So what can we learn from all of this? Well, first off, if you want to build an aggro deck from scratch, you now have a proven base to start from. If you’re only interested in maximizing speed, then my analysis of both formats suggests to build decks with 12-17 one-drops, 10-12 two-drops, 0-4 three-drops, 12-15 burn spells, and 18-21 land. Besides that, my simplified formats led to some interesting insights:
Number of lands
The time-honored tradition of playing 20 lands in aggro decks appears to be correct if the format is filled with powerful cards (such as Savannah Lions, Putrid Leech, and Lightning Bolt) and if the average mana cost of the deck is relatively low.
However, if the format is comprised of weaker cards such as Grizzly Bear, then the optimal number of lands may be less than 20, even if the deck contains several three-drops. The reason for this, I suppose, is that when cards are weaker, mana flood and mulligans are punished more severely. For example, 4 lands, 1 Savannah Lions, and 1 Putrid Leech is still a pretty fast six-card hand, whereas 4 lands, 1 Mons's Goblin Raiders, and 1 Grizzly Bear is quite slow. Hence, when the cards are weak, you may wish to decrease the risk of mana flood by cutting a land.
Finally, with my optimal decks in mind, it seems that all those 18-land mono-red decks in Return to Ravnica Block Constructed may not contain enough lands.
Every card has a role
Every card type has its advantages and disadvantages. Creatures deal repetitive damage, but they have summoning sickness. Bolts are a one-shot deal, but they have an immediate effect on the opponent’s life total. As it turns out, a mix between the two card types yields the fastest wins.
It was also interesting to see that a mix between Savannah Lions and Putrid Leech is correct. Even though you would like to maximize the probability of hitting a turn-1 Savannah Lions, there is still the random element to take into account: sometimes you draw a land-heavy hand or have to mulligan, and in those cases you’d rather have a 4-power creature than a 2-power creature in your hand. For instance, 4 land, Savannah Lions, Putrid Leech is a much better 6-card hand than 4 land, Savannah Lions, Savannah Lions.
Three-drops turned out to be too slow, especially when games are usually won on turn 4. The optimal deck in the Grizzly Bear format still contained 3 Gnarled Mass, but that’s not a lot either. It indicates that drawing one Gnarled Mass is fine but drawing multiple Gnarled Mass is horrible.
When going for speed, mulligan aggressively
Let me give a selection of hands that, according to the optimal mulligan strategy, you should toss back:
• 1 City of Brass, 1 Savannah Lions, 1 Putrid Leech, 4 Lightning Bolt
• 3 City of Brass, 4 Putrid Leech.
• 4 City of Brass, 1 Savannah Lions, 2 Lightning Bolt
• A five-card hand consisting of 4 City of Brass, 1 Savannah Lions
• A three-card hand consisting of 3 City of Brass
These could be seen as fairly aggressive mulligans, but all of these hands turned out to be too risky or too slow—if you want to win the game as quickly as possible, a random hand with one card less is better than all of the above hands. Hopefully, my analysis can serve as a useful reference for mulligan strategy discussions in more realistic formats.
I will be able to outsource the playtesting for Pro Tour Theros to my computer.
Okay, this one is a lie. The number of Standard-legal cards is greater than five, and explaining to a computer when to play around Supreme Verdict or how to navigate complex board situations would take a lot of time.
Nevertheless, I hope that this article encourages future work on simulation, optimization, and artificial intelligence in the context of Magic. Although the game is complex, we might be seeing Magic-playing computer algorithms that can defeat pro players in a decade or so.
Of course, my imaginative format has its limitations.
In my model, there are no opponents who cast Thragtusk to gain life, Doom Blade to kill your creatures, or Loxodon Smiter to attack and block. Although my goal of finding the fastest average goldfish kill is relevant when playing against a non-interactive combo opponent, it is too single-minded when facing off against interactive opponents. Accordingly, you may wish to play fewer Bolts, fewer one-drops, and more three-drops in a real-life tournament than my “optimal” decks would prescribe.
Closing out, if you have any questions about my methodology (which I didn’t describe in full because this is a Magic site and not an academic journal) or numbers (there’s plenty of stuff that I left out for brevity) then I’d be happy to answer those questions in the comments. Also, if you can think of other Magic-related applications for an analysis like this, then I’m open to suggestions!