It’s funny what a week’s looking at a format can do to change your understanding of it, and perhaps funnier still that the snow-covered lands should generally be considered a top pick for whichever colors they happen to tap for. Considering how ridiculed they were when first we met them in Ice Age, it’s amazing what a little creative design can do to change one’s opinion of a previously laughable resource. When asked initially at the Coldsnap pre-release how highly one should be drafting their snow lands, my advice was to forget that they didn’t tap for two colors of mana or crank your mana up by tapping for two total mana… and draft them as highly as you were used to drafting your Karoos in Ravnica Block. Just like Karoos — and, to a lesser degree, Signets – they are the truly limiting factor in the draft environment. Many of the best cards use snow mana, or otherwise benefit you for packing your deck full of snowy permanents, and in the end you’re going to want to always draw snow-covered mana sources… often wanting them in abundance.
“When everyone knows what they are doing”, a draft format looks very different than it does initially. When nobody knows what they are doing, the hidden gems of the format remain untouched, as the more obvious themes get understood first. After all, in Mirrodin draft’s first week hardly anyone knew that Affinity was worth chasing so hard that the artifact lands were actually incredibly high picks… and even when they did eventually figure that out, it was still a matter of months rather than weeks that the Myr and Spellbombs were properly weighed and drafted accordingly. Similarly, with Ravnica-only draft, the Selesnya Conclave was readily overlooked for quite a while… and later proved to be the best guild of the four if you knew what you were doing.
Ripple is the first stand-out mechanic in Coldsnap Limited, and it is clearly a mechanic that rewards you for trying to get as much of it as you can… if it works. Earlier this week, Julien Nuijten presented a table on the math of Rippling, showing the approximate expected value of a Ripple card given a certain number of copies in the deck and the number of cards remaining in your deck. It effectively shows where the element of luck and the element of skill intersect, putting hard numbers to a mechanic that seems inherently unpredictable, and shows quite clearly about how much bang for your buck you’ll get from trying to bend your deck as far away from the normal as you can get.
Consider this example again:
10 Surging Dementia
14 Krovikan Scoundrel
16 Swamp
Clearly the harder thing to get is ten Surging Dementia, as the place held by Krovikan Scoundrel can easily be filled by a variety of creatures that attack reasonably well and can be cast reasonably cheaply, so you can follow up your turn 2 Mind Twist with some quick drops and put the game away. Getting ten of something should be preposterously difficult, as there are eleven commons per pack and sixty-five commons in the set, leaving one copy of a card in each 5.9 packs. An eight-man draft will have 24 packs, giving an average of 4.07 of each common in the draft… good enough if you’re the guy trying to draft all the Feasts of Flesh, but not quite enough for Surging Dementia Guy. Presuming that you are attempting to draft the degenerate draft deck, scooping up the maximum “Collect Me’s” in order to capitalize on their power when stuck together in large numbers, you have to both pick every copy of “your” card at the table and pick a card that will actually be represented in numbers as the draft goes on, beating the odds to get more than four copies even if you do succeed at getting everything.
Because of this, despite the prevalence of “collect me” cards, more extensive drafting has been showing the snow-based decks to be a better deck overall. Recent trials on MTGO, in real life, and even in such obscure places as the web-applet draft program found over on CCGDecks.com have suggested that going for the synergy you can bet on instead of the synergy you can’t is a key mode to success. After all, while this is Zvi’s pet project Limited set and you can feel the throbbing of the “Degeneracy Matters!” theme, it was intended to be “Snow Matters!” In the end, it seems that Snow creatures and Snow mana are showing better results, thanks to the fact that playing the numbers game when the odds favor the house will eventually bankrupt you, even if sometimes you’ll see remarkable success.
And yes, the odds do favor the house. Magical Hack is all about running with numbers, and this means looking at things from two different perspectives. Choosing a card to collect, and even getting all the copies of them at the table, is still a bad bet. Most of the “collect me” cards are good but not amazing with four copies, because turn 3 Sound the Call, turn 4 Sound the Call is “good” but not quite “amazing” until you get another turn 5, and not ridiculous at all without another Sound the Call or two on turn 6. Sound the Call–Forest.dec is clearly pretty awesome, and it would be hard to consistently beat, but nobody’s going to get 22 of them. Even six, which might be reasonable to hope for but definitely not expect, is still merely “good” and not overwhelming, after all you still have to draw three of them before they’re really special.
Starting with the presumption that you’re going to catch them all, let’s see if we can run the numbers on how often any one common will perturb from the “standard” 4.07 copies per draft in your favor. The chances of opening any one common is 11 / 65, or 16.9%. Consequently, because it’s simple math, the chances of not opening that card in a pack is 83.1%… but fortunately you get twenty-four tries. One binomial distribution later, to take the number of events occurring in a given number of trials with a known probability, we get the following probability distribution:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|
0.01168
|
0.05711
|
0.13379
|
0.19987
|
0.21374
|
0.17416
|
0.11235
|
| 7 | 8 | 9 | 10 | 11 | 12 | |
|
0.05885
|
0.02547
|
0.00922
|
0.00282
|
0.00073
|
0.00016
|
|
| 13 | 14 | 15 | 16 | 17 | 18 | |
|
0.00003
|
0.00000
|
0.00000
|
0.00000
|
0.00000
|
0.00000
|
|
| 19 | 20 | 21 | 22 | 23 | 24 | |
|
0.00000
|
0.00000
|
0.00000
|
0.00000
|
0.00000
|
0.00000
|
Which looks like the following probability distribution, cleverly lumped in favor of biasing exactly four copies of each card:
So, to summarize basically how trying to greedily gobble multiples of “your” card goes… first you have to make sure you can get all of them that are opened, which is by no means a sure thing. Then you have to get lucky, because once you step into the neighborhood of getting five or six of a card in the draft, you start to see that happening in one draft out of seven, or one draft out of ten, rather than one draft out of five in which your card will appear exactly four times… or worse yet, three times out of five you will see four or fewer copies of an individual card appear. That Surging Dementia ripple deck I have been staying up nights dreaming of getting to play? In addition to Julien’s calculation of the EV for rippling given a specific number of Ripple cards, there’s the probability distribution above saying that it will only ever happen that you get ten Surging Dementias in a draft almost… almost!… three drafts out of every thousand.
Oh, how glorious those three drafts will be… but I digress. There was a point here, before I began running with numbers.
 |
Expecting to open an overwhelming quantity of a specific card is clearly a bad bet, when the strength of picking “your” card over everything at all times is not likely to provide the kinds of results you’d need to justify, oh, picking Krovikan Mist over Skred. The math is much better in favor of drafting parallel to the actual theme of the set, Snow Matters, and maximizing your Snow-loving cards like Rimewind Taskmage, Heidar, Rimewind Master, and Skred. Snow-Covered Lands, then, are worth chasing, as they enable your highest-quality cards, which isn’t even counting the useful applications of Snow mana that help make cards like Zombie Musher that much better in your deck, and can make unglorified 1/1 fliers into 5/5 attacking monstrosities.
Fortunately, for those who wish to try and buck the odds, these things do happen from time to time and with the sheer number of “Collect Me” cards you’re bound to see more than four of at least one of them pretty much in every draft. Some of them, like Feast of Flesh and Surging Flames, are removal spells that will be highly valued and not likely to make a circuit of the table in search of the player who loves them… and some of them, like Surging Dementia, will be nigh-unplayable even with however many copies you’re likely to see in a draft any more often than three times in a thousand (and that was rounding up in its favor). How many different cards can the wily player keep an eye on, in the hopes of perhaps getting six copies at an eight-man table?
Surging Might
Surging Sentinels
Surging Flames
Surging Aether
Rune Snag
Feast of Flesh
Sound the Call
Krovikan Mist
Kjeldoran War Cry
…
That’s quite a few cards, and using the above numbers there’s about an eleven percent chance of finding six copies of a specific common in the draft… and while clearly you don’t get to pick and choose which common is going to appear in that frequency, you can try and use the way in which numbers work to your benefit. After all, over the course of a draft you see the above probability distribution for opening a larger number of certain cards. Presumably if you are opening “normally,” you’ll see one copy in one pack of the draft, one copy in another pack of the draft, and in a third pack you’ll see two copies. However, each pack being opened is an independent event, so the 16.9% chance of opening “your” card doesn’t suddenly go down just because there were perhaps three copies of a card in the first pack. If you’ve managed to scoop up three Surging Sentinels in the first pack and are hoping today is your day to get six copies and go Ripple-crazy with them… well, you still have sixteen packs to work with in the future and the probability of your Sentinels appearing in their “average” quantity of approximately one per six packs (which means you’ll see probably two and maybe three copies, which will get you either to five or six copies of the Ripple soldier). Leaving off the higher number of copies, which are clearly ludicrous, looking at sixteen unique events to figure out how many copies of the card you are likely to get in the remaining packs shows us this:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|
0.05149
|
0.16781
|
0.25637
|
0.24371
|
0.16134
|
0.07888
|
0.02946
|
You thus have a 52.4% chance of getting to six or more copies in the draft, and a 78% chance of getting to five copies… the remainder of the packs behaving normally, with (at least) one copy in the remaining two packs despite having opened three of your allotted four already. While on the one hand hoping for multiples blindly won’t work… but “plenty of Collect Me Card X” is a possible signal to read in pack one that can potentially be followed up. The math is much more functional if you try reading a signal and acting upon it, such as following your normal guideline for drafting… read signals, pick the strongest cards, et cetera… with the sub-clause of altering your plan to include a heavy focus on a “collectible” card if you have seen a flush of them in the first pack. Picking Krovikan Mist early is definitely not something you could expect to have much value for the first Mist, but if you pick up three in the first pack (even if it’s at the expense of supposedly better cards) then your chances of earning a return on investment are reasonable.
In short, it follows with math what others have been putting as their general guideline, since so many things have to go right in the first place: first there have to be that many, then you have to get them all, and then they have to be worth more than the cards you could have been taking already. Thus, most normal human beings (once they’ve figured out “the math” behind betting your draft on one card appearing in sufficient frequency) will avoid many of the cards of this nature, unless they really want a +2/+2 enchantment, a 1/1 flier for two, or a Nightguard Patrol that taps to attack. Most players will allow such cards to go untouched in the first pack, if you want to pass the first one you see in the first pack and not plan on taking any until you’ve seen the second copy in pack one. The math is not fuzzy, but how you might want to employ it is. Do you draft “normally,” regardless of what you see as far as the number of “collect me” cards goes? Do you open yourself to the possibility of drafting Collectible X over everything except a very small subset of clearly awesome cards? Do you happen to pick one up if you have nothing really better to do? Do you go all-out and take that card over everything even before you sit down to the draft?
Here is where we come back to last week’s problem, chasing a fantasy by aiming for redundancy instead of sticking with the broader “snow matters” theme and drafting a deck more like we’ve seen from the upper echelon of drafters on the MODO beta-test server. Beta-testers and Julien Nuijten seem to agree that Green is a deep color but not necessarily a good one, and that White is basically a bad bet unless you open something powerful like Sunscour or Adarkar Valkyrie… leaving many of their decks to be Red-Black-Blue controlling decks maximizing use of Skred, Recover (especially Grim Harvest, when paired with sacrifice effects like Thermopod or, better yet, Gutless Ghoul), and the powerful nature of those three colors when powered up with snow-covered lands taken appropriately highly.
Do you want a deck that looks more like this…
5 Kjeldoran War Cry
3 Gelid Shackles
6 Krovikan Mist
6 Surging Sentinel
3 Jotun Owl-Keeper
2 Boreal Shelf
1 Mouth of Ronom
2 Snow-Covered Island
2 Snow-Covered Plains
5 Plains
5 Island
…
Or one that looks more like this?
3 Skred
2 Chill to the Bone
2 Grim Harvest
1 Coldsteel Heart
3 Rimewind Taskmage
1 Krovikan Scoundrel
2 Gutless Ghoul
3 Frost Raptor
4 Zombie Musher
1 Thermopod
1 Ronom Serpent
1 Mouth of Ronom
2 Tresserhorn Sinks
1 Frost Marsh
1 Snow-Covered Mountain
1 Snow-Covered Island
1 Snow-Covered Swamp
5 Swamp
5 Island
Frankly, both have their merits, and both look good from very different perspectives. As a representative of its species, the U/B/r deck above is pretty nice, with solid evasion, difficult-to-kill creatures, solid removal, and a strong board control element, plus the potential to get card advantage from your Recover spell. But the U/W deck is also likely to behave the same way every game:
Land, go.
Land, Mist, go.
Swing for one. Land, Sentinel, ripple a second and third copy of Sentinel into play. Go.
Land, 2 Mist before attacks, swing for nine.
Attack, War Cry, War Cry, opponent disconnects.
Fortunately for most, somewhere before the Mist-Sentinel-WarCry.dec kills its opponent, reality interferes and reminds a certain someone that he didn’t get six copies of this, six copies of that and five of the other… no, there were only three Mists, there were four War Cries but the other White mage took half of them, and there were five Sentinels but the other White mage had the same plan and took two rather than pass them to you. Planning for degeneracy is a bad bet, and so the colors that have the most to benefit from degeneracy are the ones that actually accomplish the least… thus the popularity (and, driving that popularity, success) of the Black-Blue-Red controlling snow deck.
Now that we’ve settled down and agreed to look primarily at that deck, it becomes prudent to address the question of snow-covered lands, because every deck wants to be aware of how highly they should be aiming for them. With two of the best commons of this color spread, Rimewind Taskmage and Skred, rewarding you for getting the requisite number of snow-covered permanents into play quickly, it’s clearly to your benefit to take the Snow-enabling basic lands, dual lands and even colorless lands at a reasonably high premium. After all, with there being approximately three per player, if you want to get more then someone else has to get stuck with less, and so you will get yours based on how highly you are picking your Snow lands. In Jeff Cunningham articles this week, a rough pick order of the individual colors was presented, and while it’s quite possible to draft a White deck, or draft a Green deck (especially in conjunction with either Red or Black, which complement its strategy nicely), the order for picking the Red, Blue and Black commons was most interesting. To summarize, in Jeff’s words and echoed to some degree by players who have been working hard to earn experience with the format, we saw the following put forward as a first look at actually drafting these colors:
Red:
1. Surging Flame
2. Skred
3. Ohran Yeti
4. Orcish Bloodpainter
5. Goblin Rimerunner
6. Thermopod
7. Martyr of Ashes
8. Karplusan Wolverine
9. Goblin Furrier
10. Rite of Flame
11. Icefall
I feel it is important to dissent in two key places: first, swapping Skred and Surging Flame, because Skred is incredibly powerful, in addition to being cheaper. Never hitting the face is one thing; never killing a six-toughness creature is another. Surging Flame is never going to Ripple effectively, and two damage for two is clearly weaker than X damage for one, where X can be quite a lot if your deck was drafted properly. The second place is considering Icefall to be dead last, because it is useful in quite a few more decks than Rite of Flame ever will be, and its function to pick off your opponent’s Snow mana can be an important one. I’ve seen decks where it was good enough to run, and been glad to have it more than once.
1. Skred
2. Surging Flame
3. Ohran Yeti
4. Orcish Bloodpainter
5. Goblin Rimerunner
6. Thermopod
7. Martyr of Ashes
8. Karplusan Wolverine
9. Goblin Furrier
10. Icefall
11. Rite of Flame
1. Disciple of Tevesh Szat
2. Zombie Musher
3. Rimebound Dead
4. Chill to the Bone
5. Feast of Flesh
6. Gutless Ghoul
7. Krovikan Scoundrel
8. Chilling Shade
9. Grim Harvest
10. Surging Dementia
11. Martyr of Bones
Here I dissent in another place entirely, wondering who in their right mind would honestly pick a Drudge Skeleton over Chill to the Bone and Feast of Flesh. Never mind whether it’s better or worse than Gutless Ghoul (and I think it’s worse, for the record), it clearly should be no higher than number five, and those two removal spells should move up in its place. Disciple followed by Musher sounds right, and I’d also lean towards swapping Grim Harvest with Krovikan Scoundrel… I’d be less embarrassed to have a Shade than a Scoundrel in my deck, even if there is a narrow archetype of B/R aggressive strategies that the Scoundrel functions in admirably next to its friend the Furrier.
1. Disciple of Tevesh Szat
2. Zombie Musher
3. Chill to the Bone
4. Feast of Flesh
5. Gutless Ghoul
6. Rimebound Dead
7. Grim Harvest
8. Chilling Shade
9. Krovikan Scoundrel
10. Surging Dementia
11. Martyr of Bones
Blue:
Not available at the time of this article. (Curses, it’s due out today and my time machine isn’t working properly!)
My common pick order for Blue would be as follows:
1. Rimewind Taskmage
2. Frost Raptor
3. Frozen Solid
4. Ronom Serpent
5. Drelnoch
6. Rune Snag
7. Survivor of the Unseen
8. Surging Aether
9. Martyr of Frost
10. Thermal Flux
? Krovikan Mist
Note that while I don’t consider anything at Ronom Serpent or below something I am especially pleased to be playing, basically every Blue card is playable in one way or another, and it’s only Surging Aether, Martyr of Frost and Thermal Flux I wouldn’t want to be stuck running… and each can be used in one way or another, or even be solid when applied properly (as is the case with Thermal Flux, at least). Also note that none of these include their on-color Snow land, but Snow-Covered Island should probably be drafted above everything below Frozen Solid, Snow-Covered Swamp should be drafted above everything below Feast of Flesh, and Snow-Covered Mountain might be best drafted above everything below Ohran Yeti. So “basic land” is about the fourth best common in its color… don’t you love Magic?
Note that these cards only include the commons, but there is one snow-land that should be treated as a bomb rare despite its mere Uncommon status: Mouth of Ronom. So many decks I’ve seen have added one off-color basic snow land just to up its count of snow mana and snow permanents, and yet while drafting they pass the Char that doesn’t cost your deck a slot (and that taps for Snow, besides!) in order to take something lame like a Jump Knight (Hi, Mark!). Regardless of color or archetype, Mouth of Ronom is a card you always want in your deck and it may very well be the best card IN your deck, to boot, so at the highest of echelons the pick order might be:
Sunscour
Rimescale Dragon
Adarkar Valkyrie
Mouth of Ronom
One of these appears much more often than the others, since it’s an Uncommon, and conveniently also has the benefit of fitting in any deck… so it’s an appropriate grab regardless of your color in packs two and three if you happen to open it then. To all of you out there reading: stop passing Mouth of Ronom, unless something odd happens and you actually get a chance at a Wrath or stupid game-winning flier and can actually use it. Whatever excuse you think you have for not taking it, well… you don’t. Ignorance of the rules does not excuse breaking the rules.
Hopefully we can understand a lot more about these rules later, because right now we’re still digesting a very complicated puzzle. Fortunately, now at least we have a better understanding behind the numbers game, and can begin to put plans into practice accordingly.