Frank Analysis – Optimal Decks for Ten New Goldfish Formats

Two weeks ago, I described how to determine the ultimate goldfish deck via computer simulation. Today, inspired by the overwhelming response to that article, I will continue in the same line and optimize ten new formats.

But first, a rectification and some methodological remarks…

To address a frequently asked question: I coded my simulation in Java. This language may not be perfectly suited for such experiments, but I only require basic loops, functions, variables, and if-statements that are included in virtually any programming language, and I chose Java for convenience. The original code can be found here.

Before posting my code, I made a few adjustments for readability. While doing that, I discovered a typo: in my original code for turn 4, I had written “TwoDropsInPlay=TwoDropsInPlay-2” instead of “TwoDropsInPlay=TwoDropsInPlay+2.” So, a minus sign instead of a plus sign. What does that imply? Well, suppose that you went turn 1 [card]Lightning Bolt[/card], turn 2 [card]Putrid Leech[/card], and turn 3 [card]Geist of Saint Traft[/card]. Then, on turn 4 you have 2 Putrid Leech in hand and want to play them. Under my original code, instead of jumping from 1 to 3 [card]Putrid Leech[/card], you go from 1 to -1 Putrid Leech. Every time this negative Putrid Leech attacks, the opponent gains 4 life. Awkward. To be fair, this precise scenario comes up very rarely, and even if it does, my typo doesn’t even affect the kill-turn all that often. Yet, it is an amusing error that slightly affects the optimal decks.

Running the simulations again with the corrected code, I found that the optimum for the powerful format actually had -1 [card]Savannah Lions[/card] +1 [card]Lightning Bolt[/card] compared to the “optimal deck” of my article. The average kill-turn was 4.221. The optimal deck for the weak format actually had -1 [card]Mons’s Goblin Raiders[/card] +2 [card]Grizzly Bear[/card] -2 [card]Shock[/card] +1 [card]City of Brass[/card] compared to the “optimal deck” of my article. The average kill-turn was 5.675.

Nevertheless, the general insights that I derived from my experiment remain valid. My analysis suggests that, if you want to maximize goldfish kill speed, then you should build a deck with 11-16 one-drops, 10-14 two-drops, 0-4 three-drops, 11-15 burn spells, and 19-21 land. Here’s an example of a post-Theros Standard deck using this formula:

Goldfish Red

[deck]4 Rakdos Cackler
4 Firedrinker Satyr
4 Foundry Street Denizen
4 Burning-Tree Emissary
4 Gore-House Chainwalker
4 Young Pyromancer
4 Chandra’s Phoenix
4 Lightning Strike
4 Shock
4 Dynacharge
18 Mountain
2 Mutavault[/deck]

Fast and deadly. This deck is built for speed, and speed is what it will deliver if the opponent doesn’t interfere. I find it interesting to see how closely this deck resembles the Sligh decks of old. In 1996, a Magic player called Paul Sligh showed up at a tournament with a deck featuring both [card]Goblins of the Flarg[/card] and [card]Dwarven Lieutenant[/card], just to fill out the curve. His deck showcased the concept of a mana curve, and it quickly became famous. Players all around the world learned that the ability to spend all of your mana on every turn of the game leads to victory. For a nice historical perspective on red decks, I recommend an article written by Alex Shvartsman in 2004. That article may also help you appreciate a card that is better than [card]Jackal Pup[/card] from a historical perspective. If [card]Firedrinker Satyr[/card] had been printed in 1999, people would’ve been freaking out.

Unfortunately, speed is not the only factor in a game of Magic—opponents will interact with you. In post-Theros Standard, for example, you can expect to face [card]Supreme Verdict[/card], [card]Fleecemane Lion[/card], etc. An onslaught of 2-power creatures does not match up favorably against those cards—it’s like bringing an extremely well-chiseled knife to a gunfight. Sometimes you can quickly stab your opponent before he can load his gun, but it’s difficult in general. To get past big blockers, cards like [card]Firefist Striker[/card], [card]Madcap Skills[/card], or [card]Rubblebelt Maaka[/card] may be necessary. That said, I don’t want to go into the details of positioning a red deck in Standard—my interest today will once again lie in speedy goldfish kills.

So, let’s return to my simulation optimization approach. Some of you had been wondering about the runtime of my experiments: How long does it take to determine the best deck? Well, for a given deck, its performance can be evaluated relatively quickly: on my computer, it takes roughly 0.2 seconds to simulate 100,000 games. Adding 0.1 second to figure out the optimal mulligan strategy, we can accurately determine a deck’s average kill-turn in roughly 0.3 seconds.

The problem, however, is the staggeringly large number of decks that are possible. In a format with five different cards, you have over 13 million different 60-card decks. If an algorithm needs 0.3 seconds to evaluate every single one of them, then it takes more than six weeks to finish! (And that’s in a five-card format. The number of different 60-card decks explodes when more cards are added.)

Fortunately, this time can easily be cut down. First, you can cut out huge swaths of obviously non-optimal decks. By restricting attention to decks with 15 to 25 lands, say, the number of feasible 60-card decks—if I counted correctly—reduces to 138,061 already. Moreover, if we do not take the effort to determine every deck’s optimal mulligan strategy and content ourselves with simulating 4,000 games per deck, then all feasible decks can be evaluated within 19 minutes. We trade accuracy for speed, but this is actually doable! We can also reduce time further by searching in a grid-like pattern, only considering card counts in multiples of two.

After finding a reasonable initial deck configuration in this manner, we can take several minutes to do a more accurate local search. That is, starting from the best deck found in the initial enumeration, we substantially increase the number of simulations per deck, add the mulligan optimization back in, and then evaluate all neighboring decks that are close to it. While improvement is possible, we repeatedly move to a neighboring deck until no further improvements are found. That is basically the idea behind the simulation optimization approach that I used for today’s formats.

Okay, enough with the methodological notes. On to the new formats!

1. A Format with Goblin Guide

Haste is an excellent ability for an aggro deck, and one of the best haste creatures ever printed is [card]Goblin Guide[/card]. Inspired by a question from Chad Casarotto, I wanted to investigate what would happen if I would replace [card]Savannah Lions[/card] by [card]Goblin Guide[/card] in my original goldfish format. So, only the following five cards are legal:

[draft]Goblin Guide
Putrid Leech
Geist of Saint Traft
Lightning Bolt
City of Brass[/draft]

The code to find the optimal deck can be found here. Many functions, classes, and loops are the same as before. The only difference lies in the function TurnKill, which captures the actual game-play. It now knows that the one-drop immediately attacks for 2 damage. Here’s the outcome:

The optimal deck:

27 [card]Goblin Guide[/card]
15 [card]Lightning Bolt[/card]
18 [card]City of Brass[/card]

Average kill-turn: 3.504.

This outcome was a surprise to me. I had expected that the best deck would be comprised of Goblin Guides and Mountains only. After all, Goblin Guide is so efficient! It affects the game right away and offers a source of repetitive damage. Moreover, since Goblin Guide deals an even amount of damage, Lightning Bolt is very weak unless you have multiples.

So why Lightning Bolt? The reason is that you want to maximize a third-turn kill. You can kill on turn three if the top 9 cards of your deck are exactly six Goblin Guide and three City of Brass. But you can also attain a third-turn kill by casting one Goblin Guide on turn one, two Goblin Guides on turn two, and then two Lightning Bolts on turn three. This only requires 7 cards to pull off. That is less than 9, so the optimal deck goes for the Lightning Bolt route.

2. A Format with Only Mountains and Bolts

In this format (inspired by questions from Dan Gibas and Andrey Goder), only the following cards are legal:

[draft]Lightning Bolt

The optimization code can be found here.

The optimal deck:

44 [card]Lightning Bolt[/card]
16 [card]Mountain[/card]

Average kill-turn: 4.910.

The optimal mulligan strategy for 5-, 6-, and 7-card opening hands with this deck is to keep a hand if and only if it contains 1, 2, or 3 Mountains.

Looking at the average kill-turn, we see that the strategy of collecting seven Bolts plus at least one land turns out to be almost a full turn slower than the strategy of attacking with [card]Savannah Lions[/card] and [card]Putrid Leech[/card]. This implies that if you want to maximize speed, then a creature-based strategy is usually better than straight-up burn. However, I should note that if you face off against [card]Doom Blade[/card] Guy, then the [card]Lightning Bolt[/card] deck may still give you a better chance.

3. A Format with Lotus Petal

[card]Geist of Saint Traft[/card] was not good enough to make it into my optimal goldfish deck, so for the next couple of formats, I will explore alternatives. First off, I’ll investigate what happens if we have access to [card]Lotus Petal[/card] instead of Geist of Saint Traft. In this format (inspired by a question from Waldemar Barrientos), only the following five cards are legal:

[draft]Savannah Lions
Putrid Leech
Lotus Petal
Lightning Bolt
City of Brass[/draft]

The code for this Lotus Petal format got complicated. Lotus Petals should be sacrificed right away if the mana can be used to cast a lethal number of Lightning Bolts or to cast creatures, in that order, but unused Petals should stay in play. It is important not to sacrifice Petals unnecessarily. For example, if you keep a hand with 1 [card]City of Brass[/card], 3 [card]Lotus Petal[/card], 1 [card]Savannah Lions[/card], and 2 [card]Lightning Bolt[/card], then you should not sacrifice all three Petals right away because you can still cast those Lightning Bolts later on and you might draw [card]Putrid Leech[/card] next turn. My simulation is based on that logic.

The optimal deck:

23 [card]Putrid Leech[/card]
26 [card]Lotus Petal[/card]
11 [card]City of Brass[/card]

Average kill-turn: 3.925.

That’s a grand total of thirty-seven mana sources!

The ideal opening hand for this deck contains 3 Putrid Leech, 3 Lotus Petal, and 1 City of Brass. This allows you to cast two Putrid Leech on turn one. If you subsequently topdeck a Lotus Petal or City of Brass on your second turn, then you get to cast your last Putrid Leech for a turn-three kill. Of course, this requires a specific combination of cards, and a turn-four kill is more likely.

This deck serves to illustrate the power of mana ramp. Basically, if you have powerful cards and you can get them out quickly, then running 60% or even more mana in your deck is perfectly fine. You can clearly see this philosophy at work when you see a Tron deck in Modern, but my Lotus Petal format illustrates that it holds for aggro decks, too.

4. A Format with Memnite

In this format (inspired by a comment by Ron Cadier), only the following five cards are legal:

[draft]Savannah Lions
Putrid Leech
Lightning Bolt
City of Brass[/draft]

The optimal deck:

60 [card]Memnite[/card]

Average kill-turn: 4.000.


5. A Format with Burning-Tree Emissary

In this format (inspired by comments by Jeff van Egmond and Mike DeNora), only the following five cards are legal:

Savannah Lions
Putrid Leech
Burning-Tree Emissary
Lightning Bolt
City of Brass

As I want every card to be castable off of [card]Burning-Tree Emissary[/card] mana, we start the game with an unlimited number of [card]Mana Cylix[/card] in play.

The optimization code can be found here.

The optimal deck:

15 [card]Savannah Lions[/card]
10 [card]Putrid Leech[/card]
13 [card]Burning-Tree Emissary[/card]
22 [card]City of Brass[/card]

Average kill-turn: 4.194.

This deck looks very similar to the optimal deck in the original format with Geist of Saint Traft, except that it has Burning-Tree Emissary instead of Lightning Bolt. Both cards are actually quite similar—they both eventually damage the opponent while not requiring any mana during the early turns of the game—but Burning-Tree Emissary turned out to be better.

Surprisingly, the optimal number of lands increased rather than decreased after replacing Lightning Bolt with Burning-Tree Emissary. I ran the simulation again because this outcome was unexpected, but I got the same result once more. After thinking it over, it started to make sense. When you replace one-cost burn spells with “free” two-cost creatures, then you increase the overall curve of your deck, and more lands are required to ensure you can keep a two-lander. It is no longer possible to quickly win the game with a City of Brass, double Savannah Lions, double Lightning Bolt draw. This suggests that the 18-land Burning-Tree Emissary decks in Return to Ravnica Block Constructed are not running enough lands.

6. A Format with Ball Lightning

In this format (inspired by comments by Waldemar Barrientos, Till Riffert, and Ian Williams), only the following five cards are legal:

[draft]Savannah Lions
Putrid Leech
Ball Lightning
Lightning Bolt
City of Brass[/draft]

The optimization code can be found here.

The optimal deck:

13 [card]Savannah Lions[/card]
10 [card]Putrid Leech[/card]
11 [card]Ball Lightning[/card]
26 [card]City of Brass[/card]

Average kill-turn: 4.208.

Now the optimal deck contains [card]Ball Lightning[/card] and a bunch of additional lands instead of the original Lightning Bolts. This deck can win on turn four if it casts Putrid Leech on turn two, Ball Lightning on turn three, and Ball Lightning on turn four. Haste definitely makes a difference.

The optimal number of lands is once again surprising. You may not be used to seeing 26 lands in aggro decks, and it is likely an incorrect number if you’re playing against Doom Blade Guy. But if opponents do not interact and your deck contains many powerful 3-drops, then upping the land count may increase overall goldfish speed. With this in mind, running [card]Hellrider[/card] decks on 20 lands seems like madness.

7. A Combo Format

In this format (inspired by comments from Phil Haussmann, Robert Wilbrand, and Josue Garcia Yza), only the following four cards are legal:

[draft]Volcanic Island
Splinter Twin[/draft]

I could’ve started with the eponymous [card]Channel[/card]/[card]Fireball[/card] combo, but I decided to go for a Modern-playable one. The main purpose of my code is to find the perfect distribution of cantrips, lands, and combo cards. I didn’t have the time to teach my algorithm how to [card]Ponder[/card], so I picked a draw spell that doesn’t present difficult choices.

The logic of playing is simple. First, play a land if possible. Then, if we can play Splinter Twin to win the game, then do so. Otherwise, if we don’t already have a [card]Pestermite[/card] in play, then cast one and tap our goldfish. Otherwise, if possible, play [card]Peek[/card] and start the same logic once again. If we’re out of Peeks or mana, then move to the next turn.

The optimal deck:

12 [card]Pestermite[/card]
13 [card]Splinter Twin[/card]
35 [card]Volcanic Island[/card]

Average kill-turn: 4.319.

Huh, what!? No card draw spells at all? Thirty-five lands? What is going on here?

Well, my algorithm managed to break the format by using mulligans rather than card draw spells for card selection. The optimal mulligan strategy for this deck was extremely aggressive. At seven or six cards, you keep every hand with at least one Pestermite, at least one Splinter Twin, and at least two lands, and you toss back everything else. At five cards, you do essentially the same, except that you also keep 1 Pestermite and 4 Volcanic Island. But you still mulligan 2 Splinter Twin and 3 Volcanic Island, for example.

Apparently, this crazy strategy (which is reminiscent of Vintage Dredge decks with [card]Bazaar of Baghdad[/card]) was better at assembling a turn-4 combo than a Peek-based strategy. It’s counterintuitive, and probably not recommendable if the opponent has any kind of disruption, but still awesome. Man, computers are so smart.

8. A Bigger Format with a 4-card limit for the Best Cards

“In a lot of formats, you have one good card at a spot in the curve, and have to decide how many bad cards to run. I’d be interested to see the optimal deck if you could play all 9 cards, but were limited to 4 copies of the most efficient ones.”
-Jon Stern

Excellent question, Jon!

So, in this format, you can play a maximum four copies of the following cards:

[draft]Savannah Lions
Putrid Leech
Geist of Saint Traft
Lightning Bolt[/draft]

And you can play an unrestricted number of the following cards:

[draft]Mons’s Goblin Raiders
Grizzly Bear
Gnarled Mass
City of Brass[/draft]

To limit the amount of computations needed, I enforced in my code that every deck would include 4 Savannah Lions, 4 Putrid Leech, and 4 Lightning Bolt, and I removed the mulligan optimization as there are just too many different opening hands to check.

The optimal deck:

1 [card]Mons’s Goblin Raiders[/card]
10 [card]Grizzly Bear[/card]
1 [card]Gnarled Mass[/card]
6 [card]Shock[/card]
4 [card]Savannah Lions[/card]
4 [card]Putrid Leech[/card]
4 [card]Geist of Saint Traft[/card]
4 [card]Lightning Bolt[/card]
26 [card]City of Brass[/card]

Average kill-turn: 5.221.

Apparently, you should play 4 copies of the best cards, and then favor weaker 2-drops, weaker burn spells, and lands to fill out the deck.

9. LSV’s Favorite Format

“What’s the optimal deck if the legal cards are [card]Hexplate Golem[/card], [card]Fierce Empath[/card], [card]Kessig Wolf Run[/card], and [card]Gruul Turf[/card]?”
-Luis Scott-Vargas

How do you come up with these questions, Luis?

So, in this format, only the following four cards are legal:

[draft]Hexplate Golem
Fierce Empath
Kessig Wolf Run
Gruul Turf[/draft]

The code can be found here. The game play logic, which is captured in the function TurnKill, attempts to play Wolf Runs and Turfs in the right order, win the game a Kessig Wolf Run-powered attack if possible, and play creatures otherwise.

The optimal deck:

19 [card]Fierce Empath[/card]
1 [card]Hexplate Golem[/card]
23 [card]Kessig Wolf Run[/card]
17 [card]Gruul Turf[/card]

Average kill-turn: 8.017.

All the deck wants to do is play Kessig Wolf Run on turn 1, Gruul Turf on turn 2, and Fierce Empath on turn 3. After that, play another Empath and then start pumping them with Kessig Wolf Run. This deck can do exactly that with startling consistency, and you frequently win on turn 8. Hexplate Golem usually doesn’t do much to speed up the kill, except when you draw your first Fierce Empath by turn 6, so that’s why there is still one copy in the deck.

10. A Format in Which the Opponent Starts at 40 Life

This question is relevant for multi-player games and Commander. In this format, the original five cards are legal:

[draft]Savannah Lions
Putrid Leech
Geist of Saint Traft
Lightning Bolt
City of Brass[/draft]

The code can be found here.

The optimal deck:

11 [card]Savannah Lions[/card]
13 [card]Putrid Leech[/card]
9 [card]Geist of Saint Traft[/card]
3 [card]Lightning Bolt[/card]
24 [card]City of Brass[/card]

Average kill-turn: 5.830.

As you might expect, if you have to deal more damage to win the game, then Bolts become worse and Geists become better.

Concluding Remarks

I dealt with various aggro formats, and I tackled a combo format as well. Besides aggro and combo, there is also control, but the best control deck is metagame-dependent. Moreover, control tries to play an interactive game, answering opposing threats and all. This means that simulating a control deck against given aggro or combo decks may require some artificial intelligence akin to Duels of the Planeswalkers, which can get fairly complicated. A challenge for the future, perhaps?

I hope you enjoyed this, and I hope my code for the new formats doesn’t include any mistakes. Now, I’m off to prepare for Pro Tour Theros! Until next time,
–Frank Karsten

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