Data-driven mana base studies. Every number on every page is reproducible in the live Mana Base Calculator.
These guides answer the kinds of questions you cannot answer from a textbook. Is Lórien Revealed worth four slots? Is 5-color Atraxa really harder to cast than 3-color Karador? How many lands does my Jund deck need before its double-pip Liliana actually casts on turn 3? Each one is grounded in 50,000 Monte Carlo simulations per data point, run on the same WASM engine that powers our live mana base calculator.
The guides below are independent — pick the one that matches the question you have right now. They cite each other where the math from one becomes the input to another.
Pick the question that matches your situation. Each branch routes you to the page with the most relevant numbers and decklists.
Read MDFCs and Cycling Lands: How Much Are They Worth? — measures the +23 pp cast-rate uplift from 4 Lórien Revealed in a UR Murktide shell.
Read Land Counts by Archetype — archetype-specific land-count recommendations from 650K simulated Modern games.
Read How Many Lands in MTG? — Karsten’s formula and format-by-format conventions.
Read 5-Color Commander vs 3-Color: Real Mana Base Data — measures the per-card multicolor tax and tells you when to budget vs splurge on the mana base.
Read Commander Land Count: 3.75M Games — the original archetype-by-land-count study with 5 archetypes (cEDH, combo, midrange, battlecruiser, landfall).
Open the Mana Base Calculator — paste your decklist and it computes lands + colored sources + per-card cast rates in seconds.
Read Dual Land Cycles Guide — every fetch / shock / fast / check / pain land cycle, organized by format legality and ETB condition.
Read Mana Base Theory — Karsten’s colored-source thresholds explained, plus how the simulator implements them.
How much real cast-rate does a single Lórien Revealed buy you? We hold a UR Murktide deck constant and swap one card in and out. The answer is +23 percentage points on a 6-mana payoff at 20 lands — and almost nothing in a mono-green stompy deck that already casts everything.
Side-by-side simulation of Atraxa (5C) and Karador (3C) at 32–40 lands. The headline finding: overall cast rate is statistically identical at every land count once you build a real mana base. The multicolor tax shows up per-card on multi-pip costs — Craterhoof Behemoth (GGG) loses 5 points, single-pip costs lose 0.3.
How brutally does archetype shape the answer? Aggro is land-flat (99.5% across 20–26 lands), midrange is land-brutal (+9pp swing across 22–26), control hits a triple-pip Cryptic Command ceiling at 88.6%, and combo over-runs lands. The double-pip math explains all of it.
The original archetype-by-land-count study. Five Commander archetypes (cEDH, combo, midrange, battlecruiser, landfall) across 15 land counts (28–42). The simulation that validated Karsten’s 99-card formula and inspired the rest of this hub.
The starting point if you have not read Karsten’s work. The 60-card and 99-card regression formulas, the 13/21 colored-source thresholds for one-pip and double-pip costs, and the format-by-format conventions every other guide on this hub builds on.
Every dual land cycle in MTG, organized by format legality and ETB condition. The complementary lookup for “which dual should I run” once the math above tells you how many.
Every page in this section is grounded in the same Monte Carlo engine that runs in your browser when you use the Mana Base Calculator. The engine models the London Mulligan, conditional ETB land rules (shock, check, fast, slow, reveal, battle), ramp sources with accurate mana output (Sol Ring = 2, Mana Vault = 3), Hopcroft-Karp bipartite matching for colored-pip satisfaction, and now (as of B6, April 2026) cycling lands and MDFCs with cost-aware play decisions.
The numbers are reproducible. Every guide ships its source decklists; paste them into the calculator with the appropriate format selector and you should reproduce the cast rates within statistical noise (≈ ±0.4 percentage points at 50,000 iterations).
Where we cite other research, we link the original. Frank Karsten’s articles on TCGplayer Infinite and ChannelFireball are the foundational work for every probability number used here. The Wizards of the Coast Comprehensive Rules are the authoritative source for any mechanic-level claim.