Tuesday, April 15, 2014

Life in the Fast Lane, Part 1

Combing through Gatherer in search of worst cards ever printed, even a chronic caviler such as myself has to admit that Magic’s design has come a long way. Modern sets are laid out with some care, feature tight mechanics, and are supported by solid creative foundations that most audiences recognize and enjoy.

Ryan Stiles, famous for his Griselbrand impression, on Whose Line Is It Anyway?

But gather round, if you dare, and listen to tales of darker days, when men were men, women were women, and hedge funds were a good idea. Sets were filled to the brim with inexplicable dreck like Search the City. Flavor was just a bitter taste in the back of your throat that left you gasping for air. Adam Sandler movies made money!

I know — you don’t have to say it. Adam Sandler movies still make money. Well, so did Magic, despite many of its early designs going straight from an Edward Lear fever dream to the printing press:

Sleight of Mind is amazing. What if we put it on a creature? Awesome! But it should only work on white enchantments — comboing with CoPs and Wards is crazy enough! Maybe … too crazy? Maybe you should only be able to change a card’s text once. Hmm … better tack on a cumulative upkeep, just in case.”

*Thunderous applause*

Ladies and gentlemen, name that card!

Improbably, that facetious figment contains 39 fewer characters than the original rules text for Balduvian Shaman, an Ice Age common that Kareem Abdul-Jabbar famously bet Larry Bird he couldn’t read just once.

Thankfully, it’s not just individual card design (and spelling
) that’s improved over the years. Take a moment to consider that, once upon a time, Naked Singularity, Reality Twist, Infernal Darkness, and Ritual of Subdual— cards with a beloved staple effect, to be sure — were all printed in the same set, in three different colors and on an artifact. (With an honorable mention for Illusionary Terrain.)

Of course, it’s easy to poke fun at bad old cards and sets. Magic went through some undeniable growing pains, but aside from the online client, the game’s much better now than it was 10 or 15 years ago. It wouldn’t be unreasonable to consign the past to the past, and simply enjoy the modern game for all it has to offer.

Still, it might be fulfilling to find a way to appreciate terrible cards, not just for laughs, and not because of their historical context as part of a larger phenomenon, but for what they are, and what they do — if not exactly as their designers intended, well, as close as you’re likely to get. Why not do it three cards at a time?

Three Card Magic

“Three cards ought to be enough for anybody.” — Bill Gates
Yes, yes, we all know Bill Gates didn't actually say the quote I'm bastardizing. You're so clever.

Three Card Magic is a delightful casual variant, and an easy way to play a quick game of Magic (or something like it) with a group of friends. As an added bonus, it will often expose you to cards you’d forgotten about, or never even knew existed.

To play, two or more people think of decks with only three cards in them, and then all the decks are pitted against each other in a round robin. Games are played under essentially the same rules as normal Magic, though with some necessary modifications:

  • Rule 120.4 (“A player who attempts to draw a card from an empty library loses the game the next time a player would receive priority”) is ignored.
  • At the start of each game, each player draws a hand of three cards, and mulligans aren’t allowed.
  • A match consists of two games. Each deck will be on the play once and on the draw once.
  • Any random abilities you control (like coin flips), if any, always go in favor of your opponent.
  • Players must play optimally and with perfect information. This means that, in effect, players don’t actually “play” at all. You’re really just figuring out how each deck performs against each other deck when played perfectly.

Games are generally scored 3 points for a win and 1 point for a draw (with the winning deck being the one with the highest aggregate score in a round), but that’s really up to you and your playgroup, as are any number of other possible rules and restrictions, such as maintaining a running banlist of the cards from each round’s winning deck (excluding certain mana sources, if you want.)

Even with just three cards, there are untold strategic depths to be plumbed. Chancellors, pitch spells and free spells, Black Lotus, storage lands, Null Rod and Humility effects, alternate win conditions, graveyard recursion, leylines, planeswalkers, and more. There’s a way to play almost any card, and every deck loses to some other deck.

If your banlist grows too restrictive, you can let the winner of each round unban a card. Or you can change formats (eternal, block, standard, pauper, Commander, etc.), or make up entirely new rules, for example: spells cost X less, all mana costs are colorless, mana pools don’t empty, any deck that can win unopposed before turn Y is illegal, creatures can’t attack, or anything else you can think of. The point is just to have some lighthearted fun, and it’s free and easy, as well.

Now, if you’re thinking half the potential cards I rattled off sounded like some of the best cards ever printed, well, fair enough. Three Card Magic, like regular Magic, tends to be dominated by decks full of awesome cards that do awesome things. (Though one of my favorite decks, Karakas / Ivory Giant / Leyline of Singularity, only has one “good card” in it.) In search of the inscrutable and arcane, we must go deeper.

Good Decks Gone Bad

“Have you heard that it was good to gain the day? I also say it is good to fall, battles are lost in the same spirit in which they are won.” — Walt Whitman

One hilariously askew variant of Three Card Magic is loser’s 3CM (or “crapdeck”), and it turns the concept of victory on its head. The goal in crapdeck is to make the worst possible deck that nonetheless has the capacity to win. That is, your deck must be able to win, but the last thing you want is for it actually to do so. Ranking is reversed in loser’s 3CM, so the champion deck is the one with the lowest score (fewest wins, generally) in a round.

As before, rule 120.4 is ignored, matches are two games apiece, and players are still obligated to play perfectly. Additionally, it makes sense to reverse the randomness rule, specifically, any random abilities you control, if any, always go in your favor.

But what does it mean for a deck to have the capacity to win? This is a thorny issue, though one that can be satisfactorily resolved, I think. The most sensible idea I’ve encountered is that a deck must meet the following two criteria:

  • It beats an empty chair.
  • It wins at least one game on the play or on the draw against at least one other legal deck.

Here are some examples of decks that fail to meet one, the other, and then both of those criteria:

  • Swamp / Swamp / The Rack beats an empty chair (assuming the empty chair has no cards in hand), but it can’t actually beat any legal deck. If any deck would lose by playing a card, that deck would simply opt to play nothing and draw the game instead.
  • Black Lotus / Black Lotus / Wild Evocation wins by force against Memnite / Memnite / Pact of the Titan (which itself is certainly legal), but can’t do anything against the empty chair.
  • Darksteel Citadel / Orzhov Basilica / Pillory of the Sleepless can’t beat an empty chair or any other legal deck. No opponent would play a creature for you to enchant with Pillory of the Sleepless if doing so would ultimately lose them the game. Swap out Darksteel Citadel for Forbidden Orchard, though, and you have a legal deck.

The initial instinct most people have when putting together their first crapdeck is to make use of an exceptionally slow two or three card combo. You’ll find out quickly that’s rarely (if ever) the best strategy. The best loser’s decks tend to feature obscure combinations of cards that interact with opponents in unusual ways, and the merely slow decks often play into the hands of various weirdly interactive strategies all too easily.

But what makes for poor strategy in loser’s 3CM is nonetheless — I hope you will find — an amusing Magic: The Puzzling sort of exercise. And besides being an interesting challenge, this and similar mental excursions will likely make you a more creative thinker, and perhaps even a better player and designer.

Merely Slow Decks

“It is also slow play if a player continues to execute a loop without being able to provide an exact number of iterations and the expected resulting game state.” — Magic Infraction Procedure Guide

The two most important factors for slowdecks are time and mana inefficiency. You want to approach a win condition at a snail’s pace, pay lots of mana to do it, and gather that mana as slowly as possible. Even a lowly 1/1 is an absolute powerhouse when you’re trying to drag out a game. Memnite, for example, closes games in a blistering 21 turns, which is nothing to write Renton about.

Helix Pinnacle seems almost tailor made for odd situations like this. Forest / Helix Pinnacle immediately sets a baseline of 102 turns, which can be prolonged slightly with an off-color land, forcing Helix Pinnacle to be cast through Mana Cylix. Unfortunately, this is where Helix Pinnacle shenanigans come to an end. Depletion lands, which initially look promising, can be tapped in response to the upkeep trigger, allowing you to charge the pinnacle at the usual rate. (Thanks to reader Xom for this interaction.)

102 mana is a tidy sum, but there are combos with even greater mana requirements. Sand Silos / Capsize / Leyline of Lightning is a neat idea that costs well over 100 mana, lasting 177 turns in total. Buyback isn’t the only way to engage in expensive repetition, either. Heliophial / Reito Lantern and Pyromania / Skull of Orm are both combos that consume 10 mana per cycle, and take 20 turns to play out even after accruing the necessary mana via Dwarven Hold. Both decks take a respectable 224 turns.

An important tool for even slower decks is the combination of colored mana requirements and an inefficient mana filter. The worst mana filter combo I know of is Springjack Pasture plus a storage land, which accumulates mana five times more slowly than a storage land alone. That leaves only one slot for a sluggish, color intensive win condition, but happily, Balduvian Shaman and its cumulative upkeep kin provide a wealth of options.

Springjack Pasture / Icatian Store / Illusionary Presence takes an impressive 297 turns to triumph (this despite Illusionary Presence's beefy stats), thanks to the wonders of cumulative upkeep and quadratic growth. (Incidentally, it is curious to note that Illusionary Presence was printed at rare, while Illusionary Forces, from the same set, was common.)

Replacing Illusionary Presence with Mystic Might yields two significant gains. The first is that Mystic Might has a higher cumulative upkeep cost. Second, even the colorless mana in Mystic Might's cumulative upkeep has to be paid with goats, thanks to the storage land being monopolized by Mystic Might once attacking gets underway. That’s good for a hefty boost to 471 turns.

Lamentably, both Illusionary Presence and Mystic Might are relatively efficient beaters, needing only 10 turns to deal 20 damage once they come online. It would be nice to be able to use a 1 power creature and get 10 extra turns of cumulative upkeep, but none of the 1 power creatures with cumulative upkeep have colored mana in their upkeep costs.

Splintering Wind, however, provides a method of creating 1/1 creature tokens that have a cumulative upkeep of G, which at first glance looks perfect for crushing three card slowdeck right into the quadruple digits. Unfortunately the naïve Splintering Wind strategy (create a Splinter token, attack with it for 20 turns straight) isn’t optimal. Figuring out the correct sequence of plays with Splintering Wind is a bit more complicated than doing so for any of the other decks, but according to my calculations, perfect play prevails in a paltry 311 turns.

So 1 power creatures are a bust, but there is a 0 power creature with cumulative upkeep: the exceptional Sustaining Spirit. Not only is Sustaining Spirit the only Angel in Magic without flying (from a creature type retcon due to the art, most likely), it has an excellent cumulative upkeep of 1W. Less desirable is the fact that you need a second card to increase Sustaining Spirit's power, which means there’s no room for Springjack Pasture in a Sustaining Spirit deck.

But it turns out 20 turns of cumulative upkeep 1W is just enough to make up for losing the goat multiplier. There are lots of ways to increase Sustaining Spirit's power (or turn it into a Tim), like Rustic Clachan, Flowstone Armor, Darksteel Garrison, Wolfhunter's Quiver, or Pennon Blade, but the best (by a fair margin) is Thran Forge, which clocks in at 487 turns.

As far as I know, there’s no way to surpass 487 turns with Sustaining Spirit, or 471 turns with Springjack Pasture. To further slow the pace, only two real options present themselves: Halls of Mist, or either of the two cards with cumulative upkeep costs greater than 2, namely Naked Singularity and Reality Twist.

Halls of Mist is very nearly ideal. It reduces attacking to half its normal rate, and has cumulative upkeep itself, solving two major problems in a single card. A cumulative upkeep of just 1 still demands a fearsome total of 820 mana over 40 turns, but, alas, I know no way of fitting Halls of Mist into a viable deck.

Naked Singularity, on the other hand, readily lends itself to abuse due to the glut of */* creatures that count artifacts. The devilish Sand Silos / Naked Singularity / Broodstar combo takes a stunning 666 turns to win, making it the undisputed champion of three card slowdecks.

One Bad Turn Deserves Another

“Things are never so bad they can’t be made worse.” — Humphrey Bogart

So where do we go from here? Having, to the best of my knowledge, exhausted three card slowdecks, it’s natural to think of doing the same analysis for four card decks, or five. But when do you stop? You could spend a lifetime searching for the slowest decks of increasing numbers of cards, but it’s not a terribly compelling task, at least to me.

What about the slowest deck with any number of cards, though? Of course, if you truly allow yourself arbitrarily large numbers of cards, you can make a deck that takes an arbitrarily large number of turns to win. For example:

“Heartless Maniac”
2x Heartless Summoning
Serra's Sanctum
Blessed Orator
Defy Death
Laboratory Maniac
1,000,000x Swamp

… takes about a million turns to win. Stick in a billion swamps, and it takes — wait for it — about a billion turns to win. But it’s not terribly satisfying, not least of which because you’ll eventually surpass the total number of swamps ever printed (5,000,000,000ish?), never mind actually playing the thing. So what I really mean to ask is this: what’s the greatest algorithmic complexity that can be built into a combo?

Or said in another way, with a similar (but not strictly equivalent) question, what’s the highest turns to cards ratio that can be achieved? That gives us something easy to measure, and by that metric, the Heartless Maniac deck is terrible, with a ratio of approximately 1. The Broodstar deck, with its efficient exploitation of cumulative upkeep, is orders of magnitude better, at 222.

It’s certainly possible to keep improving that ratio by adding cards to complicate the execution of the cumulative upkeep decks, and there are even ways to make decks that exhibit cubic growth instead of quadratic. But we can do drastically better with an entirely new approach, and we need look no further than Magic’s own head designer for inspiration.

No, we’re not going to print Markov Patrician months after claiming “lifelink can be very swingy, so we don't print creatures with lifelink with power greater than 2 at common.” Don’t be ridiculous! I’m talking about drawing inspiration from Mark Rosewater’s well-known and frankly disturbing obsession with doubling. (And let’s not forget about doubling’s red headed stepchild, halving, or all the Doomsday Tendrils players will have an aneurysm.)

Doubling Down

“It is awfully hard work doing nothing.” — Oscar Wilde

It’s not immediately obvious how any of the true doubling spells could be of any help, but the halving spells are fairly straightforward, and introduce a powerful idea: using your own life pool as a resource. None of the “pay half your life” spells do anything else relevant, but as we saw previously, Leyline of Lightning can turn any spell into a Gut Shot. If the only spell available is, say, Death Wish, you’d require a huge amount of life to be able to cast it 20 times.

Beyond that, all this concept is missing is a way to actually recur the Death Wish, and a one-shot source of infinite life gain. It’s important that the deck only be able to gain life once, otherwise you can go from 1 life to 2 life, pay half, rinse and repeat. As enchanting as a Farmstead deck sounds, the card is just too powerful for our purposes. Regardless, there are plenty of one-time infinite life gain cards, the quaintest of which is Icatian Moneychanger.

“Pound of Flesh” (5 cards)
Leyline of Lightning
Icatian Store
Icatian Moneychanger
Panoptic Mirror
Death Wish

This surprisingly compact deck takes approximately 2^14 (16,384) turns to deal 20 damage, with a ratio of about 3,277. (You get 2 free Leyline procs from Panoptic Mirror and Icatian Moneychanger, plus 4 “free” casts of Death Wish due to your starting life total being 20 and not 1, which you are obliged to exploit before gaining any life. Thus the exponent is 14 and not 20.)

The important thing to realize with a “half your life for 1 damage” combo is that it takes around 2^n turns to win (assuming you gain 1 life per turn), and the exponent is based on your opponent’s life. Thus the most straightforward way to further inflate the turn count is clear: force your opponent to gain life!

You can’t just throw a few Healing Salves at your opponent for no reason, though. Whatever you do to make your opponent gain life has to be necessary to the functioning of the deck. A simple way to achieve this is with Grove of the Burnwillows. If your win condition requires red or green mana, you might need to tap Groves quite a few times.

Of course, there’s a small problem. It’s not immediately obvious why a deck with the goal of repeatedly casting Death Wish (or any similar spell, all of which are black) would need large amounts of red or green mana to function. There’s also the issue that executing the kill combo itself necessarily can’t use any Groves, or else your opponent will just keep on gaining life.

We need a way of cleanly segregating a deck into two stages: the setup stage, where you assemble the combo and increase your opponent’s life total, and the execution stage, where the combo is carried out until the opponent is dead. Remarkably, there’s a singular card that readily enables such strict separation between stages: Celestial Dawn.

Celestial Dawn is, in a word, extraordinary. Not only does it allow you to cast virtually any spell, or use any ability, once on the battlefield it turns all your Groves into Plains, allowing you to use them in the execution stage without any undesirable side effects like opponent life gain. The aim of a Celestial Dawn deck is thus to bootstrap the eponymous card as inefficiently as possible, followed by limitless recursion of a Death Wish combo that otherwise can’t be executed because the deck doesn’t have access to black mana.

What do I mean by bootstrap? Well, we can borrow a trick from the Heartless Maniac deck to force certain cards to be played in a particular order. If Serra's Sanctum is your only source of white mana, you must cast two other enchantments prior to Celestial Dawn. The most expensive enchantment in terms of Burnwillow mana is the fabulously fanciful Hidden Path, and we need two. Combining all that with a slightly different kill engine (because it deals one less “free” damage) yields this lobstrocity:

“Simo Häyhä” (14 cards)
4x Grove of the Burnwillows
2x Vesuva
2x Hidden Path
Serra's Sanctum
Celestial Dawn
Golden Urn
Nuisance Engine
Goblin Sharpshooter
Murderous Betrayal

… which lasts ~2^23 (8,388,608) turns and has a ratio of ~599,186. At first blush that seems spectacular, but it’s no surprise the ratio improved so much. Every time the exponent increases by just 1 (that is, for each 1 life your opponent gains), you’d have to more than double the size of your deck before your ratio took a hit.

Given that, a simple turns per card metric doesn’t seem entirely sensible for comparing 2^n decks. It values huge, unwieldy decks over the truly elegant and aesthetic. Even though at this point we’re really just engaged in mental masturbation, it would be disappointing if the best deck were so large it could only be purely theoretical.

So, for 2^n decks, it’s better to examine the ratio of the exponent to the number of cards in the deck. (In essence, calculating how effectively the deck increases the opponent’s life total.) By that measure, Simo Häyhä fares rather poorly, as the deck has 14 cards but only manages to bump the opponent up to 28 life (23 adjusted), for a “log ratio” of 23/14, or about 1.64. Pound of Flesh’s log ratio of 14/5 (2.8) is a tad more impressive, but is still ripe for improvement.

A Gauntlet Is Thrown

So what’s the best log ratio that can be achieved? I don’t really know, but I encourage you to adapt and extend the tools in this article to build your own slowest combo. (Hint: Serra's Sanctum was part of a cycle.) If you come up with anything interesting, leave a comment, email me at infiniteherpderpgyreherpderpblog@gmail.com, or drop me a tweet at @infinitegyre, and I’ll include your deck in a followup article.

Or if you hate puzzles and just want to be told The Answer, continue on to Part 2 and Part 3, where I reveal two truly insane decks with algorithmic complexities of 2^n^3 and 2^2^n, both of which you can fit in your pocket, but would take longer than the heat death of a million billion trillion quadrillion qui—well, you get the picture—universes to play out.

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