Preamble

Most draft podcasts, prerelease primers, and strangers looking over your shoulder at your sealed pool will tell you the same thing:

"Oh, you want to splash a third colour? You need 3 sources!"

It's said with total confidence, as if it's a hard baked rule of the game and not something someone made up because it sounded reasonable.

In this article, I will look at common internet knowledge, Frank Karsten, demonstrate two sealed pools I built six and a half years apart, math (I wanted to do it myself, haha!), a calculator and some take aways.

I definitely think I've improved at limited over the years...

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What the internet actually says

Three is the number people reach for because it's better than nothing and it usually doesn't blow up in your face.
Usually.

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The math for just 3 splashes

Let's assume that you have a 40-card deck, 17 lands, 3 splashed, on the play, and a 6-drop you're hoping to cast on curve.

How often do you actually have 6 lands in hand by turn 6, and how often is one of those lands the color you splashed?

Turn	Cards seen	P(6+ lands)	P(6+ lands, incl. splash)	P(splash | 6+ lands)
6	12	38.8%	30.8%	79.3%
7	13	50.4%	40.4%	80.2%
8	14	61.6%	50.0%	81.2%
9	15	71.7%	59.0%	82.3%
10	16	80.1%	66.9%	83.5%
11	17	86.8%	73.6%	84.8%

Look at the middle column. On turn 6, with 3 splash sources sitting in your 17 lands, you have your six lands and the right color less than a third of the time.

The "3 sources" folklore isn't wrong, exactly. It's just assuming you're fine with the card being playable a few turns late.

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Exhibit A: War of the Spark, April 28, 2019 : The poor example

Enter the God-Eternals is the one that hurts to look at. It costs and , one of which is my scarcest color. A third of the time on curve. Oof.

Jiang Yanggu has an extra problem that no amount of source-counting fixes: it needs to cast, and is one of the colors it's supposed to help me find. My fixer needed fixing before it could fix anything. Cute in theory, a liability in practice.

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Exhibit B: Marvel's Spider-Man, September 20, 2025 : The good example

And the numbers stopped being a hypergeometric problem and became a "you need to simulate this" problem, because these are sequential, conditional effects, not draws from a static population. So, after a Monte Carlo Simulation, we have:

Card	On curve	+1 turn	lands only (On curve / +1 turn)
Kraven the Hunter	28.1%	72.2%	17.0% / 53.2%
Carnage, Crimson Chaos	50.4%	75.9%	17.9% / 48.9%
Spider-Man India	61.9%	77.3%	27.9% / 48.1%

Note how strong the creature fixing was; the single biggest lever being Spider-Bot.

A guaranteed on-color land next draw is worth more than almost any number of extra basics would be, because it converts a probability into a near-certainty for the one draw you actually need.

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Lands, and beyond

Everything so far has been lands: draw a card, is it a land, is it the right color.

That model has a hard ceiling, and both pools eventually ran past it. Everything below touches mana without being a plain basic:

Category	Definition	Examples
Rainbow land	Taps for any color; usually has a one-time tempo cost on entry	Gateway Plaza
Fetch land	Sacrifices itself to search for a basic and put it onto the battlefield tapped; permanently becomes that one color once fetched	Evolving Wilds, Hobbit Hole, Vibrant Cityscape
Dual land	Taps for a primary color or the splash color, usually with a tapped entry cost as the other lands above	Boros Guildgate, Godless Shrine
Tutor, to top	Searches your library for a basic and puts it on top - guarantees your next draw, but also spends it	Spider-Bot
Tutor, to hand	Searches for a basic and puts it straight into hand instead of the library - doesn't wait on a draw step	Pilgrim's Eye, Thror's Map
Mana Rock	Something that taps for any color of mana once cast	Hot Dog Cart
One-shot mana	Treasures, Gold, etc. They produce any color once and then they're gone	Professional Wrestler
Ramp	Puts an extra land onto the battlefield on resolution.	Shared Roots, Molten Man

None of these are lands, and none of them behave like a fixed 17/40 population you can draw from. That's the problem.

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From Hypergeometric Distribution to Monte Carlo Simulation

The hypergeometric distribution assumes independent, replacement-free draws from a fixed population, and that holds up fine for a deck of lands and unplayable filler, but the moment you add mana rocks, card draw, or Treasure generation, there's no longer a neat closed-form formula, because you'd need to account for player strategy, sequencing, and every possible interaction between effects.

Monte Carlo simulations literally brute-force the solution, playing games over and over again tens of thousands of times to get our probabilities.

I'm not the first person to run into this wall. Ties Westendorp wrote up the exact same problem for EDHREC in Simulating Available Mana (Beyond the Hypergeometric Distribution)

Hareruya's, Using Monte Carlo Simulation to Improve Your Manabases, writeup uses it to see how absurd it would be to cast a spell in a 2 color deck on turn 4 (40%), never mind splashing it.

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The bill comes due

Every splash land in your deck has to come from somewhere. That "somewhere" is almost always your own primary colors. Every land you take out will change the probability of how you might never draw one of your primary colors.

By 4 splash lands, your weaker main color is getting screwed nearly 3 out of every 20 games on turn 4!

This cost gets paid every game.

A dead splash card in hand is a disappointment. A screwed primary color is a game loss.

Here we assume that we have 6 sources (e.g. 6 splash lands, 6 filter lands, 1 basic + 5 fetches, etc.). This is to ensure we have a 90% chance to get our splash colour by turn 7.

Looking at the table, we can come to the following conclusions:

• See how good Dual Lands perform. While they have a tempo hit of usually coming in tapped, the penalty goes away the next turn - which is why they're prized highly by drafters.
• Filter Lands do a great job - if you're okay taking a 1 mana tax to turn one mana into another color (which you can't do in some formats).
• Effects that put lands to top / to hand are excellent since they are usually attached to spells, and thus don't tax the mana base, but it also means you're taking a tempo hit to do something that doesn't affect the board much.
• Fetch Lands like Evolving Wilds are good - but if you get them early, you might choose to get one of your primary colors instead of the splash color.
• Gateway Plaza style rainbow lands perform the best - but not all formats have them.

Try it yourself

TLDR : Conclusion

• Count your sources in your land base, per color, per pip.
• Count your enablers in your primary colors: Mana rocks, Treasures, Land Cyclers, Land Tutors, Ramp.
• Ensure the count of your splashes and enablers makes you comfortable. I'd say, 6~ish?