deck?
What’s the value of Earthquake when you’re at 4 life and staring down an army of Hill Giants?
What’s the value of a pinger when your opponent has dies-when-targeted stuff?
Those examples should show why the vacuum value of a card is totally irrelevant. It’s the current and potential effect on the game that truly matters. Measuring in FRACTIONAL (or decimal) mana expenditure is the most effective and accurate way to quantify the strength of a given play.
Remember, this is not about some sort of strategic theory on HOW to play the game. The main point here is that, instead of quantifying games in terms of Tempo, Card Advantage, etc, we have ONE metric by which to evaluate game play. There are many games where players lose and have to ask “why did I lose that one?” This is the closest thing we have to a single answer. Otherwise we have to use multiple definitions to answer the question. Parting example:
Jund mirror match. He mulls to 6 on the play and gets off the first Blightning. I still win easily because of my 2 card advantage. It’s easy to chalk that win up to card advantage, but its harder to say WHy i won because of CA. Basically, my having extra cards increased the odds that I would be able to use my mana efficiently. Because of the increase in odds, I had the Blightning when he was on two cards, removing a Siege Gang and a Malakir Bloodwitch - two cards that would have won him the game.
On the other hand, when he blightning’ed me, having the two extra cards increase the odds that I would be able to retain the most important card, the one that allowed me the BEST mana conversion in that matchup. Siege-Gang Commander. Indeed, after the dust cleared, he had no hand and I had nothing but the commander and my 5th land drop. That siege-gang ended the game, but it was actually his mulligan to 6 on the play that -won- it for me. Quantifying the win was easy: his blightning would have been more effective on the draw, since I would have had fewer options, and thus my chance to retain the best way to convert mana would have decreased.
The two primary things that theories are evaluated on are:
1) Their ability to explain phenomenon
2) Their ability to predict phenomenon
From the podcast and summary alone, I think that the GUToM’s shows incredible potential to explain a ton of things in magic that thus far have required multiple and irreconcilable theories. For instance, you can explain why red burn decks win using the ‘Philosophy of Fire’ (cards equal life) but can’t use that theory to explain why they sometimes lose to control decks. You can explain why those control decks win using ‘card advantage theory’, but not why they lose to red decks. With GUToM you can explain both: the deck that gets the most value for their mana taps wins (incidentally, this explains why the feeling of losing to red burn is similar to the feeling of losing to land destruction - both strategies essentially try to limit your access to mana and your ability to cast spells). Card evaluation also seems much better and more refined under GUToM (well covered in the podcast), etc…
Whether the theory has predictive power remains to be seen - that will be up to designers who take the theory and run with it. I’m eager to see the results
BTW I find some of the comments regarding the value of Magic theory juvenile and laughable. Does anyone dispute the value of chess theory, bridge theory, or poker theory to those respective games? Understanding theory can ‘only’ make you a better player (though admittedly misunderstanding it can make you a much worse one).
I am all for the GUToM. Certainly it is barely a sketch at this point, but it shows quite a lot of potential. And it seems to be affecting the current metagame (especially extended) already. Obviously, to be good a theory must be explanatory and predictive. So far it looks like a good explanation, since it essentially covers all the bases as to why one deck wins and another does not. Is it predictive? We have yet to see. As I see it the main problem with the theory is the valuation part. In other words, maximizing use of mana or “value” makes sense and is broadly applicable. But what is the value of a card? Certainly there will be some vacuum valuation for some cards, for example Spell Snare is always 1 for 2, but even with fairly perfect cards there will be valuation variation; ie how many 2 casting cost cards are in the metagame? So the post talking about mean value and variation in value is highly relevant. Fortunately, for the most part mean valuation in relation to a particular metagame will be probably be fairly close to right, since even highly variable cards will work well through a tournament. But I don’t think it is possible to have a workable valuation that is not metagame dependent (or at the very least format dependent). And that should explain why some cards are better in one format than another. But this is not a real weakness, because as long as some valuation can be established (even if a little fuzzy) it will probably still be usable in prediction.
I believe that there is a unifying variable that is absolutely key to the whole “unified theory:” The resource of time. It ties directly into tempo, but it is also easily recognizable as the most important resource a player has.
Time is measured in units of turns remaining. How much does a player start out with? Given a 60 card deck and that player draws 7 cards, they begin with 54 turns before they die to decking. Now, as soon as their opponent plays a Grizzly Bears, their time resource falls to 10 turns remaining. If they play a second Bears, then your turns remaining falls to 5. How much is a Shock worth in this case? About five turns. All the ways you can win a game of Magic are ways you can attack your opponents resource of turns remaining. Once that resource dips to zero, you’ve won the game.
This measure is mainly a way of comparing different win conditions, but it can also be expanded to talk about different card valuations.
How much is a goblin token worth? What hes worth is directly correlated to his ability to win the game. This would involve some calculation versus a scale from game-winning to useless. Figuring out that scale would be an excellent article. That would be fun to write, as well.