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|
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:
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 Wizard’s Lightning
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
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.
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!