Hypergeometric calculator

Chance to have the cards you need by a given turn: one or more groups of cards, each with a minimum or a range of copies, all together or at least one. Count the copies yourself or from a deck. How it works

Simulation

Goals of Mill: Hedron Crab, Ruin Crab, Archive Trap, all by turn 3

Goal At least Of By turn

More goals

Goal At least Of By turn

Mulligan and opponent

Mulligan Keep with lands from to At most

Opponent Destroys a land on turn Makes you discard on turn

Compare with a change Take out one Put in one

Goals on different turns, all together, like two lands by turn 2 and a removal spell by turn 3: 20,000 games played turn by turn. 7 cards of the deck have effects the simulation uses (see the table of cards).

How the games are played

With a deck, the cards that change what you see work as their Oracle text says, read from Scryfall: scry and surveil, draws, looking at the top cards and taking one, searching the library, cycling, mana from artifacts and creatures (creatures from the next turn). Each turn: draw, play the land that helps a goal most (lands make their colors, Urza’s lands 7 mana together, lands that enter tapped from the next turn), then spend the mana: cast a card a goal asks to cast, search for a missing card, look at the top cards, the cheapest scry and draw cards, abilities that draw, cycling. Colors are checked. Scry keeps on top the cards of the goals still open, the nearest turn first, then lands if you need more. Other spells don’t use mana, so the result is a little optimistic. The opponent acts at the start of the chosen turn of yours: it destroys the land you need most, or makes you discard the nonland card you need most.

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Counting from Mill · xerioc · Modern Challenge 64: 60 cards in the main deck.

Cards in the deck

By turn

Starting On the play On the draw

More options: extra draws, mulligans, players

Extra cards drawn Cantrips and other draw by that turn Extra cards looked at Scry, surveil, Ponder: counted as seen, an optimistic estimate Mulligans London mulligan: draw 7, put cards you don’t need on the bottom First mulligan Players With more players nobody skips the first draw

Conditions to meet All of them At least one

Condition 1 Cards from the deck Name Copies in the deck At least At most

More conditions

Condition 2 Cards from the deck Name Copies in the deck At least At most

Condition 3 Cards from the deck Name Copies in the deck At least At most

Condition 4 Cards from the deck Name Copies in the deck At least At most

Compare with Copies to add or remove Of

In place of cards of no condition: the deck keeps its size.

The 60 cards of the deck (22 different): conditions and effects

Which condition each card of the main deck counts for: the copies of a condition become the sum of its cards.
Card	Copies	In the simulation
Field of Ruin	3	—
Flooded Strand	4	tap, sacrifice: search for a plains / island card
Island	3	—
Oboro, Palace in the Clouds	1	—
Otawara, Soaring City	1	—
Polluted Delta	4	tap, sacrifice: search for a island / swamp card
Shelldock Isle	1	enters tapped
Sink into Stupor // Soporific Springs	1	—
Swamp	1	—
Undercity Sewers	2	enters tapped; when it enters: scry 1
Watery Grave	2	—
Archive Trap	4	—
Drown in the Loch	4	—
Exhibition Tidecaller	2	—
Fatal Push	3	—
Fractured Sanity	4	cycling (2 mana): draw 1
Hedron Crab	4	—
Preordain	3	scry 2; draw 1
Ruin Crab	4	—
Surgical Extraction	4	—
Tasha's Hideous Laughter	4	—
Visions of Beyond	1	draw 1; draw 3

Write how many copies of the cards you want are in the deck.

Mana sources

Lands and other sources of one color you need in 60 cards to cast a spell on curve: C is one symbol of that color in the cost, CC two, CCC three.

Chance Also for the copies each condition needs, above

Sources for a 90% chance by that turn, on the play
Cost	Turn 1	Turn 2	Turn 3	Turn 4	Turn 5	Turn 6
C	16	15	13	12	11	10
CC	—	24	22	20	18	17
CCC	—	—	29	26	24	22

A land every turn

Chance to play a land on each turn up to that one: at least one land by turn 1, two by turn 2, and so on.

23 lands in the 60 cards of the deck.

Mill decks play 22.5 lands on average, all Modern decks 21.3 (last 90 days).

A land drop on every turn up to that one
Up to turn	On the play	On the draw	Too few	Too many
1	97.3%	98.5%	2.7%	6.8%
2	89.2%	93.2%	10.8%	3.0%
3	75.5%	82.8%	24.5%	1.2%
4	58.6%	68.3%	41.4%	0.5%
5	41.7%	52.0%	31.7%	0.2%
6	27.2%	36.5%	23.6%	0.1%
7	16.4%	23.7%	17.0%	0.0%
8	9.1%	14.2%	11.9%	0.0%
9	4.7%	7.9%	8.1%	0.0%
10	2.2%	4.0%	5.4%	0.0%

Casting on curve

For each spell of the deck: chance to have, on the turn equal to its mana value, that many lands and enough lands of its colors. Hybrid and Phyrexian symbols don’t count; other mana sources (creatures, artifacts) neither.

From the riskiest spell
Card	Turn	On the play	On the draw
Archive Trap	5	41.7%	52.0%
Fractured Sanity	3	59.3%	68.0%
Fatal Push	1	70.0%	75.1%
Drown in the Loch	2	71.2%	76.8%
Tasha's Hideous Laughter	3	73.4%	80.9%
Exhibition Tidecaller	1	94.2%	96.3%
Hedron Crab	1	94.2%	96.3%
Preordain	1	94.2%	96.3%
Ruin Crab	1	94.2%	96.3%
Visions of Beyond	1	94.2%	96.3%
Surgical Extraction	1	97.3%	98.5%

Hypergeometric calculator

Sample hand

Simulation

Saved variants

Result

Mana sources

A land every turn

Casting on curve