Variance, a term that is commonly thrown around in
conversations about MTG games. It is typical to hear things such as “losing to
variance” or a deck “having too much variance.” But what is it really?
Technically, variance is a number associated with a random event (discussed in
the previous article). It is a quantity that describes how widely the
outcomes of the event can vary. In a game of magic, any of the innumerable
random events in the game, from having to mulligan to executing a combo, to
just plain winning the game, carries with it it’s corresponding probability and
variance.
Pop quiz: Can a deck have a high win percentage but also
high variance? The answer is no. This is because for any deck, if its
probability of winning is p, then the
variance associated with that same random event is p(1-p). So, as the win percentage of a deck nears either 100% (very
good deck) or 0% (very bad deck), the variance becomes smaller and smaller.
This is intuitive, since if one claims that a deck has a 90% win percentage,
then it must win most of the time and consequently, loses infrequently. But
hey, what about this guy?
Everyone remembers Aetherworks Marvel, right? Alongside its
two great loves:
Is this a counterexample? Not at all. In fact according to this article, the win percentage of Aetherworks Marvel, at least during its second
marriage to a tentacled groom, was actually just about 50% against the field,
which means that its variance is close to the maximum that the number can get
for this type of random event (which is 0.5(1-0.5) = 0.25).
What this also means is that by building a deck in a way
that increases the probability that it will be able to do certain things, one
is also naturally reducing the variance of those things happening or not. For
example, a control deck plays 27 lands in order to reduce the probability of
having starting hands with two or less lands, many of which the pilot would
most likely have to mulligan. Combo decks like UW God Pharoah’s Gift (which I
have been piloting since Ramunap Red got axed), are built in order to maximize
the probability that it is able to pull off its combo. As such, almost every
card in the deck, from its creatures (Ministry of Inquiries, Champion of Wits,
and more recently Sunscourge Champion) to its spells (Chart a Course, Search
for Azcanta, Strategic Planning) are there in order to reduce the variance of
being able to implement its game plan.
Essentially, this is what deck building is all about. The
best decks are those that are composed of cards that reduce the variance of
what the deck is trying to accomplish, and this is reflected in the deck
choices at today’s Pro Tour Dominaria:
As shown in the breakdown, the aggro decks are divided among
Red Black, Mono Red, and GX Steal Leaf Stompy, each of which play the best one
to five drop creatures in their respective colors with the objective of speedily
disposing of their opponent. Goblin Chainwhirler is the day’s all-star,
appearing in all of the decks that play red (35% of the field!). On the other
hand, a large majority (about 70%) of the control decks are on Teferi, Hero of
Dominaria. Even the White-Blue Approach decks seemed to have more copies of
Teferi than Approach of the Second Sun based on one of the feature matches.
This is simply because Teferi is the best card that a deck can have to win a
game using a control strategy. To a control deck, Teferi is functionally a 3
CMC planeswalker that can be cast on turn 5 with mana up for a myriad of
control spells like Seal Away, Essence Scatter, Syncopate, and most annoyingly,
Blink of an Eye.
Control players who deviated away from the Teferi strategy
opted for UB Control or Mono Black Control. Black offered cleaner answers in
the form of Vraska’s Contempt and Fatal Push as opposed to UW’s enchantment
based removal, and Mono Black offered a mana base that obviously removed the
probability of ever getting color-screwed (Swamps!). However, reducing the
variance of having to mulligan is hardly the only concern of a control deck. There
is also the matter of having a steady stream of cards with which to answer the
opponent’s threats and make consistent land drops, and on this matter the UWx
control decks seemed to clearly outgun the competition, as shown in Gabriel
Nassif’s win with Jeskai Teferi versus Mono Black Control.
Most of the decks that were shown in the feature matches
were known quantities except one, and the feature matches involving that deck
will be the last topic of this entry. The deck is UG Karn, and it was played by
11 people in day 1, mostly if not exclusively by Luis Scott-Vargas and his Team
Channel Fireball. More details about the deck can be found here. Essentially,
LSV referred to the deck as the best Karn deck, mainly because it played a
critical mass of artifacts to take full advantage of Karn’s -2 ability. In the
two feature matches where the deck appeared (same round), the deck
won in one but lost in the other. Watching these feature matches makes two
things apparent. First, when the deck is good, it’s really really good. The
deck is very capable of gumming the board both on land and in the air with high
toughness, difficult to remove creatures that can easily overwhelm opponents.
It also has the sweet combo of Implement of Ferocity, Scrap Trawler, and
Walking Ballista that translates to soooo much value.
However, the second thing that seemed apparent from my point
of view is that the deck does not have enough things that reduce the variance
of what it wants to do. Sure, it does have the critical mass of artifacts needed
to maximize the value of Karn, but without the planeswalker, most of the cards
are lackluster. Glint-Nest Crane is great at fetching artifacts, but there’s a
fair chance that you are actually looking for Karn and are forced to tuck it into
the bottom of your deck because you played the trinket-seeking bird. Thus, in
the games that the deck lost, it looked as though it was all over the place. This
problem arises when a deck relies considerably on synergy but fails at improving
the probability of actually realizing this synergy consistently. Comparably, BG constrictor, which was piloted by
34 players in day 1, is also a deck that relies on synergy and does not have
any means of increasing the probability of realizing that synergy (i.e. having
Winding Constrictor out as early as possible). However, the difference between
the two decks is that the constrictor deck actually is full of cards that are
just fine on their own but are amazing when the snake is in play. The same is just
not true with UG Karn. Of course, LSV alongside some of his teammates did make
it to Day 2, so we will hopefully see UG Karn some more in tomorrow’s feature
matches so we can evaluate it further.
May the shuffler be with you!
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