Oh What a Tangled Web We Draft
I'm hijacking Noah's column today to discuss a concept I've been knocking around I call the Creature Type Web. Learn it, love it and use it to thwart your enemies! It can even be extended past the new-hotness creature types of today's Lorwyn-Morningtide format back to old-and-busted mechanics of Magic's murky history. I'll get to those further on down.
Your Creature Type Web is how tribally connected your deck is. The most tribal deck possible has the appropriate creature type on all non-land cards in it. The least tribal deck possible has no matching tribes among any of its number. (I doubt this is even possible outside of drafting specifically to avoid shared creature types. Man, would your draft have had to go wrong for that to happen in Lorwyn / Lorwyn / Morningtide draft...) Usually, your deck is going to fall in between those two extremes.
Back in Lorwyn, it was easy to figure out how good your deck was at utilizing tribal effects: just count up the number of cards with that type you have. The intersection of two "races", such as Goblins and Faeries, was facilitated by only one kind of card – changelings – and so it was straightforward for each possible draft pick or deck choice how to go about evaluating tribal effects. The big shakeup comes in with Morningtide: now there are effects that care about multiple possible matches and which let you choose the kind of match you care about at the spur of the moment, and class types make it extremely easy for most limited decks to have that intersection of tribes even without changelings.
Good luck finding non-gelatinous Goblin Faeries in Lorwyn!
Visualizing three-set intersection is tricksy – maybe I can patent this crazy triangle method...
So, how do we use this crazy Creature Type Web to further our Limited games?
Matty Lab and the Monte Carlos
I tried to solve this problem using statistics and equations. I ran into what fancy analysts call the "multivariate problem": trying to reconcile a million different factors that impact a game all at once. I simplified to just worrying about kinship, since that's an effect that's interesting and new, but clearly informs use of other tribally-interested cards. But it turns out, I quickly found the math even for this is more complex than I could solve analytically. Heck, people have been trying to solve problems involving drawing with replacement from a random deck for years, so this didn't surprise me overmuch. What it did inspire me to do is what scientists always do when the math gets too hard: run an experiment!
With the help of my science buddies Todd and Sam, I created a little trial program to figure out how many kinship triggers one could expect over the course of a game, given some number of tribally connected cards. It's a grossly simplified model from cardslinging as we know it, with a number of finicky assumptions, but it's illustrative. I ran this simulation one MILLION times and recorded the results. An interesting answer emerged: sure, as you increase the total number of tribal cards in your deck, you get better kinship results as one would expect... but!
- Zero triggers is by far the most common result (the mode), even for decks that are heavily tribal. (This makes sense if you think about the number of lands you have to run.)
- You can see clear "targets" for what number of tribal cards to strive toward if you want to make efficient use of your kinship cards.
- You make every land drop.
- The game is 20 cards drawn total.
- You play the kinship card a.s.a.p.
- Your kinship guy never gets killified.
- Two kinship guys are twice as good.
- Tastes great! Less filling!
|Kinship Triggers (1 kinship card)||Tribal count|
|to hit ~10% of games||to hit ~50% of games|
|4||14+||lots of luck :)|
|Kinship Triggers (2 kinship cards)||Tribal count|
|to hit ~10% of games||to hit ~50% of games|
The dotted lines represent a three-cost kinship card (as opposed to the solid lines, which show a two-cost kinship card)–since three-cost kinship guys can't be played as early as two-cost kinship guys, the odds are slightly reduced that you can hit the mark you're looking for. However, it's a small effect (but gets larger the higher cost the kinship card is), since the cost only matters if you draw it early in the game.
Also note all of these calculations are approximate. I know a MILLION trials sounds like a lot (it better – those capital letters for emphasis don't come cheap!) but in the grand statistical scheme of things, there's still a bit of error involved with limited sample size.
Click here for a more detailed explanation of the math.
Choose—But Choose Wisely
But numbers aren't the whole story! (In fact, numbers aren't very good at telling a story at all; they're more of the silent, sensitive type.) Another perspective to take is to think around the possible options Morningtide brings to your tried-and-true Lorwyn experience. You'll find four categories of cards in Lorwyn Block Limited that utilize this Creature Type Web concept and to which we can apply the scalpel of science:
- Choose a creature type
- "Web" cards
Lords and "Count-Me" Cards
Note that there's a smattering of analogous mechanics from Magic's history that also fall into this category and that the model above fits for these too! Affinity has the same elements as a "count-me": the card with affinity plays the role of the lord (it gets better the more cards you control of the specified type, for example) and your tribe is the type it has affinity for.
Kinship is special because it cares about (at least) two different types. In fact, observing how kinship plays in limited was the whole "Eureka!" moment that motivated me to write about this Creature Type Web construction. With kinship, the connectedness of your deck is the key quality. A mono-tribal deck has no worries, but as soon as you venture into duo-tribal or further (we can't all be as close-knit as Mr. Mono-Thoughtweft and his Weenie Beatdown House of Pain) the key becomes the intersection of your tribes along the kinship condition.
You can always cheat, of course. Amoeboid Changeling, Runed Stalactite, instants like Shields of Velis Vel—these will all allow you to "boost" your kinship to trigger on any creature. Statistics is going to catch you with your amorphous hand in the cookie jar, though—overall, you have better chances maximizing your web during the draft and deck construction than you would relying on a two-card simultaneous combo that still relies on the top card of your deck.
Hybrid mana from Ravnica is the closest analog in Limited formats to the enigma of kinship—when you're building your mana base, you just need to be aware that either color match will allow you to play your hybrids. So you can reverse the numbers I have above to give you a quick and dirty rubric for the construction of your mana base—for a two-cost hybrid spell, you need to "trigger" with the land(s) of the appropriate type twice, meaning you need at least 7+ sources of the appropriate colors in your deck to consider playing it.
Choose a Creature Type
I always feel like an Iron Chef when I have any of the "choose a creature type" cards in my pile trying to construct my deck—the "choose" card is like the secret ingredient and you'll trying to see which dish will have the most bang for the judges' buck. These cards are easier to maximize than the lords, but not by much: almost always, you'll have drafted something with a major tribal theme, so these cards let you bank on your secondary or tertiary tribal counts. These are like the proverbial glove to a changeling's hand—an outlet for your biggest tribal effects without regard to their underlying type (as long as it matches).
The "wild" component of this category is partially mirrored in the converted mana cost matters cards from Scourge. You clearly get some effect from any permanent you control (well, except for your Ornithopter. Nobody likes your style, Ornithopter!) However, your Torrent of Flame is going to be much more powerful if you have lots of high converted mana cost permanent cards in your deck, just as a "choose a creature type" card is going to go to the Limit if you maximize one tribe.
Maybe get the band—I mean web—back together?
There are really only a couple cards in Morningtide that illustrate perfectly this connectedness concept, and I have dubbed them "web" cards. Reins of the Vinesteed is a clear example of a card that scales with a tightly connected web—if you can walk along connected creature types, from Elf Warrior to Treefolk Warrior to Treefolk Shaman to Elemental Shaman, you can keep this Rancor analogue in play quite a while.
Rivals' Duel addresses the same problem, but from the opponent's point of view: how vulnerable is your deck to being Rivals' Bait? The stronger your web, the less likely you are to get blown out by this card. Duel actually cares more about web tightness than Reins does, because any long connections (such as the Elf to Elemental path described above) are like chinks in your armor, opening you up to the dreaded two-for-one.
This is a deck I recently drafted here at Wizards, and it's a great illustration of the principles I outlined above. One of my pet goals for each Limited format is to draft some absurd Johnny deck (the turbo-Horde of Notions and the Mirror Entity / Ceaseless Searblades / Brion Stoutarm combo deck are two recent ones from Lorwyn), so when Morningtide appeared with five crazy small-class supporting lords, I knew I had to go for each at least once. Finally, Assassins!
When I opened the Morningtide booster, I saw two definite first-pick possibilities: Winnower Patrol and Scarblade Elite. Going into the pack, I had a whopping five Assassins already as Elite-food—the two Lys Alana Scarblades that I had successfully long-ranged, and three changelings—but I had thirteen Elves to trigger the Patrol.
If we refer back to the tables I gave above, thirteen Elves puts me at about one trigger in half my games for Winnower Patrol. Is a 4/3 for with a relevant creature type as good as the allure of multiple Dark Banishings? Although by the end of Morningtide I might be able to beef up my Elf and/or Warrior count enough that expected kinship trigger number up to two or higher, I'd rather select a card which has a much greater potential impact if I do indeed only get one use out of it.
I decided at the time that the additional power of the Assassin's effect, especially the one-two punch of discarding a changeling to Lys-Alana Scarblade and then reusing it with the Elite, was worth passing on a chance for insane multiple kinship draws—especially with more Warriors likely on the way in this booster. I kept my eye out for future changelings to power up the Elite and even found another "real" Assassin in the Weed-Pruner Poplar.
You can also see two interesting deckbuilding choices I made. One is fairly straightforward: the inclusion of two totally off-tribe Dreamspoiler Witches due to their raw power and great synergy with the instants I had drafted. This brought up a side question of whether I should play Nightshade Schemers as another kinship-like effect, due to the large number of changelings, but I quickly dismissed that option due to the huge number of 5 drops I had in my deck.
The second is a follow-on choice to that, a dilemma which I faced in adding in my final card: should I play something more powerful and subtly synergistic with those Witches and/or good on its own merits, or something more conservative and directly synergistic with the Elves I already had? I had four major tribal effects at work in Elves:
"Dave, you buffoon!" I can hear you thinking. (That's right, I can hear you thinking. Science!) "You didn't include Imperious Perfect in your list of major tribal effects at work!" Checking back against my sideboard, though, the only possible fit for the slot here if I use an Elf is a dorky 1/1 Elf. And you know what you get if you combine a dorky 1/1 Elf with Imperious Perfect? A dorky 2/2 Elf.
The More You Know
I hope I've left you with a better understanding of how to assemble a crack strike force of Rogues, Elf Assassins, Spider Goats—whatever kins your tribe—in this brave new world of Lorwyn with Morningtide. Remember, these aren't rules set in stone (they're more like guidelines, really). Don't blindly follow the numbers, but instead let them factor into your decision making process when you draft and build your deck. If you guys have any questions, comments or thoughts on my writing, feel free to comment in the forums: web development of the forums is one of my primary responsibilities, so I'll be following the discussion. Thanks for reading!
Math It Up
*dons math hat*
It's like a wizard hat, but less stars and more equations. We're about to get into some complex stuff, so hopefully only the most math-y (and least murderous) of you are reading this!
The initial problem question I thought up was:
How is the Creature Type Web affected by a change in tribal count?
Considering my conception of the Creature Type Web is more of a qualitative concept than something that can be put directly into numbers, I backed off of this and considered just the kinship mechanic:
How is the reliability of kinship affected by a change in tribal count? Specifically, are there interesting correlations between tribal count and kinship triggers?
To solve this problem analytically, I looked up hypergeometic distribution, which gives an equation for determining various probabilities on drawing without replacement. However, this distribution could not account for the intricacies of when to play the kinship card, and considering the incremental effect of sequential triggers made my head hurt.
At this point, I decided to go with the scientist's mainstay: the Monte Carlo method, which would allow me to configure the scenario as one would play it in a goldfish-type situation, and then iterate a hojillion times to get a better estimate of the trends.
As I mentioned in my article, I made quite a few assumptions to simplify this scenario and allow these simulated games to complete without complex branching into many possible states. The results I found are still valid when applied to a real-game situation. One just needs to be aware of the differences between your game and the simulated one, and use those differences to estimate the effectiveness of the Monte Carlo results.
For those interested in the algorithm behind the simulated game, here's how it went down:
- Create a deck of 40 cards.
- T of them are tribal matches to the kinship in question.
- K of them are kinship cards (which of course match each other in this analysis).
- The rest are neither T or K.
- Randomize this deck and draw twenty times (representing a game of thirteen turns).
- Assume you make every land drop.
- Assume you play the kinship cards you draw at the first opportunity.
- Assume your kinship card remains in play the remainder of the game after you play it.
- Count up the number of triggers you would have before the game ends.
I varied T (the number of tribally relevant cards in the deck) of between 1 and 15, with the assumption that 15 would be close to maxing out your creature count. Your results would be better if you played fewer lands and more matching creatures of the relevant type, and they would be better if you played tribal spells such as Eyeblight's Ending or Veteran's Armaments.
I varied K (the number of kinship cards in the deck) between 1 and 5. To simplify things, and to allow us to visualize the results at all, multiple kinship cards in play are treated as a multiplier to the effect. This is true in most, but not all, of the kinship cards' cases, such as Pyroclast Council (where two triggers would kill both) or Squeaking Pie Grubfellows (where two triggers might be giving away information for free if they have only one card in hand). At the very least, the option to trigger twice increases value.
There are plenty of library manipulation effects you could use to increase the chances of the top card matching, especially in Lorwyn / Morningtide Limited, including clash, Harbingers, and Ponder. So keep those in mind when applying these results to your own Draft and Sealed experience!