The problem in one sentence
In many card games, you need resource cards, such as lands, to pay for your other cards. Too few and you cannot cast your spells (often called being screwed). Too many and your hand fills with resources while you have nothing to spend them on (flooding). The right number is a balance, and probability is the tool for finding it.
Start with the average
The simplest calculation is the expected number of resource cards in an opening hand. If a deck has N cards, R of them resource cards, and you hold n cards, the average is n times R divided by N.
- 17 resource cards in a 40-card deck, seven-card hand: 7 times 17 divided by 40 = 2.975.
- 24 resource cards in a 60-card deck, seven-card hand: 7 times 24 divided by 60 = 2.8.
Both decks have a resource share of 42.5 percent and 40 percent respectively, and both expect close to three resource cards in the opening hand. This is the origin of many standard recommendations for deck sizes: they aim for the average hand to be able to start operating on time.
An average is only a middle, though. What matters is how often you land far from it.
The full spread for a 40-card deck with 17 resources
Using the hypergeometric distribution, the chance of holding exactly k resource cards in a seven-card hand from a 40-card deck with 17 resources is approximately:
| Resource cards in hand | Chance |
|---|---|
| 0 | 1.3% |
| 1 | 9.2% |
| 2 | 24.6% |
| 3 | 32.3% |
| 4 | 22.6% |
| 5 | 8.4% |
| 6 | 1.5% |
| 7 | 0.1% |
Adding the middle three rows, a hand with two to four resource cards occurs about 79 percent of the time. About 10.5 percent of hands have zero or one resource card, and about 10 percent have five or more. These figures are rounded, so small differences can appear when you add them yourself.
Does one more resource card matter?
It is natural to ask whether a deck is better with 16, 17 or 18 resource cards. For the same 40-card deck and a seven-card hand, the chance of holding two to four resources is about 79.0 percent with 16, about 79.5 percent with 17 and about 78.9 percent with 18. The differences are small. What changes is the direction of failure: with fewer resources, more of the missed hands are too light; with more, more are too heavy.
That is a useful finding. In the opening hand, a single resource card moves the odds only a little. The decision is better made by thinking about what your deck wants to do: a low-cost, fast deck needs fewer resources because it does not need many to function, while a deck full of expensive cards needs to reach higher resource counts and can accept more flooding risk.
The 60-card version
With 24 resources in 60 cards, the chance of holding two to four resource cards in the opening seven is about 77.5 percent, and the chance of none is about 2.2 percent. The spread is a little wider than in the 40-card example, which is one reason players often adjust ratios slightly between formats. It is a modest difference rather than a dramatic one.
Beyond the opening hand
An opening hand with the right count is only the start. Most decks need to keep hitting resource drops for several turns. The question then becomes: by turn T, having drawn some number of cards, how likely am I to have at least X resources? That is the same calculation with a different n and a different threshold. A deck that wants four resource cards by its fourth turn must be tested against that target, not just against the opening hand.
Because the question often becomes “at least X resources”, the complement trick from the probability of at least one success carries over: add up the unwanted outcomes and subtract from one. If the sums get tedious, a Monte Carlo method that shuffles and deals a simulated deck many thousands of times gives a good cross-check.
You can also work backwards. Decide the target (for example, “four resources by turn four with reasonable reliability”), compute the chance for several different resource counts, and see how much each added card moves it. You will usually find that returns diminish, and that no practical count makes the target certain.
Tools that change the numbers
Several effects shift how many resource cards you actually need:
- Card draw and selection. Seeing more cards raises your chance of hitting the target, so a deck with cheap draw effects can reasonably run fewer resource cards.
- Cards that make resources. A spell that fetches a resource or produces extra resources can count as part of your total, though it costs a card slot and may be less reliable than a basic resource card.
- A low curve. If most of your cards are cheap, fewer resources are needed. If you have expensive finishers, you need more or need ways to ramp.
- Mulligan rules. Generous redraw rules reduce the cost of a bad opening hand, which affects how much you need to protect against one. See the discussion of mulligans for how to judge a keep.
A cautious way to pick a number
- Choose a target: how many resources you want by which turn.
- Calculate the chance of meeting it for a few candidate counts.
- Consider the cost of failing in each direction: stumbling on too few, or flooding on too many.
- Pick a count that matches the deck’s plan, and treat the result as a starting point.
- Test with real games, remembering that short-run results can differ substantially from the maths.
A very rough rule widely repeated by players is that a 40-card deck often runs around 16 or 17 resources and a 60-card deck around 24, but the number depends on the game and the deck. Treat it as a place to start rather than an answer.
What probability cannot tell you
The calculation counts resources. It does not know whether a flooded hand is full of cards that do useful things with spare resources, or whether a light hand has cheap plays that still work. Also, probabilities describe frequencies across many games; in any single game the deck will do what it does. A well-built deck still sometimes floods, and a poorly built one sometimes gets lucky. Neither outcome tells you much about the list on its own.