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 Samwise Combo: Carrion Feeder, Cauldron Familiar, Chord of Calling, 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. 8 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 Samwise Combo · NickBolas90 · Modern Challenge 32: 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 (26 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
Boseiju, Who Endures	2	—
City of Brass	3	—
Dryad Arbor	1	—
Forest	1	—
Godless Shrine	1	—
Lush Portico	1	enters tapped; when it enters: scry 1
Misty Rainforest	1	tap, sacrifice: search for a forest / island card
Overgrown Tomb	2	—
Stomping Ground	1	—
Temple Garden	1	—
Verdant Catacombs	4	tap, sacrifice: search for a swamp / forest card
Windswept Heath	4	tap, sacrifice: search for a forest / plains card
Ajani, Nacatl Pariah // Ajani, Nacatl Avenger	3	—
Birthing Ritual	4	—
Carrion Feeder	3	—
Cauldron Familiar	4	—
Chord of Calling	4	search for a creature card
Delighted Halfling	2	tap: adds 1 mana; tap: adds 1 mana
Explosive Prodigy	1	—
Gilded Goose	4	tap, sacrifice: adds 1 mana
Goblin Bombardment	2	—
Haywire Mite	1	—
Orcish Bowmasters	2	—
Samwise Gamgee	4	—
Yawgmoth, Thran Physician	1	sacrifice: draw 1
Young Wolf	3	—

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

Combos in hand

Chance to have every piece of a combo by turn 3: the combos from Commander Spellbook with every card in the main deck.

Combo	On the play	On the draw
Infinite +1/+1 counters on a creature, Infinite death triggers… Carrion Feeder + Cauldron Familiar + Samwise Gamgee	7.6%	10.1%
Infinite creature LTB, Infinite creature ETB… Cauldron Familiar + Goblin Bombardment + Samwise Gamgee	5.4%	7.2%

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.

22 lands in the 60 cards of the deck.

Samwise Combo decks play 21.7 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	96.7%	98.1%	3.3%	5.6%
2	87.2%	91.6%	12.8%	2.3%
3	71.9%	79.6%	28.1%	0.9%
4	53.9%	63.7%	46.1%	0.3%
5	36.7%	46.6%	36.3%	0.1%
6	22.9%	31.3%	27.8%	0.0%
7	13.0%	19.2%	20.7%	0.0%
8	6.8%	10.9%	15.0%	0.0%
9	3.3%	5.7%	10.6%	0.0%
10	1.5%	2.7%	7.3%	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
Yawgmoth, Thran Physician	4	39.2%	47.6%
Explosive Prodigy	2	42.5%	47.4%
Goblin Bombardment	2	42.5%	47.4%
Chord of Calling	3	68.0%	76.1%
Ajani, Nacatl Pariah // Ajani, Nacatl Avenger	2	74.1%	79.7%
Orcish Bowmasters	2	74.1%	79.7%
Samwise Gamgee	2	74.1%	79.7%
Carrion Feeder	1	74.1%	79.0%
Cauldron Familiar	1	74.1%	79.0%
Birthing Ritual	2	87.2%	91.6%
Delighted Halfling	1	96.0%	97.6%
Gilded Goose	1	96.0%	97.6%
Young Wolf	1	96.0%	97.6%
Haywire Mite	1	96.7%	98.1%

Hypergeometric calculator

Sample hand

Simulation

Saved variants

Result

Combos in hand

Mana sources

A land every turn

Casting on curve