How Many Packs to Pull 金星 from 拡張パック

金星 chase methodology

This page answers exactly one question: how many 拡張パック booster packs does it take to pull 金星 #11? The numbers below come from the same per-rarity pull-rate model the PackRip 拡張パック 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 44 per pack

金星 sits in the Rare Holo rare-slot pool for 拡張パック. There are 16 Rare Holo cards in the 拡張パック pool, and the Rare Holo slot fires with probability 36.00% per pack. Since the slot is split evenly across the 16 cards in that tier, the per-pack chance of pulling this specific card is 1 in 44 — approximately 1 in 44.

Pulls are independent and identically distributed, so the number of packs until you hit 金星 follows a geometric distribution with parameter p = 0.022500. The expected number of packs is 1/p — that's ~45 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~31 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 132 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.

Concretely: if 100 collectors each opened 拡張パック packs until they pulled 金星, roughly 50 of them would have it by pack 31, 95 of them would have it by pack 132, 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

Read this table as "what fraction of openers have pulled 金星 by pack N?". A 25% band of 13 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 203. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.

Cheaper to buy 金星 as a single?

Buying 金星 as a single on TCGplayer (~$2.88) is dramatically cheaper than chasing it through packs — the expected pack-rip cost is roughly $222, well above the market price.

Pack-rip expected dollar cost for this specific card: ~$222 at $5 per 拡張パック pack. Compare to $2.88 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 金星 plus the remaining 10 cards in every pack along the way — which is why the EV calculator at /ev/pmcg1 spreads the cost across the whole pack contents instead of pinning it to one card.

About 金星 (拡張パック)

金星 is a Rare Holo card from 拡張パック, the 1996 Pokémon TCG expansion. 拡張パック is a 1996 Pokémon TCG booster expansion.

This specific card ranks as one of the top-3 most valuable pulls in 拡張パック 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 拡張パック ranking shows where 金星 sits relative to the rest of the chase pool.

Pull odds in context

For reference, a "1 in 44" pull is roughly comparable to a moderate chase — you should expect to crack a couple of boxes. The variance is the killer: any one pack could be the one. The simulation on PackRip's 拡張パック opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.

Related chases

• ニドキング — Rare Holo, $2.88 market
• カリザード — Rare Holo, $2.88 market
• All 金星 printings across 14 sets
• All top-25 拡張パック chases
• Complete the 拡張パック binder — full calculator

Open 拡張パック free

Rip 拡張パック packs free on PackRip's simulator with the same per-rarity pull rates this page is built from. The Hunt Pack mode boosts the Rare Holo slot if you specifically want to optimise for 金星-tier pulls. Coin economy is virtual — no real money on the line.

Strategy: optimising the 金星 chase

Every experienced 拡張パック 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 $2.88 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 ($222) 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 拡張パック (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit 金星 in the box, buy the single for $2.88. A 36-pack box delivers a probability of 1 − (1 − p)³⁶ ≈ 55.9% of pulling 金星 at least once, where p is the per-pack hit rate of 0.022500. So a sealed box gives you roughly a 56% 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 金星 appears. The expected total cost is ~$222, but the 95th percentile pushes that to ~$660. 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 拡張パック, not just acquiring 金星, 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 金星 from 拡張パック. Mathematically, you'd expect their results to cluster near the 45-pack expectation — but they won't. Roughly 5 will pull 金星 within the first 31 packs and feel lucky. Roughly 3 will pull between 31 and 45 packs and feel "about average". And roughly 2 will be still pulling past pack 45, with one of them potentially stretching past the 95% bound of 132. 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 金星 compares to the broader 拡張パック chase pool

金星 sits in the Rare Holo tier of 拡張パック's rare-slot pool. 16 cards share this tier, and the tier itself fires roughly 36.00% of the time per pack. That means the per-pack chance of pulling any Rare Holo card (not just 金星) is 36.00%, which makes the expected wait for any Rare Holo 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 拡張パック" rather than "金星 specifically", the math gets dramatically friendlier — the wait drops to ~3 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 金星 is no exception.