The Mathematics Behind ManaTuner
Casting your spells on curve isn't luck — it's probability. ManaTuner uses rigorous math to estimate what your mana base can deliver.
How Many Lands?
Land count changes your chance of hitting land drops on curve. No land count guarantees the right draws every game.
ManaTuner calculates an estimate of having enough mana each turn, based on your curve.
How Many Sources per Color?
Having enough lands is only half the puzzle. You need the right colors at the right time — 21 blue sources to cast Counterspell on turn 2.
ManaTuner tells you source-count guidelines for each color your deck needs under the published assumptions.
Three Engines, Three Questions
ManaTuner uses three mathematical models. Each answers a different question about your deck.
"Can I cast this spell on curve?"
Mana estimates approximate mana availability. Exact goldfish potential checks whether at least one legal sequence exists within its supported model, with foresight of the drawn history. Both assume the target spell is available.
"How many sources do I need?"
Based on Frank Karsten's published simulations: targets are conditional on enough lands after London mulligans, at 89 + mana value percent (90–96% for published turns). These are deckbuilding guidelines.
"Should I keep or mulligan?"
By default, 10,000 sampled hands per kept-hand size from your main deck. Bellman recursion calculates keep thresholds for the selected archetype’s heuristic hand score, not a win probability.
Why do castability estimates differ from Karsten targets?
The calculation and the reference table measure different events:
Mana estimates: mana available without mulligans
This estimates mana availability from the opening hand and draws through the target turn. It assumes the spell is available and applies no mulligan policy. In Estimate mode, color, tempo and acceleration calculations include approximations.
Karsten: conditional color consistency
The published model applies a specified London mulligan policy and conditions on drawing enough lands. Its target is 89% plus the mana value in percentage points (91% for a two-mana spell). This is a different probability.
A conditional source target cannot be compared directly with unconditional castability.
Two Ways to Read Your Odds
Mana estimates (default)
Event: estimated mana availability from random opening hands and draws through the target turn, assuming the spell is already available.
Realistic includes land-draw uncertainty. Perfect drops conditions on having enough lands. Source overlap, color payments and ramp sequencing are approximated using the selected ramp and removal settings.
These are two views within Estimate mode, not the choice between Estimate and Exact. Neither evaluates your specific observed hand or includes mulligans.
Exact goldfish potential (supported cases)
Event: at least one legal mana sequence can pay the cost by the target turn under the represented resource model. Choices can use the full drawn history, so this is an upper bound for play without foresight.
This mode uses 0% removal and 100% ramp survival, regardless of Estimate settings. It excludes mulligans and drawing the target spell. Unsupported mechanics or a calculation exceeding the budget produce no percentage, not 0%.
Try the basic-land exact example: 24 Plains and 36 Savannah Lions. This is a synthetic test fixture, not a legal tournament decklist.
Saved Analysis, Compare and exports: a fixed snapshot
Saved per-spell probabilities use physical-v1 lands-only potential, on the play, with no mulligans or ramp and X=2. They exclude drawing the target spell and refuse unsupported mechanics. They do not reproduce the interactive Castability settings. Compare only calculated rows under this shared contract; unavailable values are not zero. Health, Blueprint and Mulligan scores are separate heuristic indices.
The Math Under the Hood
You don't need to understand any of this to use ManaTuner — but if you're curious, here's exactly how it works.
Hypergeometric Distribution
The core formula behind castabilityImagine a bag with 60 marbles: 14 red and 46 other colors. You grab 7 at random. What are the odds you got at least one red? That's what the hypergeometric distribution calculates — except the "marbles" are your cards and the "red" ones are your mana sources.
P(X = k) = C(K,k) × C(N-K,n-k) / C(N,n)
N
Cards in deck (60)60K
Mana sources you have14 red sourcesn
Cards you've seen7 (opening hand)k
Sources you need1 red sourceConcrete example: 14 red sources in a 60-card deck, opening hand of 7 cards. Probability of at least 1 red source = 86.1%. That means roughly 1 in 7 opening hands contain no red source. This draw event differs from Karsten’s conditional casting target with its stated mulligan policy.
Monte Carlo Simulation
10,000 samples per kept-hand sizeThe simulator samples 10,000 hands for each kept-hand size from four to seven by default. It shuffles the main deck, draws seven, chooses a heuristic subset, and evaluates opening-hand quality. Bellman recursion compares keeping with another mulligan; this is not a simulation of complete games or win rate.
1
Shuffle
Your main-deck cards are randomly shuffled using an unbiased algorithm (Fisher-Yates)
2
Draw & Decide
Draw seven, then select a heuristic subset for the kept-hand size.
3
Score & Compare
Score first-turn plans under the stated model; compare sampled keep and mulligan values.
Why both? The hypergeometric formula gives exact draw probabilities under sampling without replacement. Monte Carlo can check simple draw events against those answers. Mulligan results additionally depend on the reward model and sampling uncertainty; this does not establish the accuracy of every castability estimate.
Frank Karsten's Research
The gold standard for mana base constructionFrank Karsten is a Magic Pro Tour Hall of Famer and PhD mathematician. His 2022 research provides the following 60-card reference table. It targets conditional color consistency of 89% plus the mana value, under its stated land count and mulligan policy:
Mana Cost | Turn 1 | Turn 2 | Turn 3 | Turn 4 |
|---|---|---|---|---|
| 1 Colored (e.g. {R}, {1}{U}) | 14 | 13 | 12 | 10 |
| 2 Same (e.g. {U}{U}) | - | 21 | 18 | 16 |
| 3 Same (e.g. {B}{B}{B}) | - | - | 23 | 21 |
How to read this: If your deck has a spell that costs {U}{U} and you want to cast it on turn 2 reliably, the published 60-card table recommends 21 blue sources. If you're OK casting it on turn 3 instead, 18 sources are enough.
Bellman Equation (Mulligan Math)
Optimal stopping theory for keep/mulligan decisionsThe hardest question in a game of Magic: "Is this hand good enough, or should I mulligan and risk getting a worse 6-card hand?" Bellman recursion compares keeping with continuing under the chosen reward model. Here that reward is a heuristic hand score.
It works backwards from a forced keep at four cards, then computes the continuation values for five, six and seven cards using sampled hand scores. The recursion is exact for those sample distributions; the scores are not win probabilities.
Keep if hand score > continuation value
The continuation value includes later redraws. London redraws seven, then bottoms cards for counted mulligans; a free multiplayer redraw keeps seven.
In practice: ManaTuner samples 10,000 hands per kept-hand size by default and derives thresholds from the selected archetype’s scores. A keep or mulligan indication applies to that heuristic model, not to all strategic factors in a real game.
Rules of Thumb
Land Count by Archetype
How many lands you need depends on your average mana cost and game plan:
Color Sources Needed
Published 60-card targets under Karsten's conditional model:
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