TCG Card Pull Probability Calculator

How TCG pull probability works

Know your pull odds. Estimate your packs. Understand the cost. Enter the pull probability for the specific card or outcome you are evaluating. Rarity names alone do not determine exact odds.

Choose a game and rarity label for context, then enter a pull percentage, 1–100 packs and a price per pack. Results update automatically. The defaults are Custom / Other TCG, Custom / Other, 1%, 20 packs and USD 5. No game or rarity selection changes the probability. The slider and numeric pack field represent the same quantity.

The main result always answers “at least one target card.” Use the separate copy selector for exactly one, two or three, at least two or three, or a custom count. Threshold cards answer a different question: how many packs would reach a selected chance of at least one pull? Copy result exports your validated scenario; Reset restores defaults. Controls require JavaScript, while this explanation and examples remain readable without it.

Probability formulas and method

Let p be the per-pack probability as a decimal and n the number of independent packs. The probability of no target events is (1 − p)^n. Its complement, 1 − (1 − p)^n, is the probability of at least one. For example, 1% becomes p = 0.01; it is not entered as 0.01%.

For exactly k events, the binomial formula is C(n,k) × p^k × (1 − p)^(n − k), where C(n,k) counts ways to select k successful packs. For at least k events, add the binomial probabilities from k through n; equivalently subtract the probabilities for 0 through k − 1 from 1. Expected events are n × p. These relationships require constant odds and independent trials.

The engine uses log1p and expm1 for the complement calculation, log multiplicative combinations instead of large factorials, and a compensated direct upper-tail sum for at-least-k results. This avoids subtracting two nearly equal numbers for tiny tails. Explicit 0% and 100% branches handle certainty without undefined logarithms. Outputs are bounded probabilities, not simulated openings.

Exactly one vs multiple copies

Exactly one excludes scenarios with two or more target events; at least one includes them. Exactly zero is the no-pull probability. At least zero is certain, so its probability is 100%. Custom counts are whole numbers from zero through your selected pack count. If reducing packs makes the selected count impossible, the count stays visible for correction rather than silently changing.

One Bernoulli outcome is counted per pack: target or no target. The target can be one exact card, any card in a user-defined group, or a rarity outcome, provided you enter its correct aggregate per-pack probability. The model cannot count two copies from the same pack. Multiple target-card pools, overlapping outcomes and eligible slots need additional rules and are outside this version.

How many packs for a target probability

For a desired at-least-one probability t, the smallest whole count is ceil(ln(1 − t) ÷ ln(1 − p)). The engine verifies the rounded ceiling in log space so the reported count reaches the threshold and the preceding count does not. This threshold concerns at least one event even when the copy selector is showing an exact or at-least-k probability.

The standard targets are 50%, 75% and 90%. Enable the optional custom target for 1–99.99%. Exactly 100% is accepted only when per-pack probability is 100%; otherwise a correction explains why no finite count guarantees success. At 0% odds every positive threshold is impossible. At 100% odds one pack is enough. Estimates above 1 billion packs are explicitly unavailable within the supported calculation range; they are not displayed as Infinity or treated as a guarantee.

Why 90% is not a guarantee

A 90% chance still leaves a 10% chance of no target event. The threshold is a planning probability, not a deadline by which the card must appear. Opening packs without a pull does not make the next independent pack “due.” Under constant independent odds, its chance stays p. A history-dependent product would require a different model.

Expected copies vs guaranteed copies

At the example 1% rate, 20 packs have an expected count of 0.20. This average can coexist with a high probability of zero: individual outcomes are whole counts. Expected value is an average across many repeated scenarios. It does not mean you will receive a fraction of a card, nor that buying enough packs for an expectation of one guarantees one.

How pack cost changes the decision

Estimated pack cost is price per pack × number of packs. Threshold cost uses the threshold count, which can exceed the 100-pack primary slider. The entered price is bounded from zero to 1,000,000 with cents precision. Integer-cent arithmetic keeps decimal multiplication exact; displayed currency labels do not perform conversion. Taxes, delivery, changing prices and resale values are excluded.

Compare the stated cost and uncertainty with your collecting goal and a budget you choose independently. Other ways to obtain a desired card, such as buying that card directly or trading, can be considered using their own known costs and conditions. This tool provides no live market comparison, valuation, investment recommendation or suggestion to increase spending.

Why rarity alone does not determine exact odds

Rarity labels do not determine an exact pull rate. Enter the per-pack probability that applies to the specific product you are evaluating. The four game choices only organize labels. Pokémon labels include Illustration Rare and Hyper Rare; Magic includes Mythic Rare and Special Treatment; Yu-Gi-Oh! includes Super Rare and Secret Rare. These are contextual labels, not a promise that each label applies to every product or era.

Changing game resets the rarity label to the first available option but preserves odds, packs and price. Changing rarity preserves all calculation inputs. There is no hidden rate table, booster lookup, card-name inference or connection between price and probability.

Independent-pack assumptions

BuzCalculator probability model assumptions: each pack is an independent trial, every trial has the same target probability, and at most one counted target event occurs per pack. The entered rate must already represent the outcome you mean, rather than a per-slot rate substituted for a per-pack rate.

Independence means the outcome of one pack provides no change to another pack’s odds in this model. Constant probability means all evaluated packs share the same p. Combining products with different rates or drawing from a fixed changing pool violates those assumptions. No multiple-card pool or history adjustment is implemented.

Why real product collation can differ

Check whether a product uses guaranteed rarity slots, box collation, seeded distribution, product-specific pools, alternate-art slots, multiple eligible slots, print-run effects or replacement rules. Such structures can make a simple independent target-event model unsuitable; none is simulated here. A guarantee of a rarity is not necessarily a guarantee of your exact target card.

As an official product-structure example, Wizards of the Coast’s 2023 Play Booster explanation describes different card slots and product design. It helps show why an exact product description matters. This calculator does not import any probabilities from that article or treat its historical contents as a current universal booster specification.

Using published or community-estimated pull rates

Prefer a clearly identified rate for the exact product and outcome. Record whether it describes a pack, slot, box, specific card or group of cards. A community estimate is an estimate: consider its sample size, collection method, uncertainty and whether the sample matches the product you plan to evaluate. Do not present it as an official guarantee.

You can enter multiple plausible rates to examine how sensitive a plan is to that uncertainty. This calculator does not verify supplied odds, infer missing rates or estimate a confidence interval. Its 1% default is an illustrative input, not a verified rate for Pokémon, Magic, Yu-Gi-Oh! or another game.

To describe a rate comparison, compare two stated pull rates in percentage points using the same product, outcome and probability basis. A relative change is different from a percentage-point change; neither validates the odds, removes sampling uncertainty or infers an individual card’s probability.

Worked examples

1% per pack, 20 packs, USD 5 each

At least one: 18.21% (approximately 18.2093%). Zero copies: 81.79% (approximately 81.7907%). Expected copies: 0.20. Estimated pack cost: $100.00.

• 50% chance: 69 packs; estimated cost $345.00.
• 75% chance: 138 packs; estimated cost $690.00.
• 90% chance: 230 packs; estimated cost $1,150.00.

For 50%, 68 packs fall below the target and 69 reach it. For 75%, the minimum is 138; for 90%, it is 230. These counts come from the logarithmic formula, not stored pull-rate data.

Edge cases

At 0% odds, 20 packs have no chance of a target pull, a 100% chance of zero, and zero expected copies. At 100% odds, the same 20 packs produce 100% at-least-one probability, zero chance of no target event, and 20 expected events. Every standard threshold then needs one pack. Those are mathematical endpoints of the model.

Assumptions and limitations

Independent packs with a constant per-pack probability. Actual TCG products can use rarity slots, guaranteed contents, collation rules, print distributions, or other structures that differ from this model. One target event per pack is counted; multiple copies within one pack are not modeled.

Primary pack count is a whole number from 1–100. Probability accepts finite decimals from 0–100%; values too close to 100% to distinguish from certainty are rejected. Prices use up to two nonzero decimal places. Copy count is a whole number from 0 through n. Tiny nonzero percentages use extra digits or scientific notation; nonzero probabilities smaller than binary precision are labeled below 4.94e-322% instead of 0.00%. Near-certain results show <100%, reserving 100.00% for actual model certainty. Malformed, blank, expression, exponent, script, nonfinite and out-of-range input is excluded from its dependent result, while the draft remains visible for correction.

No accounts, browser persistence, URL parameters, network calculations, external APIs, card-price lookup or analytics-specific calculator payload. Copy uses current validated values only. Reset clears copy feedback and returns to defaults. The SVG and its text table are generated locally, with no chart library, canvas or extra package.

FAQ

Sources and odds transparency

Internal model assumptions

BuzCalculator probability model assumptions: constant odds, independent packs, one counted target event per pack, and cost equal to entered price × count. The 1% default is illustrative; no publisher pull rate is implemented. Rarity labels organize context and do not validate input odds.

External mathematical and product references

Checked October 9, 2026. NIST provides the binomial probability and mean definitions. The Wizards article is a product-specific structural example, not the source of any entered rate. No third-party pull-rate table is treated as authoritative.

• NIST: Binomial distribution — probability mass, cumulative probability and mean (opens in a new tab)
• Wizards of the Coast: What Are Play Boosters? — product-specific booster structure (opens in a new tab)