# Magic Math – Shadowlands and Battlelands

After seeing the new cycle of Allied-colored dual lands from Shadows over Innistrad, I knew that I had to write an article on math and mana bases in the new Standard.

These new lands are quite interesting from a deck building and game play perspective. Although they will be mediocre late-game topdecks, they are great in the early game, where they will often enter the battlefield untapped. In that regard, they remind me of Razorverge Thicket and the like. That old cycle of lands has even seen Modern play, which bodes well for the new cycle.

# What to Call These New Lands?

Many names have been proposed, including peek lands, reveal lands, shadowlands, showlands, and hand lands. I asked for your opinion in a Twitter poll and the overwhelming majority voted for shadowlands (it would’ve been better if this poll had included “show lands” and “hand lands” as separate categories, but “shadowlands” was still way more popular than “something else.”) DailyMTG will also likely adopt that name. Taking all this into consideration, I’ll stick with “shadowlands.”

# How Many Lands of the Right Basic Type Do You Need for Shadowlands?

Shadowlands are always playable. I was already building decks with Tranquil Expanse before the new cycle was revealed, and Fortified Village is clearly better than Tranquil Expanse even if you have only a single Forest or Plains (or Canopy Vista) in your deck. But naturally, the more lands with the right basic type the better. So how many do you need?

To get a feel for the numbers, I set up a simulation under the following simplifying assumptions:

• You have a 60-card deck with 25 lands: 4 shadowlands, X basic-type lands (either actual basic lands or battlelands of the right type), and 21-X inconsequential lands (such as painlands, Evolving Wilds, or creaturelands, which are all irrelevant for the question at hand). This mana base is reasonable for an Allied-color midrange deck or a tri-color wedge deck.
• You mulligan an opening hand if and only if it contains 0, 1, 6, or 7 lands. In case of a mulligan, for simplicity, you don’t use the free scry.
• You are always on the play.
• Every turn, you choose your land drop as follows: First, if you can play an untapped shadowland, you do so. Otherwise, if you can play any inconsequential land, you do so. Otherwise, finally, if you can play a tapped shadowland or a basic-type land (which can never happen at the same time), you do so. This sequencing is chosen to maximize the probability that a shadowland enters the battlefield untapped, even if it won’t always capture perfect game play. For instance, this logic implies that you have to play Shambling Vent rather than Plains on turn 3, even when you have a 3-drop in hand. Nevertheless, this sequencing proposes a reasonable guideline that allow me to simulate games and determine relevant probabilities.

I’m mainly interested in the probability of having a basic-type land in hand at the start of the first main phase on a certain turn as a function of the number of basic-type lands in the deck. This probability represents the likelihood that a shadowland, if it would magically appear in hand at the beginning of the turn, would enter the battlefield untapped at that time. The simple Java code I used to do 1,000,000 simulations per deck-turn combination is available here. The outcome is as follows.

Click to enlarge.

Hopefully, these probabilities can provide useful insights. My perspective is as follows.

• With 6 basic-type lands, Fortified Village is about halfway in between a Tranquil Expanse and a Razorverge Thicket.
• With 10 basic-type lands, the shadowlands start to become good as they enter untapped around three-quarters of the time in the early game.
• With 14 basic-type lands or more, you can realistically rely on your Fortified Village as an untapped source for a green or white 1-drop.
• With 18 basic-type lands or more, the shadowlands might be even better than Razorverge Thicket for decks that want to curve out with spells on turns 1 until 5. (If you play a Fortified Village revealing Plains on turn 4, then its untapped nature won’t help cast Gideon, Ally of Zendikar because you might as well have played Plains on that turn. But it can help cast Archangel Avacyn on the subsequent turn. That’s why curving out until turn 5 is necessary for Fortified Village to possibly be better than Razorverge Thicket.)

Ultimately, there is no clear-cut answer to the question “how many lands with the right basic type do you need for shadowlands?” It all depends on what you are looking for and what level of consistency you are willing to accept, but I can still try to give a general recommendation: for most decks, I would aim for at least 10 basic lands of the right type. This shouldn’t be hard to achieve, especially given that battlelands count as well.

## Some Notes on the Formulation of the Research Question

As always, determining the desired probabilities for a given research question is not so hard, but formulating the research question is. Ultimately, the vague question of “How many lands of the right basic type do you need for shadowlands?” turned into the more specific “how likely are you to have a basic-type land in hand at the start of your first main phase under the specified assumptions?” but this was merely the last in a line of research question that I considered. Feel free to skip this section, but I figured I’d provide some insight into the process.

The first question that I studied was “for a given turn and deck, what is the probability that a shadowland that actually entered the battlefield on that turn did so untapped?” Unfortunately, this number had a muddled interpretation. For instance, in a deck with 10 basic-type lands, a shadowland would enter untapped in 98% on turn 1 (with the remaining 2% mostly representing opening hands with 2 shadowlands and 5 nonland spells) but would enter untapped in only 74% on turn 2 (with the remaining 26% mostly representing opening hands with 1 shadowland, 1 other land, and 5 nonland spells). That sharp drop was mainly caused because the problem with those 1-1-5 opening hands wouldn’t become apparent until turn 2. In other words, the resulting probabilities for turns 2 and turns 3 are a bit misleading because most of the time when you have a shadowland in your opening hand, you’d play it on turn 1, and when you were unable to do so, the negativity is absorbed by turns 2 and 3. I realized these numbers didn’t capture what I actually wanted to know.

To account for the issue that a shadowland played anywhere on the first 3 turns is usually played immediately on turn 1, I next considered the question “For a given deck, what is the probability that an arbitrary shadowland that entered anywhere on turns 1, 2, or 3 according to the sequencing logic entered untapped?” So just the total number of untapped shadowlands on turns 1, 2, and 3 over all simulations divided by the total number of shadowlands played on those turns. This became more insightful, but it still had some issues because any game with 3 inconsequential lands and 1 shadowland as your only lands wouldn’t count as a bad thing. So the resulting probabilities still didn’t adequately represent the overall likelihood that a shadowland could be relied upon as an untapped source of colored mana in the early game.

Finally, I decided that the question of “for a given deck, how likely are you to have a basic-type land in hand at the start of your first main phase?” resonated the most with my intuition on what is interesting, so that’s the one I ended up showcasing. I don’t condition on actually having a shadowland in hand at that point, but I still think the resulting interpretation is appealing. I could’ve shown graphs and tables for all the other research questions as well, but then I would drown you in numbers and caveats on the interpretation, which would probably do more harm than good.

# How Many Basic Lands Do You Need for the Battlelands?

I studied this question before, but that was in a world with fetchlands. Using pretty much the same code as before, which was built under similar assumptions as the ones listed for the shadowland study, I ran the numbers again for zero fetchlands.

As a note, I did not incorporate shadowlands in this simulation because of the games where you would start with a shadowland, a battleland, and two basic lands in your opening hand. If you would play a shadowland on turn 1, then such a game would count as a game where you were unable to play an untapped battleland on turn 3, but that felt misleading because if you wanted, you could’ve sequenced differently to get an untapped battleland on turn 3. So for the purpose of determining relevant numbers for battlelands, I ensured that playing a basic land would be favored over playing a shadowland.

To have battlelands enter untapped consistently enough in the midgame, you need a lot of basics. With 10 or fewer basic lands, you should expect your battlelands to enter the battlefield tapped more than half of the time. A Sunken Hollow is still better than a Submerged Boneyard in any case, but in a deck with 10 basic lands, I wouldn’t count on having an untapped Sunken Hollow. If it happens, then that’s a nice bonus, but that’s about it. You need 16 basic lands or more to have your battlelands enter the battlefield untapped over three quarters of the time, which is a number I like.

This recommended number of 16 basic lands is much higher than for shadowlands! This makes intuitive sense because finding two lands is much more difficult than finding one, especially in the early game. As a result, I expect that shadowlands will be a better fit than battlelands in most basic-strapped decks, although their synergy together shouldn’t be underestimated. There may still be decks that prefer battlelands, such as decks that thrive in the late-game with 6-mana planeswalkers—such decks really need an untapped land when they topdeck one on turn 6. But generally speaking, battlelands will be much worse than they were when we still had fetchlands in the format.

# How Many Sources Do You Need for Certain Cards?

Roughly in line with the analysis I did years ago, I have the following recommendations:

• Play at least 14 sources for a single-color 1-drop or 2-drop (such as Jace, Vryn’s Prodigy)
• Play at least 12 sources for a single-color 3-drop or 4-drop (such as Explosive Vegetation)
• Play at least 19 sources for cheap double-colored cards (such as Grasp of Darkness)
• Play at least 17 sources for more expensive double-colored cards (such as Gideon, Ally of Zendikar)
• Play at least 21 sources for tri-colored cards (such as Archangel of Tithes)

A Plains obviously counts as a single white source and a Cinder Glade obviously counts as one red and one green source. For less straightforward mana sources, I would use the following accounting system:

• An Evolving Wilds can count as a full source for either color in a two-color deck. But in a three-color deck with double-colored cards, in which there will be real choices on which land to fetch, I would count 4 Evolving Wilds as 3 sources for each color.
• I view Traverse the Ulvenwald, as long as you have enough turn-1 untapped green sources to reliably cast the sorcery, in a similar way as Evolving Wilds. The land-search spell has the added bonus fetching basics for shadowlands, but don’t get in the loop of counting those fetched basics as ones that you can reveal to a Game Trail to cast a turn-1 Traverse the Ulvenwald!
• An Oath of Nissa can count as a full source for single-color planeswalkers like Arlinn Kord. It can count as 1.5 sources for double-colored planeswalkers like Chandra, Flamecaller.
• In a black/green deck, four copies of Deathcap Cultivator can count as 1-2 source of black mana for expensive black spells, depending on the prevalence of cheap removal in the format. I view Jace, Vryn’s Prodigy in a black/blue deck in a similar way.
• For a 1-drop like Zurgo Bellstriker, you want plenty of untapped sources of mana for turn 1. Depending on the exact probabilities, 4 shadowlands will often count as 2-3 untapped sources. Note that when looking up the relevant probability for an untapped shadowland in the graph above, disregard the basic Mountains in your deck because you would be able to cast a turn-1 Zurgo anyway if you had a Mountain.
Corrupted Grafstone is a sweet mana rock, but you can’t really rely on it as a fixer. After all, barring loot or rummage tricks, you typically need to have mana of a certain color among your lands before you can even get a card of that color into the graveyard. Corrupted Grafstone could help a bit for double-colored cards, but how much really depends on your deck.

To illustrate all this, I’ll go over a number of example mana bases for the new Standard.

## Two-Color Allied Mana Bases

A reasonable 24-land allied-color mana base, say for a black/red Vampire deck with Falkenrath Gorger, Asylum Visitor, Olivia, Mobilized for War, and Exquisite Firecraft could look like this:

Overall, this gives 18 sources of red mana and 14 sources of black mana, as well as more than enough basic-type lands for Foreboding Ruins and a sufficient amount of basic lands for Smoldering Marsh. For a turn-1 Falkenrath Gorger, we have 13 sources, counting 4 Foreboding Ruins as 3 sources of untapped red for turn one. All of this yields decent consistency!

If you also want to include Drana, Liberator of Malakir, then you’ll have to replace 4 Mountain by Swamp, Cinder Barrens, or Evolving Wilds. This will come at the expense of turn-1 red sources, so Indulgent Aristocrat could be a more desirable 1-drop than Falkenrath Gorger for such a version. One way or another, sacrifices have to be made somewhere.

## Two-Color Enemy Mana Bases

A reasonable 25-land enemy-color mana base, say for a white-black midrange deck with Knight of the White Orchid, Transgress the Mind, Wasteland Strangler, and Archangel Avacyn could look like this:

This gives 20 sources of white mana and 14 sources of black mana. Very solid!

Colorless-requiring cards like Eldrazi Displacer or Thought-Knot Seer fit into enemy-color decks as well because they turn your painlands into tri-lands. For Eldrazi Displacer, the colorless mana is just a bonus, so the above mana base with possibly one extra colorless utility land instead of one Plains, would already suffice. For Thought-Knot Seer, the colorless mana is a real requirement for casting the card, so you need more. This could be difficult especially if you want to retain the double-white cards, but you can always replace Plains and Swamp with Battlefield Forge and Llanowar Wastes, or you can go for Evolving Wilds plus Wastes.

# Three-Color Wedge Mana Bases

Without powerful payoff cards like Siege Rhino or Mantis Rider, there is much less of a draw to three colors. Moreover, the mana has gotten much worse than what we had with fetchlands and tri-lands. But still, suppose we want to make a Temur deck to take advantage of Sarkhan Unbroken. Let’s add Jace, Vryn’s Prodigy, Sylvan Advocate, and Thunderbreak Regent. In such a deck, we want green on turn 2, blue on turn 2, and double-red by turn 4. A reasonable 25-land mana base could look like this:

Counting 2 Evolving Wilds as 2 green sources, 2 blue sources, and 2 red sources, and counting 4 Jace as 1 red and 1 green source, we get the following breakdown:

• 14 green sources
• 14 blue sources
• 17 red sources
• 8 lands with basic type Forest or Mountain for Game Trail
• 11 basic lands (including Evolving Wilds) for Cinder Glade
• 8 tap-lands (counting 3 Game Trail and 1 Cinder Glade as 2 tapped lands in this mana base)

It’s decent enough. The number of colored sources are all okay. The only downside is that only have 8 lands to reveal with Game Trail, but that’s to a large extent inevitable because none of the 14 blue sources can ever count. Eight tap-lands is starting to get high, but it’s still acceptable, especially because we get four creature lands for the late game. If we would go for a mana base with more Evolving Wilds and Cinder Glade rather than painlands and shadowlands, then that would only lead to more tapped lands.

A useful general insight for wedge decks is the following: One color with double-colored cards (and/or spells that need untapped mana on turn one) is okay, but two colors with such hefty requirements exerts a very hefty tax on the mana base. It is questionable whether that is worth it.

# Three-Color Shard Mana Bases

As the final sample mana base I’ll provide today, here is a good 25-land mana base for a Bant deck with Jace, Vryn’s Prodigy, Reflector Mage, Deathmist Raptor, and Collected Company:

The reason for Fortified Village over Port Town is that Deathmist Raptor encourages Forests, and the reason for Prairie Stream over Canopy Vista is that we already had enough green fixing via Fortified Village and Forest.

Counting 4 Evolving Wilds as 3 green sources, 3 white sources, and 3 blue sources, and counting 4 Jace as 1 green source and 1 white source, we get the following breakdown:

• 16 green sources
• 13 white sources
• 14 blue sources
• 10 lands with basic type Forest or Plains for Fortified Village
• 14 basic lands (including Evolving Wilds) for Prairie Stream
• 8 tap-lands (counting 4 Fortified Village as 0.8 tapped lands and 4 Prairie Stream as 1.2 tapped lands in this mana base)

I’m happy with this mana base. 16 green is a bit low for Deathmist Raptor, but you can always just morph it, and the number of sources for the other colors is okay. 8 tap-lands is starting to get high, but it’s still acceptable, especially because we get two creature lands for the late game. And we have a good numbers on Fortified Village and Prairie Stream. The mana bases for shards might look a little worse than the mana bases for wedges because shards need more basic lands, but the difference is minimal.

Adding extra white sources (at the expensive of green or blue sources, as you likely have to replace Forest or Island) would be relatively easy because all battlelands and all shadowlands in the Bant shard produce white. Moreover, Plains is the best basic land because it can be revealed to both shadowlands. The awkward thing is that white is the splash in this Bant Company deck, which clashes with the mana-base strength of shards. However, this does mean that for an Esper Dragons deck with a carefully crafted mana base, you should be able to reliably cast Silumgar’s Scorn on turn two. I’ll leave the crafting of such a mana base as an exercise to the readers where they can apply the tools described in this article.

# Conclusion

Hopefully these numbers can help you build decks for Standard with Shadows over Innistrad! At its core, a format is defined by its mana bases, and the new Standard looks quite interesting in that regard. Mana bases for 2-color decks are excellent. Mana bases for 3-color decks could work, but they require lots of tapped lands. One way or another, I’ll surely be shuffling up the new shadowlands a lot over their lifetime in Standard!

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