- Pull rates determine your expected pack spend per card — and the math usually makes singles look significantly cheaper for specific targets
- Expected cost formula: pull rate (packs needed) × pack price = expected spend. Compare to the singles price before cracking a box.
- A 1-in-72 pull rate at $5.50/pack means $396 expected to hit once — but that same card often lists on TCGplayer for $50–$120
- EV (expected value) calculations are misleading for hobbyists — they assume you can sell everything at market price with no friction, which is rarely true
- Understanding pull rates doesn't mean never buying sealed product. It means making the choice with clear numbers, not optimism.
Every TCG player has done the mental math at some point: I’ve opened six packs, I keep getting commons, I’m so close. The problem is that “so close” isn’t based on anything real. Probability doesn’t have memory. Pack six isn’t closer to the chase card than pack one was.
This post breaks down how pull rates actually work, how to calculate the expected cost of hitting a specific card, and when that math changes the decision.
What Pull Rates Actually Mean
A pull rate is a probability: the average frequency at which a specific card or card type appears across a large number of pack openings. Common formats:
- “1 in 72 packs” — on average, one in every 72 packs contains this card
- “1 in 10 booster boxes” — on average, one in every 10 boxes (typically 36 packs each) contains this card
- “0.5% per pack” — equivalent to 1 in 200 packs
Pull rates describe statistical averages, not guarantees. The “expected” result (opening X packs to hit a card) is the average of a lopsided distribution. With a 1-in-72 card, about 63% of players hit it within 72 packs and the median is around 50 packs, but the unlucky tail runs long. Some players hit the card in pack one; others open several boxes and never see it.
Where pull rates come from: Card manufacturers don’t always publish formal pull rate disclosures. Pokémon, for example, publishes card sheet layouts and rarity symbols but not specific per-card frequencies. Community-aggregated opening data (r/PokemonTCG, dedicated pull-rate databases, YouTube mass-opening compilations) is typically the most reliable source. These rates change between set releases and sometimes between print runs.
Pull rates derived from community data are estimates with real variance. A “1 in 72” rate compiled from 5,000 pack openings is more reliable than one from 200, but neither is a guarantee. Treat community rates as directional guidance, not engineering specs.
How to Calculate Expected Cost for a Chase Card
The core formula is straightforward:
Expected pack spend = pull rate (packs needed) × cost per pack
Then compare that to the card’s current singles market price.
Example calculation:
| Variable | Value |
|---|---|
| Target card | Special illustration rare |
| Community pull rate | 1 in 72 packs |
| Booster pack price | $5.50 |
| Expected pack spend | 72 × $5.50 = $396 |
| Singles price (TCGplayer) | $85 |
| Savings by buying single | $311 |
The expected spend on packs is roughly 4.6× the singles price for this example. Buying the single is almost always the rational choice if owning the card is the goal.
The chart shows the key insight: once you’ve opened roughly 15 packs without hitting the card (spending ~$83), you’ve matched the single price. Every pack after that, you’re spending more than the card costs to buy outright — while still not guaranteed to pull it.
What Are the Odds of Pulling at Least One in N Packs?
Expected cost tells you the average. The question most players actually ask is different: if I open this many packs, how likely am I to hit the card at all? The formula is:
Chance of at least one hit = 1 − (1 − p)ⁿ
Here, p is the per-pack pull rate and n is the number of packs. For a 1-in-72 card (p = 1/72):
| Packs opened | Spend at $5.50/pack | Chance of at least one hit |
|---|---|---|
| 36 (one box) | $198 | ~40% |
| 50 | $275 | ~50% |
| 72 | $396 | ~63% |
| 144 (four boxes’ worth of packs) | $792 | ~87% |
| 216 | $1,188 | ~95% |
Even at the “expected” 72 packs, more than a third of players still haven’t pulled the card. Getting to 95% confidence takes three times the expected pack count. That gap is why the singles price is the real ceiling on what a chase card should cost you.
Why EV (Expected Value) Math Misleads Most Players
You’ll often see content creators calculate a set’s “expected value” (EV) — adding up the values of every card in the set, weighted by pull rate, to arrive at a dollar value per pack.
The EV argument: “This set has $8 EV per pack at a $5.50 retail price, so you’re ‘up’ by buying packs.”
Why this misleads hobbyists:
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EV assumes you can sell every card at current market price. Most collectors can’t or won’t. Cards you don’t need sit in binders; selling requires time, a seller account, packaging, and often shipping costs.
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Market prices fall as supply increases. A set’s EV at launch (when prices are high and supply is low) is very different from EV after three months of distribution. Opening boxes in week one of a set often means pulling cards whose prices will drop 30–60% as more product hits shelves.
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Platform fees eat the margin. TCGplayer and eBay take 10–15% in fees and payment processing. Add PayPal fees, shipping, and packaging materials, and the actual net from a “high EV” card sale is meaningfully lower than the listed price.
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Your time has value. Listing, packaging, and shipping individual cards takes hours. EV calculations don’t include labor.
For hobbyists who want specific cards, EV analysis is largely irrelevant. It’s a reselling framework, not a collecting one. The simpler question is: does this card cost less as a single than my expected pack spend to pull it?
Before opening a booster box for a set, list every card you actually want from it. Look up current singles prices. Add them up. Compare to the box price. If the singles total is less than the box, buying singles is the budget play. If you want the opening experience regardless, budget for it as entertainment — not as a strategy.
Pull Rate Math for Different TCGs
Pull rates vary significantly across games and set types. These are approximate community-based figures — verify current rates for specific sets before purchasing.
| TCG | Card type | Approximate pull rate | Source |
|---|---|---|---|
| Pokémon | Special illustration rare | ~1 in 40–80 packs | Community aggregates |
| Pokémon | Full-art ex | ~1 in 15–20 packs | Community aggregates |
| Magic: The Gathering | Mythic rare | ~1 in 7.4 packs | Hasbro published rates |
| One Piece TCG | Secret rare | ~1 in 24 packs | Community aggregates |
| Lorcana | Enchanted (highest rarity) | ~1 in 576 packs | Community aggregates |
Rates shown are rough approximations. Always verify current community rates for a specific set before calculating expected costs.
The Lorcana Enchanted rate is worth noting: at 1 in 576 packs at ~$6/pack, expected spend to hit an Enchanted card is ~$3,456. Those cards list for $200–$600+ on the secondary market. The math makes the singles route look compelling.
Pokémon 30th Celebration: What a Chase Card Really Costs
Pokémon TCG: 30th Celebration came out worldwide on September 16, 2026, per The Pokémon Company’s announcement. Every card is foil. Each pack holds five foil cards, one of them a Pikachu from a set of 30, plus a foil Basic Energy and a Pokémon TCG Live code card. The Ultra-Premium Collections (Day and Night) follow on November 6, 2026, with 29 regular packs and one Classic Collection pack each.
The Pokémon Company doesn’t publish pull rates. The numbers below come from TCGplayer’s 30th Celebration pull-rate study, published September 24, 2026, which opened more than 3,000 packs. It assumes every card in a rarity is printed equally, so specific-card odds are estimates.
The headline rate is generous. TCGplayer found a Special Illustration Rare (SIR) in about 1 in 21 packs, versus about 1 in 80 in most Mega Evolution sets. The catch is that “a” SIR isn’t “your” SIR. There are 10 of them, so a specific one is about 1 in 205 packs. A specific Classic Collection card, like the Base Set Charizard reprint, is about 1 in 295.
Here’s the expected-cost formula from earlier, at $4.49 a pack. That’s the six-pack Booster Bundle at its Pokémon Center price of $26.94, as of October 2026. To run the same math for another box or a resale price, the price per pack calculator compares every 30th Celebration product.
| Chase card | Unofficial pull rate | Expected pack spend | TCGplayer market price (Oct 21, 2026) |
|---|---|---|---|
| Mew ex 152/128 (SIR) | 1 in 205 | ~$920 | ~$85 |
| Mew ex 158/128 (Futuristic Rare) | 1 in 240 | ~$1,078 | ~$45 |
| Charizard 4/102 (Classic Collection) | 1 in 295 | ~$1,325 | ~$167 |
| Lugia 149/147 (Classic Collection) | 1 in 295 | ~$1,325 | ~$195 |
| RGB Mew (3 versions) | Unknown: none in 3,000+ packs | Unknown | ~$3,740–$5,250 |
For every card with a measurable rate, the pack route costs about 7 to 24 times the single.
Now the odds of pulling at least one, using 1 − (1 − p)ⁿ:
- One Pokémon Center Elite Trainer Box (11 packs, $59.99): about a 42% chance of some SIR, but only about 5% for that specific Mew ex and about 4% for Charizard.
- One Ultra-Premium Collection’s 29 regular packs: about 13% for the Mew ex and 9% for Charizard. Its bonus Classic Collection pack should help with Classic cards, but no large-sample rate for that pack has been published yet, so it’s left out here.
- A coin flip at Charizard takes about 205 packs, roughly $920 at Booster Bundle pricing. A 90% chance takes about 680 packs, or about $3,050.
That’s at MSRP, which is hard to find. On October 21, 2026, the Booster Bundle’s TCGplayer market price was about $75, or roughly $12.50 a pack. At that price, the expected spend for the Mew ex SIR passes $2,500.
So is 30th Celebration worth it? For the opening experience, it’s one of the friendliest sets in years. TCGplayer counted a hit about every three packs. For a specific chase card, the single wins by a wide margin. If you’re eyeing sealed 30th Celebration product as an investment, read is sealed TCG product a good investment first. If the set has you buying more than you planned, here’s how to stop buying Pokémon cards without quitting the hobby.
Prices move fast in a new set. TCGplayer reported that the high pull rates were pushing most 30th Celebration prices down in the first week. Check today’s price before you buy either way.
When Does Cracking Packs Still Make Sense?
The pull-rate math points heavily toward singles for specific card targets. But buying sealed product isn’t irrational — it’s just better suited for different goals:
- You want the opening experience. This is valid. If the hobby enjoyment comes from cracking packs, budget for it as entertainment — the same way you’d budget for a movie ticket. The money buys the experience, not specifically the cards.
- You’re buying sealed product to hold long-term. Sealed TCG product sometimes appreciates. This is a speculative investment, not a collecting strategy — treat it as such.
- You’re buying a draft/limited format playgroup. Draft boxes and sealed events have a clear functional use where the format requires opening product.
- You want the set experience without a specific target. Buying a booster bundle to explore a new set casually is a reasonable way to learn what’s in it.
The key change is framing: decide before you open anything what you’re optimizing for, and pick the route that matches that goal.
How to Use Pull Rate Math in Practice
A practical pre-purchase checklist:
- Identify your target cards from the set before any packs are opened
- Look up current singles prices on TCGplayer for each target
- Find community pull rates for those card types (r/PokemonTCG, Limitless TCG, etc.)
- Calculate expected spend per card: pull rate × pack price
- Compare to singles price — if singles are cheaper, buy them
- If you still want to open product, set a sealed allocation first. When it’s gone, stop regardless of whether you hit your targets. Missing targets? Buy the singles.
This sequence removes FOMO from the equation by front-loading the math. You’re no longer “so close” — you’ve already decided what you’re doing if the packs don’t deliver.
For how this fits into a complete TCG budget: How to Budget for Trading Card Games Without Going Broke
For Pokémon-specific pull rate guidance: How to Budget for Pokémon Cards
A TCG budget in Hunter Vault shows what’s left this month, and Safe-to-Spend shows what’s free after bills and savings, so you know whether the “one more pack” is coming from your allocated budget or from somewhere else.
Related guides:
- How to Budget for Trading Card Games Without Going Broke — the complete TCG budget framework
- How to Budget for Pokémon Cards — Pokémon-specific budget guide
- Sealed vs. Singles: Which Is Cheaper for TCG Players? — full comparison
- How Much Do People Actually Spend on Trading Cards? — market data and benchmarks
Frequently Asked Questions
What is a pull rate in TCG?
A pull rate is the probability of pulling a specific card or card type from a booster pack. For example, a pull rate of 1 in 72 packs means you'd expect to need to open 72 packs on average before hitting that card. Pull rates are not guarantees — they describe the average outcome over many openings, but individual results vary significantly.
How do I calculate expected cost to pull a chase card?
Multiply the pull rate (number of packs needed on average) by the cost per pack. If a card has a 1-in-72 pull rate and packs cost $5.50 each, the expected cost is 72 × $5.50 = $396 in packs to hit the card once. Compare that to the card's singles price — if it's available for $80 on TCGplayer, buying the single saves roughly $316.
Are pull rates always published by the manufacturer?
Not always in a standardized format. Pokémon, Magic, and other TCGs publish set information but pull rates are often derived from community-aggregated opening data rather than official disclosures. Rates vary by pack type within a set (booster packs vs. ETB-exclusive packs vs. premium collection packs). Community pull-rate databases and set-specific Reddit threads are usually the best current sources.
Does buying a booster box guarantee I'll hit the chase card?
No. A booster box is a fixed size (typically 36 packs for Pokémon), so the expected value math applies but the actual result varies. A box buyer with a 1-in-72 pull rate has roughly a 39% chance of hitting the card in one box, not a guarantee. Some players open multiple boxes and never hit the card; others open one and get two.
Should I factor expected value into buying sealed product?
You can, but EV calculations are often misleading for hobbyists. EV math assumes you can sell every card you pull at current market price, which requires time, fees (TCGplayer or eBay takes 10–15%), shipping costs, and supply demand. For most collectors, singles are simpler and cheaper for specific targets. EV-based box buying is really a reselling model, not a collecting model.
What are the odds of pulling a Pokémon 30th Celebration chase card?
The Pokémon Company doesn't publish odds. TCGplayer's unofficial study of more than 3,000 packs (September 24, 2026) found some Special Illustration Rare in about 1 in 21 packs, but a specific one, like Mew ex 152/128, in about 1 in 205, and a specific Classic Collection card like Charizard in about 1 in 295. At $4.49 a pack, the Pokémon Center Booster Bundle price as of October 2026, that's roughly $920 and $1,325 in expected pack spend. On October 21, 2026, those singles sold for about $85 and $167 on TCGplayer.
