Commander deckbuilding by the numbers: the math behind lands, ramp and draw

"Play 37 lands and 10 ramp" is advice you'll hear everywhere. It's good advice, and it isn't arbitrary: it comes from the math of drawing cards from a shuffled deck. This guide shows that math, so you can see what each choice actually buys you and adjust with confidence.

The one formula you need

Drawing cards from a deck is described by the hypergeometric distribution. It answers: if my deck has a certain number of some kind of card, what's the chance I draw a certain number of them?

P(exactly k) = C(K, k) × C(N − K, n − k) ÷ C(N, n)

• N is the number of cards in your library: 99 in Commander (100 minus your commander, who starts in the command zone).
• K is how many of the card type you're counting are in the deck, such as 38 lands.
• n is how many cards you've seen: 7 for an opening hand, more on later turns.
• k is how many of them you want to see.
• C(a, b) means "a choose b", the number of ways to pick b things from a. It's the COMBIN(a, b) function in any spreadsheet.

For "at least" questions, like at least 3 lands, add up the exact chances for 3, 4, 5, 6 and 7.

A worked example: 38 lands, at least 3 in your opening hand

With N = 99, K = 38 and n = 7:

• the chance of exactly 3 lands is C(38, 3) × C(61, 4) ÷ C(99, 7) ≈ 29.6%
• exactly 4 ≈ 17.9%, exactly 5 ≈ 6.2%, exactly 6 ≈ 1.1%, exactly 7 ≈ 0.1%

Added up, that's about 55% for at least 3 lands. On average, a 38-land deck puts 7 × 38 ÷ 99 ≈ 2.7 lands in your opening hand.

How many lands

Most players keep a hand with 2 to 4 lands. A hand with 0 or 1 land is usually a mulligan. Here's what different land counts give you (all exact, from the formula above):

Lands	Opening hand has 2 to 4 lands	At least 3 lands	0 or 1 land (mulligan)	4+ lands by turn 4	Flooding: 7+ lands in your first 12 cards
34	71.9%	45.3%	23.5%	47.0%	6.4%
36	74.0%	50.1%	20.1%	52.7%	8.8%
37	74.8%	52.5%	18.6%	55.5%	10.1%
38	75.5%	54.8%	17.1%	58.3%	11.6%
40	76.4%	59.4%	14.4%	63.6%	15.0%

"By turn 4" assumes you play first, so you've seen 10 cards: your 7, plus draws on turns 2, 3 and 4.

What the table shows:

• Each extra land helps less than the last. Going from 34 to 38 lands raises your chance of a 2-to-4-land hand by only 3.6 points, but cuts land-light mulligans from 23.5% to 17.1%.
• The cost of more lands is flooding. At 40 lands, about 1 game in 7 has you drawing mostly lands by your sixth turn.
• 37 to 38 is the balance point for a typical deck: fewer than 1 in 5 hands have too few lands, and flooding stays near 1 game in 10.

The free mulligan changes the picture

Most Commander groups let you take your first mulligan without losing a card. With that rule, the chance of finding a 2-to-4-land hand in two tries is about 94% at 38 lands (and 93% at 35). This is why the land count matters most for the hands you keep: whether you hit your third, fourth and fifth land drops on time.

Ramp: counting lands and ramp together

Cheap ramp (a two-mana rock, a spell that fetches a land) does the same early job as a land. Counting lands and cheap ramp together as mana cards:

Deck	At least 3 mana cards in your opening hand
38 lands, 8 ramp	71.9%
37 lands, 10 ramp	73.8%
36 lands, 12 ramp	75.6%

That's why more ramp lets you play slightly fewer lands: 36 lands plus 12 ramp gives you more reliable early mana than 38 lands plus 8, and ramp also speeds you up. A common rule of thumb is that two cheap ramp cards can replace about one land. Don't take it further than that: ramp needs mana to cast and can be destroyed.

With 10 ramp cards, you have about a 54% chance of at least one in your opening hand.

Card draw, removal and board wipes

The same formula tells you how often you'll actually have a type of card when you need it:

Category	Copies	Chance of having at least one...
Card draw	10	...by turn 5: 71%
Targeted removal	8	...by turn 6: 66%
Board wipes	2	...by turn 8: 26%
Board wipes	3	...by turn 8: 37%

Two things stand out:

• Ten card-draw sources give you a good chance of drawing extra cards by midgame, which matters in long multiplayer games.
• Board wipes are unreliable in small numbers. With two, you have one by turn 8 only about a quarter of the time. If your deck relies on wiping the board, play four or more; if it doesn't, two or three are insurance.

How many sources of each color

A source is any land or ramp card that can make that color. Here's how many sources you need to have one ready 90% of the time:

You need one source of a color by...	Sources for 90%	Sources for 80%
Turn 2	24	18
Turn 3	22	16
Turn 4	20	15
Turn 5	18	13

Needing two sources of the same color (a cost like ) is much harder: about 33 sources by turn 4 for 90%. In practice, only cast two-pip cards early in your main color, and treat them as mid-game plays in your other colors.

A splash color for a few late-game cards needs less: with 12 sources you'll have the color by turn 7 about 83% of the time.

Dual lands and cards like Command Tower count toward every color they make, which is how three- and four-color decks reach these numbers. For which lands to choose, see Mana bases for Commander.

Putting it together: a starting template

Category	Starting point	Why
Lands	37 (36 with 12+ ramp, 38 to 40 if your commander costs 6+)	Fewer than 1 in 5 land-light hands, little flooding
Ramp	10	Over half your openers have one; reliable early mana
Card draw	10	A draw source by midgame about 7 games in 10
Targeted removal	8	An answer by turn 6 about two games in three
Board wipes	2 to 3 (4+ if your plan needs them)	Insurance, not a plan, at low counts
Your strategy	about 30	What your commander wants to do

These numbers assume an average deck. Lower your land count if most of your spells cost three or less; raise it if your deck is full of expensive spells. Building your first Commander deck walks through filling each slot.

Check your own deck

You can run these numbers yourself in any spreadsheet: =1-HYPGEOM.DIST(2, 7, 38, 99, TRUE) gives the chance of at least 3 lands in a 7-card hand with 38 lands. On Podtable, a deck's Stats tab shows its mana curve and color needs, and Test hand deals sample openers so you can see these odds play out.