How Many Packs to Pull Pikachu ★ from Holon Phantoms

Pikachu ★ chase methodology

This page answers exactly one question: how many Holon Phantoms booster packs does it take to pull Pikachu ★ #104? The numbers below come from the same per-rarity pull-rate model the PackRip Holon Phantoms 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 52 per pack

Pikachu ★ sits in the Gold Star rare-slot pool for Holon Phantoms. There are 3 Gold Star cards in the Holon Phantoms pool, and the Gold Star slot fires with probability 5.80% per pack. Since the slot is split evenly across the 3 cards in that tier, the per-pack chance of pulling this specific card is 1 in 52 — approximately 1 in 52.

Pulls are independent and identically distributed, so the number of packs until you hit Pikachu ★ follows a geometric distribution with parameter p = 0.019333. The expected number of packs is 1/p — that's ~52 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~36 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 154 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.

Concretely: if 100 collectors each opened Holon Phantoms packs until they pulled Pikachu ★, roughly 50 of them would have it by pack 36, 95 of them would have it by pack 154, 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 Pikachu ★ by pack N?". A 25% band of 15 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 236. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.

Cheaper to buy Pikachu ★ as a single?

Pack-ripping breaks even or beats singles on raw cost for Pikachu ★ — but you'd absorb the rest of the pack contents along the way. Most hunters still mix: rip for the experience, buy the single if RNG turns sour.

Pack-rip expected dollar cost for this specific card: ~$259 at $5 per Holon Phantoms pack. Compare to $1342.74 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 Pikachu ★ plus the remaining 8 cards in every pack along the way — which is why the EV calculator at /ev/ex13 spreads the cost across the whole pack contents instead of pinning it to one card.

About Pikachu ★ (Holon Phantoms)

Pikachu ★ is a Gold Star card from Holon Phantoms, the 2006 Pokémon TCG expansion. Holon Phantoms (2006) pushes the Delta Species idea further than the set that named it: 51 of its 111 cards carry the delta marker. Metal leads the type spread at 21 and the set carries 11 Energy cards. Only 14 illustrators worked on it, a narrow credit list for a set this size. Three ex cards (#99 to #101) sit below three Gold Stars — Gyarados delta #102, Mewtwo #103 and Pikachu #104 — with Mew #111 as the Secret Rare.

This specific card ranks as one of the top-3 most valuable pulls in Holon Phantoms 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 Holon Phantoms ranking shows where Pikachu ★ sits relative to the rest of the chase pool.

Pull odds in context

For reference, a "1 in 52" 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 Holon Phantoms opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.

Related chases

• Gyarados ★ δ — Gold Star, $1200.00 market
• Mew ex — Pokémon-ex, $512.44 market
• All top-25 Holon Phantoms chases
• Complete the Holon Phantoms binder — full calculator

Open Holon Phantoms free

Rip Holon Phantoms packs free on PackRip's simulator with the same per-rarity pull rates this page is built from. The Hunt Pack mode boosts the Gold Star slot if you specifically want to optimise for Pikachu ★-tier pulls. Coin economy is virtual — no real money on the line.

Strategy: optimising the Pikachu ★ chase

Every experienced Holon Phantoms 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 $1342.74 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 ($259) 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 Holon Phantoms (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Pikachu ★ in the box, buy the single for $1342.74. A 36-pack box delivers a probability of 1 − (1 − p)³⁶ ≈ 50.5% of pulling Pikachu ★ at least once, where p is the per-pack hit rate of 0.019333. So a sealed box gives you roughly a 50% 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 Pikachu ★ appears. The expected total cost is ~$259, but the 95th percentile pushes that to ~$770. 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 Holon Phantoms, not just acquiring Pikachu ★, 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 Pikachu ★ from Holon Phantoms. Mathematically, you'd expect their results to cluster near the 52-pack expectation — but they won't. Roughly 5 will pull Pikachu ★ within the first 36 packs and feel lucky. Roughly 3 will pull between 36 and 52 packs and feel "about average". And roughly 2 will be still pulling past pack 52, with one of them potentially stretching past the 95% bound of 154. 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 Pikachu ★ compares to the broader Holon Phantoms chase pool

Pikachu ★ sits in the Gold Star tier of Holon Phantoms's rare-slot pool. 3 cards share this tier, and the tier itself fires roughly 5.80% of the time per pack. That means the per-pack chance of pulling any Gold Star card (not just Pikachu ★) is 5.80%, which makes the expected wait for any Gold Star 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 Holon Phantoms" rather than "Pikachu ★ specifically", the math gets dramatically friendlier — the wait drops to ~18 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 Pikachu ★ is no exception.