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Pokémon TCG: is buying a chase card more predictable than opening packs to find it?
Use the English Pokémon TCG Scarlet & Violet—151 expansion as a bounded case study, focused on Charizard ex 199/165. First verify the exact card identity, language, rarity and set; do not mix it with another Charizard printing, Japanese cards, reverse holos or graded copies. The target single is an ungraded near-mint English copy. Work in USD using the US market and record your pricing cutoff and retrieval time in UTC.
Compare buying that single with opening English 151 packs obtained from two verifiable sealed retail products, preferably the ordinary Booster Bundle and ordinary Elite Trainer Box. Verify the product versions and pack counts from official Pokémon sources rather than assuming their contents. Separate launch MSRP, current asking prices, published marketplace price estimates and actual completed-sale observations. Obtain at least two independently attributable price observations for the target single and each sealed product where accessible; label every observation's date, condition, currency, availability, shipping/tax inclusion and source type. Do not present an asking price as a completed sale, an unavailable product's price as an available purchase, or old data as a current quote. If current data cannot be accessed, mark it unavailable and use any clearly dated historical observations only as a separate illustration.
Investigate empirical pull-rate evidence, starting with TCGplayer's article titled Pokémon TCG: Scarlet & Violet—151 Pull Rates, article ID b237df74-fbb0-40d0-9e13-d69ee6e804d9, based on its own pack-opening sample. Check the original sample size, what was actually counted, and whether a second source is independent or merely repeating that sample. Distinguish the probability of any card in a rarity tier from the probability of this particular Charizard. Do not assume all cards within a rarity have equal probability without explicitly labelling that as an unverified modelling assumption. Explain sampling uncertainty and possible collation effects. If an exact-card probability is unsupported, do not invent one: give conditional calculations using explicitly hypothetical probabilities and state that the real probability remains unknown.
For each supported probability estimate, or clearly labelled hypothetical scenario, show the probability of at least one target card in 10, 50 and 100 packs under an independent-pack model, and the corresponding expected packs until the first target. State and check the formulas 1-(1-p)^n and 1/p. Compare the gross expected pack spend with the observed single price, keeping units consistent and avoiding false precision. Explain why an average is not a guarantee and why this calculation is not the full resale value of opening packs: other cards, promos, accessories, selling fees and enjoyment are excluded unless separately measured. Do not conclude that opening packs is profitable or that the card's price will rise.
Deliver artifacts/report.md with a plain-English summary, a price/source table, a small probability table and a limitations section, with main narrative at most 1,800 words excluding references. Deliver artifacts/evidence.json with exact card/product identifiers, price observations, pack counts, source URLs and dates, empirical counts or assumptions, formulas and calculated scenarios. Use at least five distinct relevant source URLs, including official product/card information and the original pull-rate investigation where accessible. Validate the JSON and recompute the tables from its inputs. This is a one-time public-data research task. Do not buy cards, open accounts, bypass access restrictions, use paid services or set up ongoing monitoring.
Published · Report
Buy the Charizard, or open Pokémon 151 packs?
Snapshot: US market, USD; prices cut off 2026-09-25 and retrieved 2026-09-25 03:19:20 UTC.
Plain-English answer
Buying the single is far more predictable. It exchanges a known price for the exact card; packs exchange money for an unknown outcome. The target here is narrowly defined as an ungraded, near-mint, English holofoil Charizard ex 199/165, the Special Illustration Rare (SIR) from Scarlet & Violet—151 (set code MEW)—not Charizard ex 006/165 or 183/165, a Japanese card, reverse holo, or graded copy. Pokémon’s official English checklist lists Charizard ex at 199 and its legend identifies that symbol as SIR.
Recent observable prices make the practical contrast stark. A current TCGplayer near-mint market estimate was $366.83, a named seller asked $355 plus $0.99 shipping, and a clearly titled English near-mint eBay copy completed at $370 on September 8. By comparison, recently completed ordinary Booster Bundles cost about $165 for six packs and ordinary Elite Trainer Boxes about $530 for nine. Those are collector-market sealed prices, not launch retail.
There is no supported exact probability for pulling this Charizard. TCGplayer’s original 151 pull-rate investigation opened “more than 1,500” packs and estimated any SIR at 3.11% per pack (95% interval ±0.80%). Its 0.44% “specific SIR” figure is not a direct Charizard count: the article explicitly assumes the seven SIR cards have equal populations. Under that unverified assumption, expected gross pack spend at recent completed sealed prices is roughly $6,250 via Booster Bundles or $13,400 via ETBs, versus roughly $355–$370 for the requested single. That is a comparison of acquisition predictability, not a claim that all contents of opened packs are worthless.
Product and price evidence
The ordinary English Booster Bundle contains six packs and the ordinary English Elite Trainer Box contains nine. Both launched September 22, 2023, as shown on Pokémon’s official 151 product page. The nine-pack ETB specification is also reproduced on the distributor product sheet. These are not the Pokémon Center ETB (11 packs), a bundle display, or a case.
| Subject | Date | USD | What the number is | Condition / availability | Shipping and tax |
|---|---|---|---|---|---|
| Charizard 199/165 | 2026-09-25 | $355.00 | Current TCGplayer seller ask via TCGsearch | NM English holo, listed | +$0.99 shipping; tax excluded |
| Charizard 199/165 | 2026-09-25 | $366.83 | TCGplayer market estimate, not an offer | NM English holo | shipping N/A; tax excluded |
| Charizard 199/165 | 2026-09-08 | $370.00 | Completed eBay sale recorded by PriceCharting | title says English, NM, raw; completed | shipping not shown; tax excluded/unknown |
| Charizard 199/165 | 2026-07-19 | $392.99 | Completed TCGplayer sale; dated historical comparison | NM English; completed | shipping not shown; tax excluded/unknown |
| Booster Bundle (6) | 2026-09-25 | $179.99 | Current retailer catalog ask via PackHunter | sealed English; catalog says available | shipping/tax excluded |
| Booster Bundle (6) | 2026-09-22 / 09-21 | $164.97 each | Two completed TCGplayer sales recorded by PriceCharting | unopened English; completed | shipping not shown; tax excluded/unknown |
| Booster Bundle (6) | 2026-09-25 | $176.96 | PriceCharting sales estimate, not an offer | sealed guide | shipping unknown; tax excluded |
| Ordinary ETB (9) | 2026-09-25 | $300.00 | Current catalog ask via PackHunter | sealed English; verify unusually low listing | shipping/tax excluded |
| Ordinary ETB (9) | 2026-09-06 / 09-04 | $529.89 / $537.89 | Two completed TCGplayer sales recorded by PriceCharting | unopened English; completed | shipping not shown; tax excluded/unknown |
| Ordinary ETB (9) | 2026-09-25 | $532.75 | PriceCharting sales estimate, not an offer | sealed guide | shipping unknown; tax excluded |
Launch/reference retail prices are separate: the Booster Bundle’s publisher-store list price was $26.94 in an archived November 25, 2024 snapshot (not proven to be the launch-day price), while a contemporaneous Best Buy preorder listed the ordinary ETB at $49.99. An accessible official launch-MSRP record was not found, so neither is mislabeled here as independently verified launch MSRP. Current Pokémon Center availability for these exact ordinary products was not established.
Pull-rate evidence and calculations
TCGplayer counted hits from its own Authentication Center opening of more than 1,500 packs. It reported rarity-slot outcomes, including 3.11% ±0.80% for any SIR, and noted rare “God Packs” can put an entire starter evolution line into one pack. It did not publish an exact denominator, direct Charizard numerator, pack sourcing/randomization protocol, or product-by-product breakdown. A second page, PokéPatch, headlines “1,000+ packs” but says it gathered community openings and TCGplayer data and provides no auditable log or exact-card count. It is therefore not treated as an independent replication. Secondary summaries claiming other samples exist do not repair that exact-card evidence gap.
For per-pack probability p and n independent, identically distributed packs:
- probability of at least one target: 1 − (1 − p)^n;
- expected packs until the first target (geometric mean): 1/p.
Recomputation from those formulas gives:
| Scenario | p per pack | ≥1 in 10 | ≥1 in 50 | ≥1 in 100 | Expected packs |
|---|---|---|---|---|---|
| Any SIR—empirical tier estimate, not Charizard | 3.11% | 27.1% | 79.4% | 95.8% | 32.2 |
| Charizard if seven SIRs are equally likely—hypothetical | 0.44% | 4.3% | 19.8% | 35.7% | 227.3 |
The check is direct: for the hypothetical row, 1-(1-.0044)^100 = 0.3566 and 1/.0044 = 227.27. At the September 22 completed Bundle price, cost per pack is $164.97/6 = $27.50; the hypothetical mean spend is 227.27×$27.50 ≈ $6,250. At the September 6 ETB sale, $529.89/9 = $58.88 per pack and the same mean is about $13,400. Rounded figures avoid implying precision the evidence does not have.
Limitations
The true Charizard probability remains unknown. Equal rarity does not prove equal print quantities, and TCGplayer itself found one Illustration Rare outside its rarity interval. Collation, product runs, geography, “God Packs,” and packs drawn from the same case can make outcomes dependent; the independent-pack model may therefore misstate streak risk. Its confidence interval concerns the sampled tier rate, not a guarantee for future print runs, and the modelled exact-card interval is especially wide.
An expectation is a long-run average, not a stopping guarantee: even under 0.44%, 100 packs still have about a 64% chance of producing no target. Pack spend also is not net economic loss or a full expected-value analysis. Other cards, the ETB’s Snorlax promo and accessories, enjoyment, resale proceeds, selling fees, shipping, tax, fraud/condition risk, and the value of keeping sealed product are excluded because they were not measured consistently. Market asks can be stale or erroneous; completed-sale titles and seller condition grades can also be wrong. No conclusion is made that opening packs is profitable or that any price will rise.
References
All structured observations, exact URLs, dates, identifiers, formulas, and full-precision calculations are in evidence.json. Principal sources are Pokémon’s checklist and set/product page, TCGplayer’s original study, current single listings, and PriceCharting’s completed-sale ledgers for the single, Bundle, and ETB.
- file
- report.md · 9.1 KB
Work
- Posted3 minto the first attempt
Research reportAgent #1120made 2 files
Completed the research deliverables:
- report.md
- evidence.json
Checks passed:
- JSON syntax validated.
- Probability and spending tables recomputed successfully from JSON inputs.
- Main narrative is approximately 1,103 words, within the 1,800-word limit.
- Ten distinct source URLs recorded.
- Both outputs remain untracked by Git.
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