Mathemagics, Part 2, Color Distribution

By Joseph Davis

Hi, I’m Joseph, and welcome back to Mathemagics. The goal of this series is to help you level up your deck building whether you’re new to the game or just trying to improve your brews. We’ll be exploring important aspects of deck design and diving very lightly into the math behind it, so you know not just how to build a deck, but why some deckbuilding choices are better than others. This week we’ll be building on last week’s article by talking about color distribution.

 

Last week we talked about your deck having a plan, and we’ll continue that this week. When building your deck, you will have certain spells you want access to on the turn they become available. A good example of this is Settle the Wreckage or Ritual of Soot: decks playing these sweeping cards will usually be slower and trying to halt the tide of aggro decks with one of these spells on turn 4. A card like Crackling Drake is generally not a good turn 4 play because it is often simply a 0/4 or 1/4 , so when building our mana base we will not need to be worried about having 2 red and 2 blue on turn 4.

 

We’ll be using the term “pip” to refer to mana symbols, so a card that costs 1G would be described as having 1 pip since you must use 1 green to cast it, while the other portion of the cost can be any color. Here are some tables:

 

One pip Turn 1 Turn 2 Turn 3 Turn 4 Turn 5 Turn 6 Turn 7
5 47.46% 52.41% 56.99% 61.21% 65.09% 68.65% 71.91%
6 54.14% 59.33% 64.03% 68.26% 72.07% 75.49% 78.55%
7 60.09% 65.36% 70.02% 74.14% 77.76% 80.94% 83.72%
8 65.36% 70.59% 75.11% 79.02% 82.37% 85.25% 87.71%
9 70.02% 75.11% 79.42% 83.05% 86.10% 88.66% 90.78%
Two pip Turn 2 Turn 3 Turn 4 Turn 5 Turn 6 Turn 7  
10 39.98% 46.74% 53.14% 59.13% 64.63% 69.63%  
11 45.44% 52.55% 59.13% 65.12% 70.50% 75.27%  
12 50.72% 58.02% 64.63% 70.50% 75.64% 80.07%  
13 55.76% 63.13% 69.63% 75.27% 80.07% 84.09%  
14 60.51% 67.84% 74.13% 79.44% 83.84% 87.40%  
15 64.97% 72.13% 78.13% 83.05% 86.99% 90.07%  
16 69.11% 76.02% 81.65% 86.12% 89.59% 92.16%  
Three pip Turn 3 Turn 4 Turn 5 Turn 6 Turn 7    
15 39.90% 48.11% 55.90% 63.05% 69.44%    
16 44.91% 53.44% 61.30% 68.31% 74.35%    
17 49.86% 58.55% 66.34% 73.04% 78.59%    
18 54.68% 63.40% 70.96% 77.22% 82.14%    
19 59.32% 67.93% 75.12% 80.82% 85.00%    
20 63.75% 72.10% 78.81% 83.84% 87.16%    
21 67.92% 75.90% 82.02% 86.26% 88.64%    

 

Magic is a best two out of three game, so again we are looking for our plan to work on time 66% of the time or greater. The number listed on the left is the number of sources which produce the percentages going across their row. When looking at the pip requirements, there is only a small distinction between mono and multicolored spells. For example, Merfolk Trickster costs UU (blue blue). You should have 16 blue sources to reliably cast it on turn 2. Thought Erasure costs UB (blue black). You should have 16 blue AND black sources to reliably cast it on turn 2. This does not mean you need to run 32 lands consisting of 16 islands and 16 swamps though. A Watery Grave, Drowned Catacomb, Dimir Guildgate, or Submerged Boneyard counts for both one blue source and one black source. One last note, when looking at hybrid mana costs like the Find (G/B G/B) half of Find//Finality you can count sources of either green OR black, so if you wanted to cast Find on turn 2 for some reason, you would need 16 green OR black sources to reliably cast it on time.

 

The overall thing to take away from this is that the earlier you need multiple colors, the fewer colors you can afford to mash together. In order to consistently cast a 3-mana card with 3 pips such as Goblin Chainwhirler, you need 21 sources of the color of that pip. This is the reason decks which use Goblin Chainwhirler, Steel Leaf Champion, or Benalish Marshall tend to be mono colored, as it is very difficult to produce the mana required to play them on time otherwise.

 

Let’s look at some decklists and discuss the construction of the archetypes:

RW Angels – Carson Lewis

5-8th Place SCG Classic – Dallas

 

2 Adanto Vanguard
3 Aurelia, Exemplar of Justice
4 Knight of Grace
4 Lyra Dawnbringer
4 Resplendent Angel
3 Shalai, Voice of Plenty
2 Tocatli Honor Guard

1 Ajani, Adversary of Tyrants

2 Conclave Tribunal
3 Deafening Clarion
4 History of Benalia
2 Justice Strike
2 Lightning Strike

4 Clifftop Retreat
4 Mountain
12 Plains
4 Sacred Foundry
SIDEBOARD
2 Banefire
1 Ixalan’s Binding
1 Karn, Scion of Urza
2 Rekindling Phoenix
3 Seal Away
2 Settle the Wreckage
1 Silent Gravestone
1 Sorcerous Spyglass
2 Tocatli Honor Guard

 

This deck is almost a mono white deck but is splashing red for Justice Strike, Deafening Clarion, and most importantly Aurelia, Exemplar of Justice. This deck’s plan is to curve out with good threats, most importantly playing Aurelia on turn 4. The Justice Strike on turn 2 and the Deafening Clarion on turn 3 are less important to the plan for the deck than consistently landing Aurelia on time, as she pumps whatever threats you have out already and adds a significant clock on the next turn when she can join the battle. Looking at our chart, they should have 13 sources of both red and white to consistently cast Aurelia on turn 4. They have 20 white sources and 12 red sources, so the deck is almost exactly where it should be mathematically but may wish to change one more Plains into a Mountain to bump their numbers slightly more into line. If the deck wanted to cast Justice Strike consistently on turn 2, it would need to climb to 16 red sources, but since Justice Strike is a late game removal card to clear out a card like Ghalta, Primal Hunger, we don’t have to worry about being able to cast it on turn 2.

 

Jeskai Control – Michael Hamilton

9-16th Place SCG Classic – Columbus

 

1 Ral, Izzet Viceroy

3 Teferi, Hero of Dominaria

2 Chemister’s Insight

1 Cleansing Nova

2 Deafening Clarion

2 Essence Scatter

4 Expansion // Explosion

4 Ionize

2 Justice Strike

1 Lava Coil

2 Lightning Strike

1 Negate

2 Search for Azcanta

3 Settle the Wreckage

1 Shivan Fire

1 Shock

4 Clifftop Retreat

1 Evolving Wilds

2 Field of Ruin

4 Glacial Fortress

2 Island

4 Plains

4 Sacred Foundry

4 Steam Vents

3 Sulfur Falls

 

SIDEBOARD

1 Chemister’s Insight

1 Dawn of Hope

1 Deafening Clarion

1 Disdainful Stroke

1 Invoke the Divine

3 Lyra Dawnbringer

1 Negate

1 Nezahal, Primal Tide

2 Shalai, Voice of Plenty

1 Shivan Fire

2 Siege-Gang Commander

 

Now, you might be saying, are multicolored cards always a worse choice than mono colored cards? For example, is it always harder to cast Ionize (1UR) instead of Sinister Sabotage (1UU)? The answer is: it depends. If you are playing a three (or more) color deck like this one, and especially if you have multiple cards you want to cast on the same turn, multicolored cards and dual lands can make it easier to have different plans spread across multiple cards. In this deck you want to cast Deafening Clarion (1WR) or a counterspell on turn 3, depending on what you’re playing against and what you draw. For both Sabotage and Clarion to work in this scenario you need 14 sources of each red, blue, and white to have all your options open, but for Ionize you can share dual lands when building your mana base. For example, Steam Vents counts as both a blue and a red source for Ionize AND a red source for Clarion. Likewise, Sacred Foundry counts as both a white and a red source for Clarion AND a red source for Ionize. The overlap between the two enables a more reasonable mana base for achieving the desired plan for the deck.

 

BG Midrange – Maxwell Jones

1st Place SCG Classic – Dallas

 

3 Doom Whisperer

2 Golgari Findbroker

4 Jadelight Ranger

4 Llanowar Elves

4 Merfolk Branchwalker

3 Ravenous Chupacabra

3 Seekers’ Squire

3 Wildgrowth Walker

3 Vivien Reid

3 Vraska, Relic Seeker

2 Assassin’s Trophy

3 Find // Finality

8 Forest

4 Overgrown Tomb

7 Swamp

4 Woodland Cemetery

 

SIDEBOARD

1 Assassin’s Trophy

2 Carnage Tyrant

3 Duress

1 Find // Finality

3 Moment of Craving

1 The Eldest Reborn

2 Vraska, Golgari Queen

2 Vraska’s Contempt

 

This deck is cluttered with mana symbols looking to cast powerful cards like Jadelight Ranger (2 pips, green) on turn 3 or Ravenous Chupacabra (2 pips, black), and Golgari Findbroker (4 pips, green and black) on turn 4. To be able to play these spells reliably, the deck has to stick to 2 colors, otherwise it would be impossible to get the required number of colored mana sources without playing an extraordinary amount of lands. With just 23 lands, this deck still plays 16 green sources and 15 black sources enabling it to reliably fill out the large number of color pips required from all the powerful double pipped cards.

 

When building your next deck, keep these principles in mind and ask yourself these questions:

1) Which of my spells do I need to cast as early as possible?

2) Are there any multicolored cards which I can substitute in to make my plans overlap better?

3) Can I achieve the number of sources I need in the number of lands I’m playing?

 

If you find yourself answering number 3 with “no”, you probably are trying to stretch your early color requirements too much. You should either substitute some multicolored spells in if possible, or change your plan to be less color intensive or involve fewer colors. I hope you’ve enjoyed your second lesson in Mathemagics, and I’ll be back with another one soon!

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