Suppose that you’ve drafted the following blue-green deck:

All that’s left to do is to add 17 lands. But this time there’s a twist: The land station has an unlimited amount of Forests and Islands in addition to an unlimited number of Woodland Streams. You can add as many tapped duals as you want! What mana base would you choose?

Naturally, there’s a trade-off. Tapped duals (like Woodland Stream or Evolving Wilds) increase the likelihood that you have the right sources of colored mana to cast your spells. But they can also prevent you from curving out perfectly. So, there’s no one obvious mana base that is clearly the best.

Let’s break down the deck once more in text form:

This distribution over the various mana costs in the main color and the support color is close to the average distribution found in 2-color Draft decks from the Top 4s of recent Limited GPs. (Specifically, from GP HoustonGP LondonGP LiverpoolGP PhoenixGP Indianapolis, and
GP Metz, spanning Hour of Devastation, Ixalan, and Rivals of Ixalan Draft.) So the mana costs are a good representation of the average Limited deck. Sure, I ignored noncreature spells and multicolor cards because this greatly simplified my gameplay simulations later on, but the curve and number of double-colored cards are representative of a typical Draft deck.

Now let’s return to the question: which mana base would you pick? Personally, my first guess would be nine Forest, six Island, and two Woodland Stream, but that’s just based on intuition and some rules of thumb that I’ve developed over the years. For instance, I generally find eleven sources to be sufficient for a main color with several double-colored spells and eight sources to be sufficient for a support color with no double-colored spells. Also, I felt that a third Woodland Stream would increase the risk of drawing multiple dual lands (which really screws up the curve) to unacceptable levels.

But let’s do something a little more scientific.

Metholodogy

I set up a simulation optimization model based on the following assumptions:

  • I aim to optimize the turn on which I win the game (“average kill-turn”) against a pseudo-goldfish. A pseudo-goldfish is an opponent who counters the first two creatures of 2 or more mana I play (they ignore 1-drops) but doesn’t interact afterwards. After their two counterspells, they don’t do anything the entire game.
  • I am always on the play.
  • The mulligan rule is as follows: Keep any hand that has three or four lands with at least one card that can be cast with those lands. Keep any hand that has five lands with both colors of mana. Keep any hand with two lands with both colors of mana or at least one card that can be cast with those lands. Keep every four-card opening hand. Mulligan the rest. In case of a mulligan, I ignore the free scry for simplicity.
  • Every turn, I attack with all creatures without summoning sickness. Obviously. I’m trying to win the game, after all.
  • Every turn, from the lands I have in my hand, I pick the one that lets me maximize my total mana spent on that turn. In case of a tie, I favor Woodland Stream over Forest, and I favor Forest over Island. This means that if I start the turn with two Forest and one Island in play and Jungleborn Pioneer, Deadeye Rig-Hauler, Island, and Woodland Stream in hand, then I would play Island, Deadeye Rig-Hauler. But if my hand didn’t contain Deadeye Rig-Hauler, then I would play Woodland Stream, Jungleborn Pioneer.
  • Given the lands I have after my land drop and given the spells I have in hand, I pick the combination of at most three spells that lets me maximize the total mana spent on that turn. I break ties by favoring the most stringent mana costs, i.e., I favor a 3GG card over a 4U card, which in turn I favor over a 2GG card. The remainder of the priority list is ordered as 3G, 3U, 1GG, 2G, 2U, 1G, 1U, G, U. This means that if I have three Forests and one Island after playing my land for the turn and hold Deadeye Rig-Hauler, Swift Warden, Deeproot Warrior, and Shaper Apprentice, then I cast Deadeye Rig-Hauler. (This may not be optimal if I want to maximize the total power added to the board, but given the impact of 4-drops, it more closely resembles how I’d usually play a real game of Magic.) If I remove Deadeye Rig Hauler from that hand, then I would play Deeproot Warrior and Shaper Apprentice. If I also remove Shaper Apprentice, then I would play Swift Warden.
  • My mana auto-tapping logic is superior to the one currently implemented on MTG Arena, as it actually makes sense. If I hold Deeproot Warrior and Shaper Apprentice and control three Forest and one Island, then I would tap two Forest to cast Deeproot Warrior, leaving one Forest and one Island untapped for Shaper Apprentice. Also, if I would hold Deeproot Warrior and Mist-Cloaked Herald and control two Forest and one Island, then my algorithm will take my hand into consideration when choosing which lands to tap: In this case, it will tap two Forest to cast Deeproot Warrior, leaving one Island untapped for Mist-Cloaked Herald.
  • I simulate 10 million games for every mana base I want to check. This sample size ensures the standard error in the estimated average kill-turn is no larger than 0.001.

Of course, this is a model. If I had infinite time, then I would try to figure out which mana base would give me the best chance to win against a real opponent under an optimized mulligan and gameplay strategy. But since determining that is nearly impossible, I went for the simpler “fastest kill-turn against a pseudo-goldfish” criterion. I believe that this criterion is insightful and that my accompanying assumptions are useful. The multicolor setup isn’t easy, but it’s still simple enough for me to hardcode it in a reasonable amount of time. I used Java because it allowed me to adapt some earlier work, but any programming language with loops, variables, conditionals, and functions would do. You can find my raw code here.

The Result

The three best mana bases are as follows:

So my own first guess with two tapped duals got the bronze medal. Did you do better and guess the “best” mana base with a single tapped dual right away?

Either way, let’s continue by analyzing the impact of various other factors.

The Impact of the Number of Lands

The U/G deck was fixed at 17 lands, but what if we would have one more or one fewer land by removing or adding a Jungleborn Pioneer?

In the 16-land setting with five Jungleborn Pioneer, the best mana bases are:

In the 18-land setting with three Jungleborn Pioneer, the best mana bases are:

Conclusion: One tap dual stays optimal for slightly different land counts. The best mana bases match the ones in the 17-land setting after cutting or adding an Island/Forest. Also, since the best 16-land deck and the best 18-land deck kill slower on average than the best 17-land deck, I’m happy to stick to 17 lands for this U/G deck.

The Impact of Double-Colored Cards

My base U/G deck has three double-green cards and zero double-blue cards, but what if I changed those numbers?

If I reduce the green color requirements by replacing one Swift Warden and one Ripjaw Raptor in my base deck with one Jungleborn Pioneer and one Jade Guardian, then the best mana bases are:

If I increase the green color requirements by instead cutting one Jungleborn Pioneer and one Jade Guardian while adding one Swift Warden and one Ripjaw Raptor, then the best mana bases are:

Finally, if I were to increase the blue color requirements by replacing two Watertrap Weavers in my base deck with two Kopala, Warden of Waves, then the best mana bases are:

Conclusion: One tapped dual stays optimal even if I reduce the number of double-colored spells. But when I further intensify the green requirements, two tap duals become optimal. Generally speaking, the more double-colored cards you have, the more tapped duals you want.

The Impact of Interaction

My pseudo-goldfish opponent countered the first two 2+ mana creatures I played. What if I gave them one fewer counter (which would represent a noninteractive format revolving around damage races and little to no blocking)? And what if I gave them one extra counter (which would represent a more interactive format with lots of removal spells and combat trades)?

In the setting where they only have one counter, the best mana bases are:

In the setting where they have access to three counters, the best mana bases are:

Conclusion: The faster the format, the fewer tapped dual lands you want. Indeed, if opponents don’t interact much and curve-outs are essential, then the optimal mana base contains no Woodland Stream at all. Conversely, if opponents have more interactive spells and games last longer as a result, then all of the best mana bases have one or two tapped duals.

Conclusion

For the U/G deck, whose mana cost distribution is representative for well-performing draft decks, a single Woodland Stream is worth it. But, given the trade-off between color consistency and a slower mana base, you shouldn’t run more than one tapped dual in your base setting.

Still, there are reasons to add a second Woodland Stream, including a higher density of double-colored spells or a more interactive format. Though I should stress that the outcomes really depend on the specific modeling assumptions used.

Nevertheless, if you accept the usefulness of my general model setup, then I can leave you with a general piece of actionable advice for Drafts: the first Woodland Stream (or Evolving Wilds, or Forsaken Sanctuary if you’re drafting B/W instead) is a valuable pickup, but a second copy should not be prioritized (it might even end up in your sideboard depending on how many double-colored spells you have), and a third one is overkill for most 2-color decks.