Effective Card Advantage Theory
Greetings from Russell's old room. Some have thought me a fool for remaining silent on this card advantage issue for so long, but now I'm about to open my mouth, as the old saying goes, and remove all doubt. After what seems like an eternity, it's time to wrap it all up, a package from mama, signed, sealed, and delivered with care. Along the way, I have a lot of things to say about theory in general, alternative card advantage solutions, and why you shouldn't bite down on a piece of tinfoil.
Seems like I've written about twenty card advantage articles, doesn't it? Much has been made of my argument with Oscar Tan. On MiseTings, there was even a piece called"Card Advantage Gladiators" where I was pitted against the mighty Oscar Tan in"a bout to knock the other guy out."
Man, I've written two articles. Just two. I know, it blows my mind. This will be the third, but it's too late to stop the cynical and acid-tongued from laying the Tait/Tan punchline on thick. I'd be lying if I said that this whole shebang turned out exactly as I wanted, but so too would it be a falsehood to call it a waste of time. The show must go on. My grandfather, an old vaudevillian, taught me that.
Ok, he wasn't an old vaudevillian. He was a refrigerator repairman. But there was no 'fridge repair girl in Fox Force Five.
[Geordie's first two articles on card advantage can be found here:
On Writing Theory, And How To Stop Worrying And Love The Card Advantage
I guess we might as well begin with the topic that's been lodged in the front of my brain like that pesky splinter that mommy can't quite reach with the tweezers. It's no secret that I've been a little bit disappointed with the (at times) negative reaction to the theory articles that have recently been appearing on StarCity, and this isn't just because my own articles have been amongst those grouched upon by forum wits who would rather read pretty much anything else. I would be lying if I said the criticism didn't sting a little. At times, more than a little. It frustrates me to see such a worthwhile pursuit as game theory being dismissed as"useless" and"boring," especially with the effort that gets put into the articles from my end.
I'm not sure why a surge in theory articles should bother people so much. More than that, I'm not sure why folks with aversions to theory and debate decided to make it a personal crusade to say negative things about any attempt to explore how the game works. I mean, I personally have no use for articles about Five Color Magic (not that I don't lament that fact from time to time!), and I sadly can't find anything constructive in articles discussing budget decks. Despite my status as a non-5C playin', non-budget buildin' son of a gun, was I clamoring for a gag order in the forums of Abe Sergeant or Chris Romeo? Of course not. That would be asinine. There was plenty of other stuff going up day in and day out that was able to capture my interest - articles on draft, T2, Extended, and issues articles of all kinds. So why are anti-theory grouches always running down the theory guys? I think that's a poor attitude, skip. Poor attitudes don't win ballgames.
I prefer to look at StarCity as Magic: The Gathering ice cream shoppe, with plenty of flavors for all. If you've grown loathe of Geordie Tait's Strawberry Card Advantage Sorbet, feel free to go down the menu and grab a double-scoop of Romeo Triple Chocolate Surprise, or sample Tim Aten's"Nut High" Sundae, or prepare your palette for the concoction that ice-cream aficionados refer to only as Oscar Tan's"Type Fudge." There's a world of ice cream out there - so why bristle and complain when someone puts out a flavor you don't like? I've never been much of a Chocolate Mint fan, but as long as there's such a thing as Tin Roof Sundae, I'm happy as a pig rolling in his own leavings. My ice cream dance card is full, as long as vanilla and chocolate-coated peanuts exist in this world. Despite reams of articles that are useless to me being served up every day, I will never complain! There's plenty of good ice cream.
So come on, turn that frown upside down. Don't be a square, daddy-o! I can understand why Oscar the Grouch is grouchy (as Dave Chappelle opined, he lives in a trash can, he's entitled!), and I have sympathy for hobos and fellow liberals (so often one and the same!) who have a right to get a mite testy when life deals 'em an ugly card. But come on readers! What's your excuse? Are you disappointed that I'm not writing about the things I used to write about? Don't be! I'm trying something new and different, (haven't you meat and potatoes men always wanted to get up to some mischief?) and when I started this series out, I was apprehensive at first, too. That's normal. In the end, I think it turned out really well! Three pieces tied up in a nice tidy package. There are only so many set reviews, issues articles, and road trip reports you can do before you have to expand your horizons.
I actually had quite a few people communicate to me that they wanted to see less of this stuff and more of"the Geordie Tait of old." Still more people made remarks to the effect of"the quality of Geordie Tait articles is going downhill." I understand the first sentiment, but not the second. Sure, I'm not quite the same I guy I was when I started writing here at StarCity. I miss the Daily Shot sometimes, too. All the goofy jokes, rambling set reviews, little stories about Magic in general and the crazy things that happen. When I hear a voice say "Someone bring the old Geordie back!" I get all misty-eyed with fond recollections. It's like finding that board-stiff Victoria's Secret catalog under your old bed ten years after moving out of the house.
All I can say is, have faith. There's still a lot of fun to be had by all. And as always, it's only as far away as the next page.
Pure Card Advantage Wrap-Up
The first article of this series was about"Pure Card Advantage." 'Twas a fine effort, all told, but if you go back and read it now, it's pretty clear that I wasn't quite prepared for what I was getting into. It was probably the first time where I've actually taught myself something with my own article. The piece itself is a nice little ditty on the basics of card advantage by the numbers, and because it was only one-third of the full system, the forum response was misguided. It didn't help that I wouldn't come close to really finalizing the tenets of PCA until the following article - the whole concept was just an unformed ball of gas at that point, hanging in limbo before forming the planet I now know it to be.
Planet... Card Advantage! Set course, ensign!
Knowing what I do now, the entire argument about tokens and so forth was a waste of time, and I blame myself for not realizing earlier that comparing PCA to Oscar Tan's ideas about card advantage was a classic case of Apples vs. Oranges. It wasn't really fair to PCA, which is a"dummy" system designed to count pure cards and act as a foil to more advanced concepts, to be compared with"old school" card advantage ideas in their totality. I ended up having to defend the position that PCA by itself stands up favorably in every case, which obviously isn't true. Of course, I didn't let that stop me.
It took me (and everyone else) about twenty pages of forum response over the course of two articles before we figured out exactly what it was we were arguing. Actually, many people still haven't figured it out. To make matters worse, some of the more impatient mutants had already thrown up their hands and started populating the threads of all card advantage articles with pinnacles of tolerance like "These articles have to stop."
Perhaps the most stinging criticism came from Adrian Sullivan, who I'd hoped would enjoy the article. Like many others, though, Adrian was upset at the way I'd dealt with the"PCA vs. Old School" argument. Again, I can't stress enough that all I did was compare PCA to an incomplete, crippled version of"Old School," which is exactly what people were doing to my card advantage theories, but in reverse. PCA was just one third of a system, and that didn't stop people from trying to shoot it down. If I had it to do over again, I'd certainly make that more clear. For now, I just hope that Adrian and others might give the article a second read and perhaps reconsider its merits.
So yeah, things were a little muddled. Still, I think that stopping the discussion after article two would have been literary coitus interruptus of epic proportions. There were good things coming, but only to those willing to wait, fire some points back and forth, and kick around the old masters a little.
I want to make it clear, right now, that Pure Card Advantage generally can't compare favorably with the more established system when it comes to evaluating complex plays involving virtual card advantage. It's not really fair to even require it to do so, since it was never designed to do so. PCA is sufficient to quantify probably 95% of all plays in Magic, taken effect by effect, and that's a great starting point for the rest of the article series. I only wish I could have made this more clear at the outset, so as to avoid most of the commotion that resulted from the first two articles.
To understand Pure Card Advantage as a theory, you need to read the following:
- the first article,"Card Advantage Without All The Hullaballoo"- keep in mind that a couple of the examples in the article are actually incorrect
- the forum response to the above article (there's a lot, but it's great reading if you're interested in theory)
- the introduction to the second article,"Virtual Card Advantage Theory"
- the forum response to the second article (again, there's a lot)
As you read through that, you'll see a lot of point and counterpoint, a lot of examples, a lot of jostling for position. Try to ignore the comparisons drawn between PCA and older card advantage theories and focus on PCA itself. As I mentioned, those comparisons were a waste of time, and I was more the fool for even trying to defend a position more perforated than the pasta-tosser at East Side Mario's. That mistake, though, doesn't mean that PCA is without merit. It is an integral part of the big picture.
I didn't know it at the time, but the real monster theory was still to come.
Virtual Card Advantage Wrap-Up
The second article in the series was about"Virtual Card Advantage." At the time I started writing, I didn't know how deep I would end up going, (sorta like Omar Epps in that movie!) and before the article was done, I'd ended up surprising myself by changing how I personally looked at concepts like tempo and mana denial, and, really, the game in general.
I'm not sure if I did the same for anyone else.
Aside from the usual primer about known virtual card advantage concepts (Moat, The Abyss, Circle of Protection: Red, Chalice of the Void), I included a couple of examples about land destruction and fast tempo that really only scratched the surface of what I believe the theory to cover. Later, I would exchange emails with noted theorist Zvi Mowshowitz (namedropping!), and things would get really in-depth as I would discover, almost by accident, my favorite new concept - that of"Virtual Card Count Zero."
Part of one of my replies is reproduced below:
Tempo, in my opinion, is mostly about denying the opposing deck opportunities to draw and use a sufficient number of answers. At 20 life, the number of cards that might be considered"useful to prevent losing" is large. At 10 life with creatures bearing down, the number dwindles - you have some virtual card disadvantage - cards that don't answer the attacking force or at least search for cards that do are null draws. At 4 life with two Neurok Spies across from you, the number of answers often drops to zero, and when that happens, you've reached complete Virtual Card Disadvantage. Every card is useless. Good tempo allows the aggro deck to maneuver itself into that"no opposing outs" situation faster.
Every Magic game is, really, a race to reduce an opponent's virtual card count to zero.
As Keanu Reeves once said:
I set out to write a"fundamentals" article and ended up redefining my own view of Magic. Even this dummy knows that something like that doesn't occur every day. Some people don't have much use for the idea of"every victory as VCA," (Zvi didn't seem to think there was much to be gained from such a theory), but for me, at least, it's an enchanting idea. Your mileage may vary!
If you want wrap your mind around Virtual Card Advantage as a theory (as I've written it, anyway) make sure you read the following:
- the second article,"Virtual Card Advantage Theory"
- the forum response to the second article
If you're interested in alternative viewpoints, there is a wealth of information available on card advantage all over the web, and especially just recently here at StarCity.
And now...on with the show!
Effective Card Advantage
It's the last piece of the puzzle, but not the largest one. (Virtual Card Advantage is the big daddy.) Effective Card Advantage is the part of card advantage theory that explains why a one for one trade isn't always an even trade. One of the things that anti-theorists use to decry the usefulness of rigid systems is the fact that everything in Magic is relative, the fact that card value fluctuates like a Christmas waistline from matchup to matchup. Luckily for those in the know, even this seemingly infinite pile of variables can be quantified to some extent. It only requires testing.
I'll start off with a simple example. A friend of mine named Trevor had decided to get back into Magic, and I recommended that he build a version of Jim Ferraiolo's"Dark Affinity" in order to play at FNM events and get back into the flow. It's cheap, it's easy to learn, and it's Tier 1. (I would have recommended Sarnia Affinity, but Trevor isn't exactly Albert Einstein when it comes to using countermagic effectively - I figured he should just drop men and smash.) Unfortunately, he didn't have access to Broodstars or Glimmervoids, so he was at a serious disadvantage, especially in the mirror. I remember one evening where he dropped match after match to J"The Muscle" Vanderwielen, playing Dark Affinity with Broodstars, instead of the Somber Hoverguards and Lodestone Myr that Trevor was running.
Yes, his name is just"J", no typo. I guess when you spend your days putting up scaffolding, you don't need a long name for people to know you're bad ass.
Anyhow, the value of Broodstar in the matchup was immense. Taking the"function" cards from the deck (ignoring cards that only serve to draw you more cards) and assigning values in the mirror, you'd end up with something like this.
Now, these are rough numbers. Not only can the value of many of these cards change as the game progresses (land is more important early on, for example, and Broodstar is dead for the first few turns of the game), but I'm not 100% sure on these values in any case. I'm just using this as an example. Fans of chess, that great old mental sport, might see what is going on here, and draw a parallel between the values assigned to each piece on a chessboard and the values assigned above to the cards in Affinity.
In chess, trading a couple of pawns for a queen is generally a great trade. If you scoffed and told Kasparov that he was"down a piece," you'd probably get rubbed out by the KGB. (And yes, it can be a poor trade if you give up board position and tempo and so on, but that sort of problem is what makes chess... well... chess). I could see the same thing happening in the games with Trevor and J.
Trevor would have gladly traded three lesser cards to get rid of Broodstar. And for good reason - Broodstar was wrecking him. It was too big, hard to counter because of the cheap cost and J's own countermagic, and there was almost no time to find an answer after it was on the table because the clock was so fast. Sometimes, though, he'd manage to do it, and those were the games where he'd either win or come close to it.
If you refer to the chart above, you can see that casting Mana Leak on Broodstar to counter it is a great trade, even though PCA says it's only one for one. Even casting two Mana Leaks isn't bad - you're still countering 2.50 worth of cards with 2.00 of your own. Trades like this occur in every game of Magic, and they are good trades, despite the loss of Pure Card Advantage. Pyrite Spellbomb and Electrostatic Bolt team up to kill Clockwork Dragon. Molder Slug feels the pain of Barter in Blood, even if the caster loses a Nim Shrieker and Myr. Forbid used to pop up all the time to counter but one card, with two useless land taking the hit.
A good knowledge of Effective Card Advantage really helps with your deckbuilding. Once we'd determined that the Broodstars (and to a lesser extent, the Myr Enforcers) were dominating the matchup, I had Trevor remove his sub-par creatures for Dark Banishings, and the matchup immediately became almost even. Broodstar, that 2.50 juggernaut of a card, generally worth a couple of opposing cards, was getting popped by Dark Banishing on a regular basis, and all was right with the world.
Dark Banishing was clearly a 1.25! J was able to set up favorable ECA trades for himself, though - using Aether Spellbomb. The Dark Banishing would sometimes trade with the Spellbomb (0.75 and some tempo) instead of the Broodstar (2.50) and in those cases, J could keep the pressure on with his flying beater.
ECA is all over the place, in Limited and Constructed formats. It's easy to track in Limited, where you can assign values to cards according to where they are generally selected in draft. If your eighth pick trades with an opposing first pick, you're up some ECA. All things being equal, if you trade a couple of middling utility cards for a couple of monster picks, you're in great position when your own monster picks come up. Hopefully you have some! Spikeshot Goblin gets drilled with that sixth pick Irradiate all the time. Molder Slug, #1 card in the set, falls easily to Terror, not an unconditional first pick. The 5/5 token from One Dozen Eyes or Promise of Power sometimes gets sent home with late pick trash like Regress (not that Regress is that bad, but it does go late), and if you go into other formats, you see even more extreme examples.
Demystify, for example. No pick in all of OLS so consistently traded with a pick so much higher than itself. Lavamancer's Skill. Pemmin's Aura. Death Match. Centaur Glade. Form of the Dragon. Aurification. The same phenomenon could be seen with Counterspell back in Masques Block draft. Power Matrix would sometimes hit the bin, and all because of a late pick. It was once said that Disenchant is a power card in Limited because it destroys power cards, and I understand exactly where that sentiment is coming from. That's what Effective Card Advantage is all about. Cards that trade your own less valuable cards for more valuable ones can be measured in terms of ECA. Brainstorm would be a good example, as would Scroll Rack.
Before we get too deep though, try out the following table for picks in Limited:
Pick 1- 2.00
Pick 2- 1.50
Pick 3- 1.00
Pick 4- 0.90
Pick 5- 0.75
Pick 6- 0.66
Pick 7- 0.50
Picks 8 & 9- 0.45
Picks 10, 11, & 12- 0.33
Picks 13 through 15- 0.25
And so on. You can see from this rough table that trading two eighth-pick caliber cards for a fourth-pick caliber card will generally work out in your favor. We're judging in terms of general card strength here, not the position the card was actually drafted. For example, it's quite possible to have more than three"first picks" in your draft deck, despite having only three actual, official"first picks" in any given draft.
For the purposes of this system,"first picks" are those cards that are unconditional first picks, or very strong. More typical first picks will generally go in the"Pick 2" column. Let's go through a quick example of the system at work.
Your opponent casts Molder Slug. (Pick 1 for sure, 2.00). You untap and lose an Iron Myr (Pick 5 or so, 0.75). On your opponent's upkeep, you wait for him to lose his Talisman of Impulse (Pick 6, 0.66) and then cast Terror (Pick 3, 1.00) on his Molder Slug.
You lost 1.75 ECA worth of cards, he lost 2.66. You're ahead in effective card advantage. What do the other, parallel card advantage systems say about this transaction? PCA says that your Iron Myr and Terror traded for his Molder Slug and Talisman of Impulse. An even trade. VCA likewise says that things are even, but the key here is that they very nearly weren't. In fact, it's likely that if left alive, that Slug would have rendered many, many cards in your deck completely useless, gaining your opponent massive virtual card advantage. It's even, and as a player you should thank your lucky stars that it's even, because that Molder Slug was about to start dominating the game, reducing your viable lines of play, piling of dead draws on your side, and generally being ridiculous.
The above is one example of how the three systems tie together. Before we go too nuts, though, we have to remember that card values are relative, and that at some times it is appropriate to give a card an ECA rating of 0.00, a.k.a. the Big Goose Egg. This is where ECA ties in with VCA, Virtual Card Advantage. If all draws that aren't useful are null draws, it stands to reason that the ECA value of such cards is 0.00.
Here's another example. You and your opponent both have plenty of land in play in a casual T1 game. He casts Thorn Elemental, you cast Forbid with buyback, discarding two lands. Now, we don't know the respective values of Thorn Elemental and Forbid without playtesting the matchup in question, but we can guess. Going from a baseline value of 1.00, and with the knowledge that it's the late game (where Thorn Elemental is pretty damn powerful) we can assign the Thorn Elemental a value of 2.00. I'd gladly trade any two cards of middling usefulness to get rid of a Thorn Elemental if I was playing Blue, and that's how I arrived at that rating. Yours will vary, but that doesn't mean the system doesn't work, or that it's clumsy or inexact - it only means that you have to apply it with care.
The lands are completely useless draws, and we're assigning them a value of 0.00. [Because you also have Forbid, the lands have considerably more value in your hand than they would on the board, demonstrating that variable value of even seemingly"useless cards" is zone dependent. - Knut] What do our respective systems say about this play? PCA says that you just traded two cards for one opposing card, and you're down a card as a result. This is true, but it's a trade you're happy to make. (The fact that Pure Card Advantage numbers so often only scratch the surface of a play is the main reason why I can't believe that people are unable to accept the fact that Beast Attack is worse than Durkwood Boars under PCA. All sorts of strategically superior plays return negative PCA numbers. That's how the system works.)
VCA says that things are even. Of course, if the Thorn Elemental had resolved, they sure as hell wouldn't be, and the Blue player would now likely only have a few cards in his deck that could save him, a substantial reduction in viable lines of play. Lots of virtual card advantage. That didn't happen, so it's even. Thank heavens for countermagic!
And ECA? You've traded two 0.00 cards for a 2.00 card. You're up 2.00 ECA. This is nothing new to fans of the San Francisco Giants, who make a trade like this every few seasons, except in reverse. They send off an All-Star and get something from ballplayers anonymous in return. (To be fair, this was much more of an early 90's affliction, and SBC Park fans haven't had to suffer as much lately.)
So how do you apply ECA to your own games?
- If it's Limited, start with a baseline value for cards depending on how strong of a pick a particular card generally is. In order to find these baseline values, I recommend reading articles by our own Tim Aten, Nick Eisel, Ken Krouner and Mike Turian. Modify these listings (which generally tell you how high you should pick a card) by listings gleaned from real life (ie. how late you will get a card). For example, Spellbomb draft proponents know they are a vital part of the strategy, but you can and will pick them up late. This should be reflected in your rough ECA valuations.
- If it's Constructed, assign the baseline value based on how valuable a card is in the matchup. This will take testing, but since you should be testing anyhow, I'm sure you'll have no problem doing it, if you feel so inclined. You don't need to keep exact numbers - just a general idea of which cards are the strongest would be a great starting point.
- Once you have these rough numbers (or not so rough, if you're a hardcore theorist), modify them according to the game state and virtual card advantage theories. If it's turn 1, there's no way in hell you'll trade one of your precious land for anything less than a gamebreaking card. Decks need mana to run. Once you have mana, though, trading your now-useless land (0.00 ECA) for opposing useful cards becomes a luxury. The same goes for any cards that are nullified because of virtual card advantage on the part of your opponent. A Meddling Mage on Circular Logic might reduce the ECA of the card to 0.00, but what if you throw one out to keep your Mongrel alive (effectively trading it for a Mongrel on board, probably worth at least 1.00), or loot it away to draw one of your Waterfront Bouncers against that WW deck (trading a 0.00 card for a 2.00 bomb in the matchup).
That's ECA. Find some rough values, modify them by the game state, and you'll find that it's easy to have a concrete idea of which trades are good and which are awful. 0.00 ECA values are very important in Magic. Useless cards aren't cards at all, so you can get rid of them without any qualms. Betrayal of Flesh entwined is four cards to get two, but who cares? Three of the cards spent are 0.00 ECA cards a lot of the time - three useless land. Get the idea? This sort of thing is what Magic is all about!
I hope you enjoyed the PCA/VCA/ECA article series. It's been fun, and though the ride was a little rough during some parts, I'm proud of the work I've done here. Magic is a game of minutiae, and it's often a lot of fun to just roll up your sleeves and jump in to see what you can discover. If you have any questions about the system as a whole (it's evolved somewhat since the start) or about ECA in particular, feel free to email me or chime in on the forums! I'll be happy to answer anything you might send my way.
Until next week, it's been real.
GT_ on #mtgwacky
FP_GLyM on MODO