How Many Packs to Pull Zacian V from Sword & Shield
| Card | Zacian V — Sword & Shield #211 |
|---|---|
| Rarity tier | Secret Rare |
| Per-pack odds | 1 in 120 |
| Expected packs to pull | 121 |
| 50% confidence band | 83 packs |
| 95% confidence band | 358 packs |
| TCGplayer market | $19.14 |
| Pack-rip break-even | 4 packs @ $5 |
Zacian V chase methodology
| Formula | Specific-card odds = Secret Rare tier rate (5.00%) ÷ 6 cards; confidence bands solve 1 - (1 - p)^N. |
|---|---|
| Assumptions | Independent pack rolls, uniform selection within the rarity tier, no pity timers, no box mapping, no first-edition/condition split, no duplicate protection. |
| Data source | Card identity and rarity from the bundled Pokemon TCG API catalog; pull-rate constants from the live simulator; market price from the bundled TCGplayer snapshot. |
| Update cadence | Regenerated by prerender; price values update when the TCGplayer snapshot is refreshed through the data pipeline. |
| Limitations | The page estimates probability and raw market cost only; it does not model grading premiums, counterfeit risk, sealed-product appreciation, or individual print-run collation. |
This page answers exactly one question: how many Sword & Shield booster packs does it take to pull Zacian V #211? The numbers below come from the same per-rarity pull-rate model the PackRip Sword & Shield simulator runs on, mirrored from packGenerator.ts. TCGplayer pricing refreshes every build, so the buy-vs-rip verdict at the bottom reflects current market.
The math: ~1 in 120 per pack
Zacian V sits in the Secret Rare rare-slot pool for Sword & Shield. There are 6 Secret Rare cards in the Sword & Shield pool, and the Secret Rare slot fires with probability 5.00% per pack. Since the slot is split evenly across the 6 cards in that tier, the per-pack chance of pulling this specific card is 1 in 120 — approximately 1 in 120.
Pulls are independent and identically distributed, so the number of packs until you hit Zacian V follows a geometric distribution with parameter p = 0.008333. The expected number of packs is 1/p — that's ~121 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~83 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 358 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.
Concretely: if 100 collectors each opened Sword & Shield packs until they pulled Zacian V, roughly 50 of them would have it by pack 83, 95 of them would have it by pack 358, and a handful would still be chasing past that. Expected ≠ guaranteed; the geometric distribution is famously long-tailed on the right side.
Confidence bands — packs vs cumulative probability
| P(pulled by N packs) | Packs needed | Sealed cost at $5/pack |
|---|---|---|
| 10% | 13 packs | ~$65 sealed cost |
| 25% | 35 packs | ~$175 sealed cost |
| 50% | 83 packs | ~$415 sealed cost |
| 75% | 166 packs | ~$830 sealed cost |
| 90% | 276 packs | ~$1,380 sealed cost |
| 95% | 358 packs | ~$1,790 sealed cost |
| 99% | 551 packs | ~$2,755 sealed cost |
Read this table as "what fraction of openers have pulled Zacian V by pack N?". A 25% band of 35 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 551. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.
Cheaper to buy Zacian V as a single?
Buying Zacian V as a single on TCGplayer (~$19.14) is dramatically cheaper than chasing it through packs — the expected pack-rip cost is roughly $600, well above the market price.
Pack-rip expected dollar cost for this specific card: ~$600 at $5 per Sword & Shield pack. Compare to $19.14 for the single on TCGplayer (Unlimited / non-graded copy at current market). The single buy obviously delivers exactly this card; the pack-rip approach delivers Zacian V plus the remaining 9 cards in every pack along the way — which is why the EV calculator at /ev/swsh1 spreads the cost across the whole pack contents instead of pinning it to one card.
About Zacian V (Sword & Shield)
Zacian V is a Secret Rare card from Sword & Shield, the 2020 Pokémon TCG expansion. Sword & Shield (2020) opens the Galar era with 216 cards and two new tiers: 17 cards at rarity Rare Holo V and four at Rare Holo VMAX. PackRip draws V from a 16.7 percent slice of the rare slot and VMAX from a much narrower 5.56 percent, so the VMAX cards are roughly three times scarcer inside the same pack. Seventy-one illustrators contributed. All four VMAX cards also appear as Rare Rainbow prints at #203 to #206.
This specific card ranks as one of the top-3 most valuable pulls in Sword & Shield by TCGplayer market value, which is part of why the chase math is what it is — high market value tends to track with rarity-tier depth, since lower pool sizes concentrate value into fewer cards. The complete top-25 Sword & Shield ranking shows where Zacian V sits relative to the rest of the chase pool.
Pull odds in context
For reference, a "1 in 120" pull is roughly comparable to a deep chase — multi-box territory, often case-level commitment. The variance is the killer: any one pack could be the one. The simulation on PackRip's Sword & Shield opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.
Related chases
- Snorlax VMAX — VMAX, $61.80 market
- Marnie — Full Art, $37.16 market
- All Zacian V printings across 7 sets
- All top-25 Sword & Shield chases
- Complete the Sword & Shield binder — full calculator
Open Sword & Shield free
Rip Sword & Shield packs free on PackRip's simulator with the same per-rarity pull rates this page is built from. The Hunt Pack mode boosts the Secret Rare slot if you specifically want to optimise for Zacian V-tier pulls. Coin economy is virtual — no real money on the line.
Strategy: optimising the Zacian V chase
Every experienced Sword & Shield hunter eventually picks one of three approaches for a specific chase card. The cheapest is the snipe: skip pack-ripping entirely, set a TCGplayer alert at or below the current $19.14 market, and wait for a motivated seller. This is the route most efficient-frontier collectors take when the chase is locked behind a deep rarity tier — and the math above shows why. The expected pack-rip cost ($600) is typically multiples of the single price, and the variance on that expectation is wide enough that a single bad streak can blow past the 95% confidence bound. The single buy is dollar-for-dollar cheaper and emotionally cheaper too — no more refreshing pack-pull videos at 3am.
The middle path is the box-rip-then-snipe: open a sealed booster box of Sword & Shield (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Zacian V in the box, buy the single for $19.14. A 36-pack box delivers a probability of 1 − (1 − p)36 ≈ 26.0% of pulling Zacian V at least once, where p is the per-pack hit rate of 0.008333. So a sealed box gives you roughly a 26% chance of hitting this card "for free" alongside the rest of the box contents, plus the rip experience. If you miss, you backstop by buying the single — total worst-case cost is the box price plus the single. Most rational hobbyists end here.
The expensive path is pure-rip-to-pull: keep opening packs until Zacian V appears. The expected total cost is ~$600, but the 95th percentile pushes that to ~$1,790. Almost nobody who does this comes out ahead financially — but it produces the binder story, the YouTube content, and the cumulative pulls of the entire pack contents along the way. If your real goal is collecting all of Sword & Shield, not just acquiring Zacian V, the pure-rip path has an internal logic the singles path doesn't.
Variance is the entire story
Here's a concrete illustration of how wild the geometric distribution gets at low p. Consider 10 hypothetical openers all chasing Zacian V from Sword & Shield. Mathematically, you'd expect their results to cluster near the 121-pack expectation — but they won't. Roughly 5 will pull Zacian V within the first 83 packs and feel lucky. Roughly 3 will pull between 83 and 121 packs and feel "about average". And roughly 2 will be still pulling past pack 121, with one of them potentially stretching past the 95% bound of 358. The unlucky ones will swear the simulator is rigged, the rates are wrong, or that they have terrible RNG — but the math says exactly this distribution should happen every time. The geometric distribution has no memory: each pack is an independent draw, and a 100-pack dry streak does not increase the odds of the next pack hitting.
How Zacian V compares to the broader Sword & Shield chase pool
Zacian V sits in the Secret Rare tier of Sword & Shield's rare-slot pool. 6 cards share this tier, and the tier itself fires roughly 5.00% of the time per pack. That means the per-pack chance of pulling any Secret Rare card (not just Zacian V) is 5.00%, which makes the expected wait for any Secret Rare card much shorter than the wait for this specific one. Pull-rate intuition: a single chase from a 6-card tier is 6× rarer than the tier itself. The deeper the pool, the longer the chase. This is also why "wide" sets with many chase cards in a single tier feel grindier per individual card despite the tier hit rate being identical — a thicker tier dilutes each card's specific share.
If your real goal is "any chase card from Sword & Shield" rather than "Zacian V specifically", the math gets dramatically friendlier — the wait drops to ~21 packs on average for the tier as a whole. Most binder collectors approach it this way: chase the tier broadly across multiple sets, accept whatever pulls, and snipe the specific holes via TCGplayer later. Targeting one card from a thick tier is the most expensive way to play the chase, and Zacian V is no exception.