Masterset Calculator
A masterset means one of every card in the set. Set your cost per pack, choose which rarity tiers you want every card from, and the calculator estimates how many packs — and how much money — it takes to finish. Everything is built on the 1,380-pack (46-box) sample behind our Storm Emeralda pull-rate page — the fixed rates for the set.
A Japanese booster box (30 packs) runs around $130–150, so roughly $5 per pack. Use your real cost — the total scales straight off it.
Toggle the tiers you want every card from. Turn on the SAR and MUR chase tiers for a “true” masterset — watch the number explode.
| Tier | Cards | Per pack | Packs to finish | Cost |
|---|---|---|---|---|
| Special Art Rare (SAR) Special Art Rares. A handful of distinct cards at ~0.14% each — completing the SAR set alone dwarfs the rest of the masterset. Off by default. | 8 | 0.14% | 14,995 ~90%: 23,889 | $74,975 |
| Mega Ultra Rare (MUR) The 4 textured Mega Ultra Rares. Pack-pullable but at ~0.14%, so four of them is a lottery, not a plan. Off by default. | 4 | 0.14% | 5,747 ~90%: 10,032 | $28,736 |
| Art Rare (AR)Bottleneck Art Rares. Estimated count — Growlithe (078/076) and Groudon (084/076) are confirmed; a set this size typically carries a low-double-digit AR pool. | 12 | 6.7% | 556 ~90%: 848 | $2,779 |
| Super Rare (SR) Super Rares (full-art ex, Mega ex, supporters). Estimated count; completes at a similar pace to the ARs since both sit near ~6.7% per pack. | 12 | 6.7% | 556 ~90%: 848 | $2,779 |
| gold Ultra Rare (UR) Gold Ultra Rare items / tools / energy. Fewer distinct cards but a lower ~3.3% rate — usually finishes just inside the AR/SR window. | 6 | 3.3% | 445 ~90%: 735 | $2,227 |
Each row is what that tier alone would take to complete. Your masterset finishes when the slowest included tier does, so the headline number tracks the bottleneck row (highlighted) — the others fill in well before it.
How to Read the Number
The calculator gives you two headline figures, and the gap between them is the whole point:
- Average (expected) — if you could run the masterset attempt many times, this is the typical pack count. It is the mean, and for a task like this the mean sits well below what most people actually experience.
- ~90% confidence budget — the pack count that finishes the set in about 9 of 10 attempts. This is the number to actually plan around, because completion has a long right tail: the unlucky runs are much longer than the lucky ones.
Multiply either by your cost per pack and you have the money figure. The tool defaults to a rough per-pack price from a Japanese booster box, but the honest input is whatever you pay — a cheaper box drops the per-pack cost and scales the whole total down.
The Stats: Why It Costs So Much
Completing a set is a textbook “coupon collector’s problem.” The counter-intuitive part is that the last few cards cost far more than the first many, and that is exactly what makes a masterset so expensive. Here is the reasoning the calculator uses.
For a rarity tier with n distinct cards, where each pack has probability P of yielding some card from that tier, the expected number of packs to collect all n is:
That trailing sum (the harmonic number) is why the tail hurts. When you have 1 of 12 Art Rares, almost every AR you hit is new. When you have 11 of 12, you have to wait — on average — for 12 more AR pulls just to see the single missing card. Since an AR only shows up in ~6.7% of packs, that final card alone can cost well over a box.
A worked example on the current data, tier by tier:
| Tier | Distinct cards (n) | Per-pack rate (P) | ≈ Packs to complete |
|---|---|---|---|
| Art Rare (AR) | 12 | 6.7% | ~560 |
| Super Rare (SR) | 12 | 6.7% | ~560 |
| gold Ultra Rare (UR) | 6 | 3.3% | ~445 |
| SAR (Special Art Rare) | 8 | 0.14% | ~15,000 |
| MUR (Mega Ultra Rare) | 4 | 0.14% | ~5,750 |
These are the per-tier figures the calculator uses. n-values are estimates of the distinct-card count (the confirmed anchors are 2 ARs — Growlithe and Groudon — and 4 Mega ex driving the MUR count); adjust as the Japanese checklist firms up. The SAR/MUR rates come from just 4 combined pulls.
The Bottleneck Explained
Notice the tiers finish at wildly different rates. The gold UR tier is done in ~445 packs; the AR and SR tiers in ~560. But those same packs are also rolling for SARs and MURs — so if you include the chase tiers, you are nowhere near done on them when the reliable tiers finish. The masterset only completes when its slowest included tier does, which is why the headline number tracks the bottleneck (the highlighted row in the calculator), not the sum of every tier.
For the default core masterset (AR + SR + gold UR), the bottleneck is the AR / SR tiers at ~6.7% per pack — roughly 560 packs (about 19 boxes) on their own, with the gold UR completing comfortably inside that window. Flip on the SAR or MUR tiers and one of them instantly becomes the bottleneck: a handful of cards at ~0.14% is its own kind of brutal, pushing the estimate into five figures.
Three caveats keep this honest, and the calculator states them inline:
- Independence assumption: the model treats each pack as an independent draw at the average rate. Real print runs cluster hits, so a live attempt can over- or under-shoot.
- Coarse-grained inputs: the SAR/MUR rates come from 4 pulls and the distinct-card counts are estimates pending the checklist; the rare tiers move the total the most.
- Some cards aren’t pack-obtainable: the Mega Gallade ex promo and event variants never drop from standard packs, so a true 100% masterset needs singles on top of any pack count.
The bottom line: the reliable AR / SR floor makes a core masterset a realistic (if pricey) opening project at ~560 packs, but the chase tiers are decided by their rarest, most numerous cards — and coupon-collector math means the last handful dominate the cost. For nearly everyone, opening to a point and then buying the singles you are missing — especially the Mega Rayquaza ex SAR and MUR — is far cheaper than ripping to completion.
Frequently Asked Questions
How many packs to complete a masterset?
About 560 on average for the core AR / SR / gold UR masterset (~19 boxes), and closer to 850 to be ~90% sure. Add the SAR and MUR chase tiers and it climbs past 10,000. The calculator shows the live figure and lets you add or drop tiers.
How much will it cost?
Enter your cost per pack — it multiplies straight through. At ~$5 a pack that’s roughly $2,800 for the core masterset average and ~$4,250 for the ~90% budget. The chase tiers push it into five figures.
Why is the last card so expensive?
Coupon-collector math: once you own most of a tier, nearly every hit is a duplicate, so the final missing card can take as many packs as the first several combined. That tail is where most of the cost lives.
Can I finish a masterset from packs alone?
No — the Mega Gallade ex tournament promo and event variants never come from standard packs. The calculator prices the pack-obtainable tiers; the rest must be bought.
Disclaimer: All figures are modelled from the fixed 1,380-pack Japanese sample and estimated per-tier card counts; the SAR/MUR tiers come from 4 combined pulls, so they are the coarsest inputs. The model assumes independent packs at the average rate and equally likely cards within a tier; real openings can over- or under-shoot. The Pokémon Company does not publish official pull rates. This is not financial advice.