How Many Packs to Pull Blaine's Moltres from Gym Heroes

Blaine's Moltres chase methodology

This page answers exactly one question: how many Gym Heroes booster packs does it take to pull Blaine's Moltres #1? The numbers below come from the same per-rarity pull-rate model the PackRip Gym Heroes 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 53 per pack

Blaine's Moltres sits in the Rare Holo rare-slot pool for Gym Heroes. There are 19 Rare Holo cards in the Gym Heroes pool, and the Rare Holo slot fires with probability 36.00% per pack. Since the slot is split evenly across the 19 cards in that tier, the per-pack chance of pulling this specific card is 1 in 53 — approximately 1 in 53.

Pulls are independent and identically distributed, so the number of packs until you hit Blaine's Moltres follows a geometric distribution with parameter p = 0.018947. The expected number of packs is 1/p — that's ~53 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~37 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 157 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.

Concretely: if 100 collectors each opened Gym Heroes packs until they pulled Blaine's Moltres, roughly 50 of them would have it by pack 37, 95 of them would have it by pack 157, 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 Blaine's Moltres by pack N?". A 25% band of 16 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 241. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.

Cheaper to buy Blaine's Moltres as a single?

Buying Blaine's Moltres as a single on TCGplayer (~$98.61) is dramatically cheaper than chasing it through packs — the expected pack-rip cost is roughly $264, well above the market price.

Pack-rip expected dollar cost for this specific card: ~$264 at $5 per Gym Heroes pack. Compare to $98.61 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 Blaine's Moltres plus the remaining 10 cards in every pack along the way — which is why the EV calculator at /ev/gym1 spreads the cost across the whole pack contents instead of pinning it to one card.

About Blaine's Moltres (Gym Heroes)

Blaine's Moltres is a Rare Holo card from Gym Heroes, the 2000 Pokémon TCG expansion. Gym Heroes (2000) hands 104 of its 132 cards to a named owner — Brock's, Misty's, Lt. Surge's, Erika's and Rocket's Pokemon all carry the prefix. Ken Sugimori illustrates 95 cards, more than the rest of the set's five artists combined. Unusually for the era, five of the 19 Rare Holos are Trainers rather than Pokemon: Brock #15, Erika #16, Lt. Surge #17, Misty #18 and The Rocket's Trap #19. Seven Stadium cards round out the Trainer pool.

This specific card ranks as one of the top-3 most valuable pulls in Gym Heroes 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 Gym Heroes ranking shows where Blaine's Moltres sits relative to the rest of the chase pool.

Pull odds in context

For reference, a "1 in 53" 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 Gym Heroes opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.

Related chases

• Sabrina's Gengar — Rare Holo, $392.50 market
• Erika's Dragonair — Rare Holo, $101.21 market
• All Blaine's Moltres printings across 2 sets
• All top-25 Gym Heroes chases
• Complete the Gym Heroes binder — full calculator

Open Gym Heroes free

Rip Gym Heroes 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 Blaine's Moltres-tier pulls. Coin economy is virtual — no real money on the line.

Strategy: optimising the Blaine's Moltres chase

Every experienced Gym Heroes 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 $98.61 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 ($264) 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 Gym Heroes (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Blaine's Moltres in the box, buy the single for $98.61. A 36-pack box delivers a probability of 1 − (1 − p)³⁶ ≈ 49.8% of pulling Blaine's Moltres at least once, where p is the per-pack hit rate of 0.018947. 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 Blaine's Moltres appears. The expected total cost is ~$264, but the 95th percentile pushes that to ~$785. 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 Gym Heroes, not just acquiring Blaine's Moltres, 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 Blaine's Moltres from Gym Heroes. Mathematically, you'd expect their results to cluster near the 53-pack expectation — but they won't. Roughly 5 will pull Blaine's Moltres within the first 37 packs and feel lucky. Roughly 3 will pull between 37 and 53 packs and feel "about average". And roughly 2 will be still pulling past pack 53, with one of them potentially stretching past the 95% bound of 157. 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 Blaine's Moltres compares to the broader Gym Heroes chase pool

Blaine's Moltres sits in the Rare Holo tier of Gym Heroes's rare-slot pool. 19 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 Blaine's Moltres) 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 Gym Heroes" rather than "Blaine's Moltres 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 Blaine's Moltres is no exception.