How Many Packs to Pull Rayquaza & Deoxys LEGEND from HS—Undaunted

Rayquaza & Deoxys LEGEND chase methodology

This page answers exactly one question: how many HS—Undaunted booster packs does it take to pull Rayquaza & Deoxys LEGEND #90? The numbers below come from the same per-rarity pull-rate model the PackRip HS—Undaunted 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 47 per pack

Rayquaza & Deoxys LEGEND sits in the LEGEND rare-slot pool for HS—Undaunted. There are 4 LEGEND cards in the HS—Undaunted pool, and the LEGEND slot fires with probability 8.56% per pack. Since the slot is split evenly across the 4 cards in that tier, the per-pack chance of pulling this specific card is 1 in 47 — approximately 1 in 47.

Pulls are independent and identically distributed, so the number of packs until you hit Rayquaza & Deoxys LEGEND follows a geometric distribution with parameter p = 0.021400. The expected number of packs is 1/p — that's ~47 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~33 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 139 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.

Concretely: if 100 collectors each opened HS—Undaunted packs until they pulled Rayquaza & Deoxys LEGEND, roughly 50 of them would have it by pack 33, 95 of them would have it by pack 139, 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 Rayquaza & Deoxys LEGEND by pack N?". A 25% band of 14 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 213. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.

Cheaper to buy Rayquaza & Deoxys LEGEND as a single?

Buying Rayquaza & Deoxys LEGEND as a single (~$222.59) edges out pack-ripping on raw cost. Pack-rip expected value is ~$234 for this specific pull.

Pack-rip expected dollar cost for this specific card: ~$234 at $5 per HS—Undaunted pack. Compare to $222.59 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 Rayquaza & Deoxys LEGEND plus the remaining 9 cards in every pack along the way — which is why the EV calculator at /ev/hgss3 spreads the cost across the whole pack contents instead of pinning it to one card.

About Rayquaza & Deoxys LEGEND (HS—Undaunted)

Rayquaza & Deoxys LEGEND is a LEGEND card from HS—Undaunted, the 2010 Pokémon TCG expansion. HS-Undaunted (2010) is the smallest HGSS set at 91 cards and the only one where Darkness leads the type spread, at 15 cards. Its six Primes are Espeon #81, Houndoom #82, Raichu #83, Scizor #84, Slowking #85 and Umbreon #86; the LEGEND pairs are Kyogre & Groudon (#87 and #88) and Rayquaza & Deoxys (#89 and #90). Alph Lithograph #THREE is the Secret Rare.

This specific card ranks as one of the top-3 most valuable pulls in HS—Undaunted 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 HS—Undaunted ranking shows where Rayquaza & Deoxys LEGEND sits relative to the rest of the chase pool.

Pull odds in context

For reference, a "1 in 47" 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 HS—Undaunted opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.

Related chases

• Umbreon — Prime, $514.48 market
• Kyogre & Groudon LEGEND — LEGEND, $499.00 market
• All Rayquaza & Deoxys LEGEND printings across 2 sets
• All top-25 HS—Undaunted chases
• Complete the HS—Undaunted binder — full calculator

Open HS—Undaunted free

Rip HS—Undaunted packs free on PackRip's simulator with the same per-rarity pull rates this page is built from. The Hunt Pack mode boosts the LEGEND slot if you specifically want to optimise for Rayquaza & Deoxys LEGEND-tier pulls. Coin economy is virtual — no real money on the line.

Strategy: optimising the Rayquaza & Deoxys LEGEND chase

Every experienced HS—Undaunted 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 $222.59 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 ($234) 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 HS—Undaunted (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Rayquaza & Deoxys LEGEND in the box, buy the single for $222.59. A 36-pack box delivers a probability of 1 − (1 − p)³⁶ ≈ 54.1% of pulling Rayquaza & Deoxys LEGEND at least once, where p is the per-pack hit rate of 0.021400. So a sealed box gives you roughly a 54% 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 Rayquaza & Deoxys LEGEND appears. The expected total cost is ~$234, but the 95th percentile pushes that to ~$695. 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 HS—Undaunted, not just acquiring Rayquaza & Deoxys LEGEND, 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 Rayquaza & Deoxys LEGEND from HS—Undaunted. Mathematically, you'd expect their results to cluster near the 47-pack expectation — but they won't. Roughly 5 will pull Rayquaza & Deoxys LEGEND within the first 33 packs and feel lucky. Roughly 3 will pull between 33 and 47 packs and feel "about average". And roughly 2 will be still pulling past pack 47, with one of them potentially stretching past the 95% bound of 139. 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 Rayquaza & Deoxys LEGEND compares to the broader HS—Undaunted chase pool

Rayquaza & Deoxys LEGEND sits in the LEGEND tier of HS—Undaunted's rare-slot pool. 4 cards share this tier, and the tier itself fires roughly 8.56% of the time per pack. That means the per-pack chance of pulling any LEGEND card (not just Rayquaza & Deoxys LEGEND) is 8.56%, which makes the expected wait for any LEGEND 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 HS—Undaunted" rather than "Rayquaza & Deoxys LEGEND specifically", the math gets dramatically friendlier — the wait drops to ~12 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 Rayquaza & Deoxys LEGEND is no exception.