Odds of drawing a specific card in a 99-card deck

In a singleton deck every card has one copy. Here: the chance to see one specific card by turn 5 in multiplayer Commander; the table goes on turn by turn, and the number next to the condition says how many cards like it you would need for 90%. How it works

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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 Name Copies in the deck At least At most

More conditions

Condition 2 Name Copies in the deck At least At most

Condition 3 Name Copies in the deck At least At most

Condition 4 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.

Reset

12.1% by turn 5 in multiplayer

Seeing 12 of 99 cards: the opening hand of 7 and 5 draws.

The card: at least 1 of 1 copies, 12.1% on its own · 17 copies for 90%

All the conditions together, turn by turn

By turn

All the conditions together, turn by turn
By turn	On the play	On the draw
1	8.1%	8.1%
2	9.1%	9.1%
3	10.1%	10.1%
4	11.1%	11.1%
5	12.1%	12.1%
6	13.1%	13.1%
7	14.1%	14.1%
8	15.2%	15.2%
9	16.2%	16.2%
10	17.2%	17.2%

How many copies you see

Among the 12 cards seen by turn 5, without mulligans.

The card (1 copies): 0.12 on average

Copies	Exactly	At least	At most
0	87.9%	100.0%	87.9%
1	12.1%	12.1%	100.0%

Opening hands

Use the usual keepable-hand rule: 3 to 5 lands in 7 cards, with 37 lands

Chance that the opening hand alone meets the conditions, keeping the first good one (London mulligan).
Hand	This hand	Kept by then
First hand · 7 cards	7.1%	7.1%
After 1 mulligan · 7 cards	7.1%	13.6%
After 2 mulligans · 6 cards	7.1%	19.7%

Mana sources

Lands and other sources of one color you need in 99 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	24	22	20	18	17	16
CC	—	36	33	30	28	26
CCC	—	—	44	40	38	35

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.

Lands in the deck

A land drop on every turn up to that one
Up to turn	On the play	On the draw	Too few	Too many
1	98.7%	98.7%	1.3%	17.0%
2	94.2%	94.2%	5.8%	9.3%
3	85.3%	85.3%	14.7%	4.8%
4	72.6%	72.6%	27.4%	2.4%
5	58.0%	58.0%	20.1%	1.1%
6	43.5%	43.5%	14.4%	0.5%
7	30.7%	30.7%	10.0%	0.2%
8	20.5%	20.5%	6.9%	0.1%
9	12.9%	12.9%	4.6%	0.0%
10	7.7%	7.7%	3.0%	0.0%

Simulation

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. 0 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.

Goal At least Of By turn

Mulligan Keep with lands from to At most

Opponent Destroys a land on turn Makes you discard on turn