Mathemagics, Part 1

by: Joseph Davis

Hi, I’m Joseph, and welcome 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. First up is a classic question: how many lands should you play?

 

There are two important points to consider when thinking about how many lands to put in your deck. First, what is the critical number of lands to be able to reliably make a drop each turn? Your deck has a plan and some part of that plan needs to happen on time. Figure out which turn is the most mission critical to arrive at successfully, whether you only need 3 lands to play every card in your deck or you want to cast some more expensive spells. Second, what is the minimum number of lands possible to play in your deck so that you reliably hit that number? Lands are the worst draw late in the game, so you don’t want to play too many or else you’ll run out of good things to do.

 

As a very brief aside in case you want to follow along, we’ll be using a mathematical formula to help figure out how many lands we’ll draw on average for each turn from turn one to turn seven. This formula is called hypergeometric distribution. Here is a big chart which I’ll explain below:

 

Land count Turn 1 Turn 2 Turn 3 Turn 4 Turn 5 Turn 6 Turn 7
20 95.17% 82.42% 63.75% 43.91% 26.87% 14.28% 5.76%
21 96.02% 84.96% 67.92% 48.77% 31.28% 17.44% 7.34%
22 96.73% 87.22% 71.81% 53.53% 35.82% 20.84% 9.11%
23 97.33% 89.22% 75.40% 58.13% 40.39% 24.41% 11.03%
24 97.84% 90.96% 78.68% 62.50% 44.91% 28.06% 13.05%
25 98.26% 92.47% 81.63% 66.58% 49.29% 31.69% 15.10%
26 98.61% 93.76% 84.24% 70.33% 53.41% 35.21% 17.12%
27 98.89% 94.86% 86.53% 73.69% 57.19% 38.49% 19.04%
28 99.13% 95.78% 88.49% 76.62% 60.55% 41.44% 20.77%
29 99.32% 96.54% 90.13% 79.09% 63.40% 43.94% 22.24%
30 99.47% 97.16% 91.44% 81.06% 65.66% 45.93% 23.40%

 

Magic is a game which is played best 2 games out of 3. Because of this, any plan which works less than 66% of the time is not a good idea, since you want to be winning 2/3 of your games. This applies to lands more than anything, so for whatever critical turn is most important, you should plan to arrive at it on curve at least 66% of the time. Let’s go through some examples with up-and-coming archetypes in Standard:

 

Steam-kin Aggro

Marc Kaake – 4th place, SCG Standard Classic, Columbus OH

4x Fanatical Firebrand                        Sideboard:

4x Ghitu Lavarunner                           2x Banefire

4x Goblin Chainwhirler                       3x Diamond Mare

4x Runaway Steam-Kin                      3x Fight with Fire

4x Viashino Pyromancer                    3x Lava Coil

3x Experimental Frenzy                      3x Legion Warboss

4x Lightning Strike                              1x Shivan Fire

3x Risk Factor

4x Shock

4x Wizard’s Lightning

22x Mountain

 

This aggressive strategy relies on playing aggressively on turns 1, 2, and 3 – playing out hasty creatures or deploying burn spells to clear the path or deal damage to the opponent. A big tempo swing usually comes on turn 3, when Goblin Chainwhirler hits the battlefield, clearing the way of tokens and pushing through an extra point of damage on the opposing player and any planeswalkers they’ve played. The deck does not have any real acceleration to it and relies heavily on hitting its land drops naturally but cannot afford to draw too many or it will lose tempo and putter out. According to our chart, this deck should be playing 21 lands since it cannot accelerate itself ahead of the normal behavior of drawing 1 card and playing 1 land per turn.

 

Mono Green Stompy

William McDonald – Top 32, SCG Team Open, Columbus OH

2x Ghalta, Primal Hunger                   Sideboard:

4x Jadelight Ranger                            2x Carnage Tyrant

1x Kraul Harpooner                            2x Deathgorge Scavenger

4x Llanowar Elves                              2x Kraul Harpooner

4x Merfolk Branchwalker                   4x Prey Upon

4x Nullhide Ferox                               3x Thrashing Brontodon

4x Pelt Collector                                 2x Vivien Reid

4x Steel Leaf Champion

2x Territorial Allosaurus

4x Thorn Lieutenant

1x Thrashing Brontodon

3x Vine Mare

23x Forest

 

This deck is built around curving into big nasty hexproof threats and the key number for this deck is 4. At 4 mana they can cast both Vine Mare and Nullhide Ferox to curve out into Ghalta, Primal Hunger. Looking back at the table above, you’ll see this deck will want to end up at 25 lands so that it can reliably hit these threats on time. Green has the ability to play creatures which accelerate their mana curve though. Playing Llanowar Elves is about half as good as playing a forest, since it does add an extra mana source, but it has summoning sickness and dies to removal. Because of this we can treat a deck with 4 copies of Llanowar Elves as needing 2 fewer lands to really work well. You will find mono green decks playing 23 lands comfortably due to the presence of Llanowar Elves, plus any other creatures with Explore that will help smooth their draws, such as Merfolk Branchwalker and Jadelight Ranger.

 

Esper Control

Orlando Lucas

Top 16 – SCG Standard Classic, Columbus, OH

1x Chromium, the Mutable                             4x Glacial Fortress

4x Teferi, Hero of Dominaria                          4x Island

3x Cast Down                                                 4x Isolated Chapel

4x Chemister’s Insight                                    1x Plains

1x Disdainful Stroke                                       3x Swamp

2x Essence Scatter                                        4x Watery Grave

3x Moment of Craving                                    Sideboard:

3x Ritual of Soot                                             1x Arguel’s Blood Fast

2x Search for Azcanta                                    2x Disdainful Stroke

4x Sinister Sabotage                                       2x Duress

3x Syncopate                                                  2x Fungal Infection

3x Vraska’s Contempt                                    2x Invoke the Divine

4x Drowned Catacomb                                   1x Negate

2x Evolving Wilds                                            1x Ritual of Soot

1x Field of Ruin                                               2x The Eldest Reborn

2x Vona, Butcher of Magan

 

The control deck in the new meta, piloted to great success by a local player from the VA beach area, looks like it will be an Esper (blue white black) deck featuring Teferi, Hero of Dominaria plus a lot of counterspells and removal spells. This deck relies very heavily on hitting a sweeper (Ritual of Soot) or removal (Vraska’s Contempt) in order to avoid dying. They also have very powerful threats and board control to take control of the game on turn 5 (Teferi, Vona). This deck needs to reach turn 5 on time so it can deploy stabilizers such as Teferi or Ritual of Soot. Running the math as shown in the table above would suggest this deck should be playing 30 lands! The trick that blue decks have up their sleeve is that they can draw extra cards and get ahead of the curve with extra chances to draw a land. Cards like Chemister’s Insight and Search for Azcanta will usually end up drawing the equivalent of 2 extra cards by turn 5. If we count Chemister’s Insight, Search for Azcanta, and Sinister Sabotage (all with effects that let us look at extra cards and find lands) as 1/3 of a land drop, similar to how I mentioned Llanowar Elves is equivalent to ½ a land drop, we can safely run 27 lands in a deck like this one.

 

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

1) What is the critical turn I need to hit (3, 4, 5)?

2) Do I have any mana acceleration (mana creatures, artifacts which tap for mana)?

3) Do I have any ways to draw extra cards or filter what I draw (surveil, explore, card draw spells)?

 

From there, start at 21, 25, or 30 lands and then fill that many lands or land effects. Mana accelerants should count for half of a land per copy, and card draw should count as a third of a land, since they do not replace lands directly but rather increase your likelihood of drawing them. If you have cards which draw you lands directly, or directly put lands into play, consider what mana level you need to hit to reliably play them and avoid going below that number. For instance, if you have 4 District Guides in your deck, you should still not go below 21 lands, since you’ll need to hit 3 to use the Guides themselves. I hope you’ve enjoyed your first lesson in Mathemagics, I’ll be back with more soon!

 

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