What this actually computes
A manabase question is a drawing-without-replacement question, which means the hypergeometric distribution answers it exactly. There is no simulation and no estimate here: given a deck size, a number of cards seen, and a number of sources, the probability of holding enough of them is a closed-form calculation.
So this page works the other way round. You say how reliable you want to be, and it finds the smallest number of sources that gets you there.
The formula
Where N is the deck size, S the sources, n the cards seen by that turn, and k the pips you need. On the play you have seen 7 + (turn − 1) cards; on the draw, one more.
What the numbers come out at
A 60 card deck, on the play, aiming for 90 percent:
| Cast on turn | One pip (C) | Two pips (CC) | Three pips (CCC) |
|---|---|---|---|
| 1 | 16 | 27 | 35 |
| 2 | 15 | 24 | 32 |
| 3 | 13 | 22 | 29 |
| 4 | 12 | 20 | 26 |
| 5 | 11 | 18 | 24 |
| 6 | 10 | 17 | 22 |
The second pip is where decks break
Look along any row. Going from one pip to two is not a small step: on turn 2 it moves from 15 sources to 24, which is 60 percent more of your deck committed to a single colour.
That is the real reason two colour decks with double-pip costs are hard to build. Twenty four sources of one colour in a sixty card deck leaves very little room for the other colour, and the moment both halves want CC on turn 2 the arithmetic simply refuses. Either the mana gets greedy and the deck stumbles, or one of the two colours becomes a splash.
Three pips on turn 3 wants 29 sources, which is close to half the deck. That is why CCC costs almost always live in decks that are effectively mono-coloured, whatever the second colour on the card might suggest.
Why Commander is a different game
A 99 card deck changes the answer completely. A single pip on turn 1 needs around 27 sources rather than 16, because your opening seven is a much thinner slice of a much bigger deck.
This is worth knowing before importing a 60 card intuition into Commander. It is not that Commander manabases are built by different rules; it is that the same rules, applied to a deck nearly twice the size, give very different answers.
Where these numbers sit against the published tables
If you have seen Frank Karsten's colored-source tables, which are the reference most deckbuilders work from, you will notice these figures run a card or two higher. That is a difference of assumption rather than of arithmetic.
His tables allow for mulliganing to find your colours, which effectively gives you more looks at the deck and therefore lets you run fewer sources. This calculator assumes you keep your opening seven, which is the more conservative reading and the one that describes the game where you did not want to mulligan.
Neither is wrong, and his work is the reason anybody thinks about manabases numerically at all. If you want to model the mulligan itself, the opening hand calculator handles the London mulligan properly, and that is genuinely a different question: chasing one specific card is not the same problem as building a manabase that supports a whole curve.
What counts as a source
Anything that reliably produces that colour when you need it. Basic lands, dual lands, fetch lands that can find one, and mana creatures or rocks that will already be in play by the turn in question.
A dual land counts for both of its colours, which is exactly why they are valuable rather than merely convenient: one card doing two jobs is the only way the arithmetic above ever comes out in favour of a two colour deck. Lands that enter tapped still count, but not for the turn they arrive, so shade your estimate down slightly if your manabase leans on them.