Drawing Your Cards
Every deckbuilder eventually asks the same question: if I put this card in my deck, when will I actually see it? These tables answer that exactly, and the answers are consistently more pessimistic than intuition suggests.
All odds assume you are on the play, so by turn T you have seen your opening seven plus T−1 draws. Tutors, cantrips, and other selection are not modelled; they all improve your real odds. Every number is an exact hypergeometric probability computed at build time.
Seeing at least one copy: 60 card decks
| Copies | Turn 1 | Turn 2 | Turn 3 | Turn 4 | Turn 5 | Turn 6 | Turn 8 | Turn 10 |
|---|---|---|---|---|---|---|---|---|
| 1 | 11.7% | 13.3% | 15.0% | 16.7% | 18.3% | 20.0% | 23.3% | 26.7% |
| 2 | 22.1% | 25.1% | 28.0% | 30.8% | 33.6% | 36.3% | 41.5% | 46.6% |
| 3 | 31.5% | 35.4% | 39.1% | 42.7% | 46.2% | 49.5% | 55.6% | 61.3% |
| 4 | 39.9% | 44.5% | 48.8% | 52.8% | 56.6% | 60.1% | 66.5% | 72.2% |
Two numbers here are worth internalising. A single copy of a card in a 60 card deck appears in your opening hand about 12 percent of the time, and you have still only seen it 20 percent of the time by turn six. A full four copies is in your opening hand about 40 percent of the time, and has appeared by turn six only about 60 percent.
That second figure is the one that reshapes deckbuilding. Four copies is the legal maximum, and it still means your "always" card is missing from four games in ten by turn six. A plan that depends on drawing a specific four-of is not a plan.
How much redundancy a target actually takes
Inverting the question: to have seen an effect by a given turn with a given reliability, how many copies of it would you need in your deck?
| Reliability | By turn 1 | By turn 3 | By turn 5 | By turn 7 |
|---|---|---|---|---|
| 60% | 7 | 6 | 5 | 4 |
| 70% | 9 | 7 | 6 | 5 |
| 80% | 12 | 10 | 8 | 7 |
| 90% | 16 | 13 | 11 | 9 |
Every useful number in that table is larger than four, which is the entire lesson. You cannot reach reliability with copies of one card, because the rules cap you at four. You reach it by counting effects rather than cards: four removal spells plus four more that do a similar job is eight sources of "kill their creature," and eight is a number the table says something encouraging about.
This is why experienced deckbuilders talk about "eight-ofs" and "virtual copies." When you hear that a deck runs eight one mana interaction spells, the player is not describing eight identical cards. They are buying the reliability this table prices.
Drawing two copies
For cards that need a partner, or combo pieces where one is not enough, the odds fall off a cliff:
| Copies | Turn 1 | Turn 2 | Turn 3 | Turn 4 | Turn 5 | Turn 6 | Turn 8 | Turn 10 |
|---|---|---|---|---|---|---|---|---|
| 3 | 3.4% | 4.4% | 5.6% | 6.9% | 8.4% | 9.9% | 13.3% | 17.1% |
| 4 | 6.3% | 8.2% | 10.3% | 12.6% | 15.0% | 17.5% | 23.0% | 28.7% |
| 6 | 14.0% | 17.8% | 21.8% | 25.9% | 30.2% | 34.4% | 43.0% | 51.2% |
| 8 | 23.2% | 28.8% | 34.4% | 40.0% | 45.4% | 50.7% | 60.5% | 69.1% |
This is why combo decks are built the way they are. Assembling two specific pieces by drawing them naturally is unreliable at any legal copy count, so combo decks spend their remaining slots on tutors and card selection rather than on more copies.
Limited: 40 card decks
The smaller deck helps considerably, which is part of why a single bomb matters so much more in Limited than a single powerful card does in Constructed:
| Copies | Turn 1 | Turn 2 | Turn 3 | Turn 4 | Turn 5 | Turn 6 | Turn 8 | Turn 10 |
|---|---|---|---|---|---|---|---|---|
| 1 | 17.5% | 20.0% | 22.5% | 25.0% | 27.5% | 30.0% | 35.0% | 40.0% |
| 2 | 32.3% | 36.4% | 40.4% | 44.2% | 47.9% | 51.5% | 58.3% | 64.6% |
| 3 | 44.8% | 49.8% | 54.5% | 58.9% | 63.0% | 66.8% | 73.7% | 79.5% |
| 4 | 55.2% | 60.7% | 65.6% | 70.0% | 74.0% | 77.6% | 83.6% | 88.4% |
How to use these tables
- Count effects, not cards. Group cards that do the same job in a matchup and read the row for the total.
- Be realistic about your critical turn. "By turn ten" odds are comforting and usually irrelevant; most games are decided long before that.
- One-ofs are flavour, not strategy. A singleton in a 60 card deck is a card you will see in one game in eight. If it matters, it needs copies or a tutor.
- Selection beats copies. A cantrip that digs three cards deep improves your odds more cheaply than a fifth copy you are not allowed to play.
Related: the mana tables, lands by curve, and how to mulligan. Spotted an error? Write us at contact@bopmtg.net.