Calculating Cheerios

by Taufik Indrakesuma on 09 February 2017, Thursday

Modern 
Taufik Indrakesuma

Calculating Cheerios

 

Hi everyone! Today, let's talk about Modern.

 

My next big tournament will be GP Brisbane, which will be my first foray into post-ban, post-Aether Revolt Modern. One of the decks I have been spending a lot of time testing and thinking about is Cheerios, or the Puresteel Paladin combo.

 

Sram, Senior Edificer Puresteel Paladin

 

The combo involves playing a bunch of 0 casting cost artifacts (hence the name, Cheerios) to draw cards with Sram, Senior Edificer and Puresteel Paladin, eventually building up a storm count to cast a lethal Grapeshot at the opponent's face. Though this deck isn't very popular at the moment, it is actually one of the few Modern decks still capable of a Turn 2 kill.

 

Among the lists available online, it is clear that there is not yet a consensus on how to build the deck. The numbers are all over the place. Some run 15 lands, others run 16. Some run 3 Serum Visions, others run the full playset plus an extra Sleight of Hand. Some run 1 Grapeshot, others run 2.

 

So, I thought I'd contribute to the discussion with a more mathematical approach. How do we build the deck to maximize the potential of “going off” on turn 3? I'll be using hypergeometric probabilities for this exercise, but I'll try to keep it as simple as possible.

 

 

 

 

Anatomy of a Cheerio

 

In breaking down a Cheerios deck, I'd lump the cards into six major categories:

 

  1. Lands + Mox Opal

  2. Engines (Paladin + Sram)

  3. Retracts

  4. Artifacts

  5. Kills

  6. Flex slots

 

The question now is how to build the deck to maximize the probability of having a combination of cards that allows you to goldfish a turn 3 kill. I will ignore the possibility of opponents interacting (through removal, discard or countermagic) for now, so for now I'll focus on maximizing the probability of “going off” and minimizing the probability of fizzling.

 

 

 

15 or 16 Lands?

 

When considering the number of lands we want to play, we have to think not only about the success scenario but also the different types of failure scenarios that we can encounter.

 

Success scenario: We have drawn 2 or 3 lands by our turn 3.

Failure scenario 1: We have only drawn 1 land by our turn 3.

Failure scenario 2: We have drawn 4 or more lands by our turn 3.

 

The first few scenarios are pretty straightforward: we want enough lands to cast our engine (ideally with mana open for Retract or a protection spell), but we don't want too many in our hand when we start to go off. However, another failure scenario could happen after we start going off: we might draw too many lands and not enough gas to continue going off! So, let's also set a “Failure scenario 3”, where we have drawn 8 or more lands in our top 20 cards instead of relevant combo cards.

 

How do the different counts stack up for the success and failure scenarios?

 

 

As you can see from the charts, running 15 and 16 lands doesn't really make much of a difference to our probability of success in initiating the combo. The first two failure scenarios even themselves out: run 15 lands and you're more likely to be short, run 16 lands and you might flood. However, where it does make a difference is in “failure scenario 3”. Running 16 lands instead of 15 increases your odds of fizzling mid-combo by 3%. To be fair, drawing 8 lands in your top 20 cards isn't necessarily a failure, because you can still draw enough to continue the combo even with some dead land draws. However, we should do whatever we can to minimize the fizzle rate.

 

When you consider that we're also running 4 Mox Opals (which do not count as dead draws, because we can use them all as Lotus Petals in the same turn), the possibility of getting mana screwed goes even lower. Also, running 4-6 fetch lands helps you lower the remaining land count even further, which pushes the failure rate down even more. Fifteen lands, it is!

 

Verdict: Play 15 lands.

 

 

 

Do we need 8 engine cards?

 

The “auto-pilot” decision when thinking about building this deck is to include 4 copies each of Puresteel Paladin and Sram, Senior Edificer. After all, if you're building your deck around a draw engine, you need to draw it to win. However, you only need 1 or 2 copies on the battlefield to combo off, whereas any extra engine cards you draw mid-combo are dead draws, much like the extra lands were before.

 

Success : Draw one or two of the engine cards by our turn 3

Failure 1 : Draw any other number by our turn 3 (0 and we can't go off, 3+ is too many)

Failure 2 : Draw at least 6 of our engine cards in our top 20 cards

 

 

Here, our success rate goes up by 2% on the play and 1% on the draw if we have 8 engine cards rather than 7, but our “Failure 2” scenario also goes up by 1%. This one is close. I'd probably opt for 8 engine cards because of other factors that aren't taken into account here, namely our opponent having removal or discard for our first engine card. However, going down to 7 engine cards is perfectly acceptable, and it might be something to consider during sideboarding.

 

Verdict: Either way works, but I'd opt for 8.

 

 

 

Do we play 4 or 5 Retract effects?

 

This is perhaps the only slot where everyone has reached consensus with only 4 Retracts. No one (so far) has run Hurkyl's Recall in the maindeck as additional Retracts. Setting aside the fact that Hurkyls' Recall is a 2 mana card, which makes it much worse than Retract, does the additional redundancy add value?

 

Retract Hurkyl's Recall

 

 Unlike the engines and lands, we want as many of the Retract effects as possible, because they keep the combo going. However, we don't really need to see our first Retract until card number 12 or 13, after we've played our first wave of equipment.

 

Success : Draw at least 1 Retract in our top 12 or 13 cards

Failure 1 : Draw zero Retracts in our top 12 or 13 cards

Failure 2 : Draw only 1 or fewer Retracts in our top 20 cards

 

 

 

Turns out, the fifth Retract effect adds a lot of consistency. Aside from that, there's also an argument for playing Hurkyl's Recall as an answer to any maindeck Chalice of the Void we might encounter. All the more reason to try it out!

 

Verdict: Play an extra Hurkyl's Recall.

 

 

 

How many 0-cost equipment?

 

Accorder's Shield Sigil of Distinction

 

 This slot usually varies between 20 and 21 pieces of equipment, but let's see how the numbers look with 17 and 22. You really just want “as many as possible”, so let's define the fail scenario as only drawing 5 or fewer pieces of equipment in your top 20 cards, which is low enough that you'll probably fizzle.

 

 

I'm not sure if this tells us anything aside from “more is better”. It's not clear what an “acceptable” failure rate is, given that the failure scenario doesn't factor in the number of Retracts you drew. If you have multiple Retracts or two engines, even 3 or 4 pieces of equipment can be enough to dig past your 20th card. So, does it really matter? Maybe we should decide instead based on how many of the equipment cards are actually useful.

 

This chart is also useful for sideboarding: you may need to cut some equipment to make room for interactive cards. Just be wary of how each equipment you cut affects your failure rate.

 

Verdict: Any number between 19-21 would probably work.

 

 

 

Do we really need more than 1 Grapeshot in the deck?

 

Grapeshot

 

You obviously need to draw 1 to actually win, but you really, really, really don't want to see it until you're ready to cast it, because it's a dead draw until that point. However, there is a possibility that your kill spell will be too deep into your library that you are unable to reach it.

 

Failure 1 : Draw Grapeshots in your top 15 cards

Failure 2 : Fail to draw any Grapeshots in your top 45 cards

 

 

So, adding the second Grapeshot adds 19.1% to your odds of getting dead draws, but it also reduces your “can't find a Grapeshot and lose” probability by the same percentage.

 

The difference is that you can minimize the probability of the Failure 2 scenario by playing a second Puresteel Paladin before attempting the combo. The second engine card will give you enough to draw your whole deck, so you will definitely find the Grapeshot.

 

Verdict: Play two if you're paranoid, but one is probably enough.

 

 

 

What do we do with the flex slots?

 

First, let's recap to see how many slots we have left to work with:

 

15 Lands

4 Mox Opal

8 Engines

5 Retracts

1 Grapeshot

19-21 Equipment (let's say 20 to simplify)

 

That leaves room for between 7 flex slots. What are our options?

 

Serum Visions Sleight of Hand

 

First, we have card drawing/filtering spells, namely Serum Visions and Sleight of Hand. As any combo player will tell you, casting one of these spells on turn 1 greatly improves your odds of going off, because it allows you to dig two or three cards deeper to find missing combo pieces.

 

So, do we just run 4 Serum Visions and 3 Sleight of Hand? In an ideal world where no one has interactive spells, yes. However, because the real world is a cruel place where people will push, bolt, or exile our poor Paladins and Edificers, we might want to have some number of protection spells in the mix.

 

Of the protection spells, we have plenty to choose from at 1 mana, such as Spell Pierce, Swan Song, Dispel, and Apostle's Blessing. Choose whichever suits your metagame best, but I'd probably run only two slots maximum.

 

For the last slot, if you're only running 1 Grapeshot, I'd probably opt for 1 Noxious Revival. Noxious Revival can act extra copy of any card in your deck, which improves consistency and makes you more resilient to discard or removal spells.

 

 

 

The Finished Product

 

Maybe something like this?

 

Cheerios (Modern - Others)

Gallery View

Modern by

deck download

 

So, after all the complicated analysis, I end up with a list that looks fairly close to stock, with the exception of the Hurkyl's Recall. But at least now you know how I justified every single slot. I do hope I didn't bore or confuse you with the use of numbers.

 

Next time: the sideboard!




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