How Pull Rates Work: Odds, Sample Size, and What Stats Can’t Promise
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Quick answer
A pull rate is the estimated frequency of a card or rarity appearing in packs — for example, "about 1 in 100 packs." Most pull rates are observed from community openings, not published by publishers, so they are estimates with real uncertainty. Even a solid estimate never guarantees results: at 1 in 100, opening 100 packs gives you only about a 63% chance of at least one hit.
What a pull rate is
A pull rate expresses how often a card, rarity, or category of hit shows up per pack opened. "≈ 1 in 8 packs" means that across a large number of packs, roughly one in every eight contained that kind of card. It describes long-run frequency — it says nothing about what your next pack contains.
Observed vs official odds
Most TCG publishers do not publish per-card odds. Wizards of the Coast shares some ratios for Magic (mythic rares appear in roughly 1 in 7–8 rare slots, varying by set), but Pokémon, Bandai, Konami and Ravensburger generally do not. So nearly every pull rate you see online — including ours — is observed: someone opened a lot of packs, counted hits, and divided. Observed rates are useful, but they inherit all the limits of the sample behind them.
Why sample size matters
Small samples produce noisy estimates. If a card truly appears in 1 in 100 packs, a 360-pack sample (ten Pokémon boxes) would be expected to contain about 3–4 copies — but getting 1 or 7 would not be surprising. An estimate built on 5,000 packs is far more trustworthy than one built on 300, which is why we report sample sizes and confidence levels alongside any rate.
The at-least-one formula
The most useful bit of math in pack opening: if a hit appears with probability p per pack, the chance of at least one hit in n packs is 1 − (1 − p)^n. In words: work out the chance of missing every single pack, then subtract from 100%. Each pack is independent — misses do not make the next pack more likely to hit.
Worked example: a card observed at about 1 in 100 packs means p = 0.01, so each pack misses 99% of the time. Over 100 packs, the miss chance is 0.99 multiplied by itself 100 times — about 37%. So the chance of at least one hit is roughly 63%. Read that again: even opening a full hundred packs, about one person in three walks away without the card. That is what "1 in 100" actually means.
| Packs opened | Chance of at least one | Chance of none |
|---|---|---|
| 10 | ≈ 10% | ≈ 90% |
| 50 | ≈ 39% | ≈ 61% |
| 100 | ≈ 63% | ≈ 37% |
| 200 | ≈ 87% | ≈ 13% |
| 300 | ≈ 95% | ≈ 5% |
Warning
Stats do not change randomness. A 50% statistical chance does not guarantee a pull, and no number of packs takes the chance of missing to zero.
Why estimates differ between sites
- Different samples: two honest datasets of a few hundred packs each can disagree noticeably just by chance.
- Different definitions: one tracker may count all "hits," another only a specific rarity tier.
- Different regions and print runs: pack configurations can vary by region and sometimes by print wave.
- Different timing: early data from launch weekend is smaller and noisier than data collected over months.
How to actually use pull rates
Use pull rates to set expectations, compare sets, and decide whether opening packs is worth it to you versus buying the single. Do not use them to plan on pulling a specific card — the math above shows why that plan fails often, even when the estimate is accurate.
Estimates, not guarantees
Pull statistics on TCG Pax are estimates based on available data and may vary. Stats are estimates, not promises. Pack openings are random.
