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Exploitation VS Exploration In Ikoria Limited

Should you go with the proven strategy or try something new? Ryan Saxe shows the benefits of exploring new archetypes!

Porcuparrot, illustrated by Chris Seaman

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The multi-armed bandit problem is a mathematical problem dedicated to resource allocation in order to maximize some gain. More specifically, the focal point of this problem is on the trade-off between exploitation and exploration. The problem is described as such:

Let’s say there is a slot machine with many arms. Each arm has an unknown probability distribution that describes how it pays when the arm is pulled. Every time you pull an arm, you get some reward belonging to that probability distribution. Your goal is to pull the sequence of arms that maximizes your reward. 

In the world of Magic, gain isn’t in dollars, but rather game wins. Furthermore, Draft can be described as a “restless bandit problem.” This means that the probability distributions are also dependent on the draft pool. At any given point in a draft, a player is trying to take a card out of a pack in order to maximize the expected win percentage of the deck they will end up with, given the pool they currently have. The pool is the state. Each card is a slot machine. The goal is to take the card that maximizes your expected win rate. 

When I draft a deck, I then play the games. Those games give me information related to the reward distributions of each card in my deck with respect to each other. This updates my understanding of each card. It only took casting Zenith Flare once to drastically update my prior thoughts of how I expected it to impact my win rate.

But why does this problem definition matter? It’s just inapplicable theory, right?

The importance of identifying Draft as a bandit problem is that it demonstrates that optimizing your win rate is directly tied to the trade-off between exploitation and exploration. Win rate isn’t just a function of each individual draft decision as it relates to the current deck. Win rate increases with the skill of internalizing information from exploratory decisions. This means that, in the long run, taking the incorrect pick for the purpose of learning can often yield higher reward.

The line between exploiting strategies known to work and exploring new ones is hard to discern. It’s a skill to cultivate, and one with huge long-term benefit. In fact, it motivated my draft below starting as early as Pack 1, Pick 3.

Pack 1, Pick 3

The Picks So Far:

The Pack:

The Pick:

My take!
This pack supports a ton of different potential paths. Titanoth Rex is the best reanimation target for Back for More and Unbreakable Bond. Startling Development is a one-mana cycler that helps with spell synergies like Spelleater Wolverine. Given that Footfall Crater is one of the worst cyclers, it could actually wheel from this pack, making the Startling Development more enticing than it initially appeared. And then both Boot Nipper and Insatiable Hemophage are solid black cards to go with my bomb rare. Finally, Pacifism is a good removal spell.

So many riches here. What’s correct to take?

I believe the correct pick is Titanoth Rex. Cycling is often overdrafted now, making me less likely to speculate on lower quality cycling cards. Both Boot Nipper and Insatiable Hemophage are solid cards, but they’ll rarely be the best cards in my deck. Pacifism is a good removal spell, but it doesn’t compare to the ceiling of Titanoth Rex. This format is so synergy-driven that I think it’s best to navigate the draft hedging hard towards the most powerful synergies. Titanoth Rex is the best reanimation target, but also just a strong card for any green deck. However, it’s not what I took.

I took what I believe to be the worst of the options — Insatiable Hemophage. This pick is about exploring. I’m about 45 drafts into this format and have yet to draft a base-black mutate deck. With Dirge Bat already in my pool, I believe this is reasonable motivation to dip my toes into that water. I have a great payoff and am strongly incentivized to draft black. Might as well take advantage of the situation and explore mutate in a non-Simic archetype.

Pack 1, Pick 4

The Picks So Far:

The Pack:

The Pick:

My take!
I’ve said it many times in the last couple of weeks: the good green decks are reanimating Greater Sandwurm. Originally I did not have Greater Sandwurm in my top green commons but now I currently have it as the second-best green common, because that’s what I want my green decks to be doing. But is that better than a premium cycling payoff or a solid removal spell?

I believe it’s correct to take Greater Sandwurm over Rumbling Rockslide here, but incorrect to take it over Snare Tactician. One reason Snare Tactician, Prickly Marmoset, and Drannith Stinger are such high picks is that they’re good outside of the cycling deck. An Orzhov mutate deck or Humans deck is very likely to have a lot of cards with cycling. Snare Tactician will make my white decks almost always, and if I get lucky enough to see Boros Cycling as the open archetype, I’ll have the best deck at the table.

Pack 3, Pick 1

The Picks So Far:

The Pack:

The Pick:

My take!
A companion, a premium two-drop with cycling, and a one-mana removal spell all aren’t even in the same tier as Porcuparrot given my draft pool.

At Pack 1, Pick 1, I would take Obosh, the Preypiercer and Drannith Stinger over Porcuparrot. But given that it’s impossible to draft cycling or have Obosh as my companion, this is a clear Porcuparrot. Mutating onto a deathtouch creature is game over. It even comes with protection from Heartless Act if mutated onto a Boot Nipper. Yes, it removes the deathtouch, but that’s still a very positive exchange.

Overall, exploring into black mutate decks opened up my eyes to a subset of archetypes. This deck felt extremely powerful and I’m excited to explore more versions of this deck in the future.

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