How Many Packs to Pull Darkrai LV.X from Great Encounters
| Card | Darkrai LV.X — Great Encounters #104 |
|---|---|
| Rarity tier | Lv.X |
| Per-pack odds | 1 in 47 |
| Expected packs to pull | 47 |
| 50% confidence band | 33 packs |
| 95% confidence band | 139 packs |
| TCGplayer market | $138.26 |
| Pack-rip break-even | 28 packs @ $5 |
Darkrai LV.X chase methodology
| Formula | Specific-card odds = Lv.X tier rate (8.56%) ÷ 4 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 Great Encounters booster packs does it take to pull Darkrai LV.X #104? The numbers below come from the same per-rarity pull-rate model the PackRip Great Encounters 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
Darkrai LV.X sits in the Lv.X rare-slot pool for Great Encounters. There are 4 Lv.X cards in the Great Encounters pool, and the Lv.X 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 Darkrai LV.X 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 Great Encounters packs until they pulled Darkrai LV.X, 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
| P(pulled by N packs) | Packs needed | Sealed cost at $5/pack |
|---|---|---|
| 10% | 5 packs | ~$25 sealed cost |
| 25% | 14 packs | ~$70 sealed cost |
| 50% | 33 packs | ~$165 sealed cost |
| 75% | 65 packs | ~$325 sealed cost |
| 90% | 107 packs | ~$535 sealed cost |
| 95% | 139 packs | ~$695 sealed cost |
| 99% | 213 packs | ~$1,065 sealed cost |
Read this table as "what fraction of openers have pulled Darkrai LV.X 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 Darkrai LV.X as a single?
Buying Darkrai LV.X as a single on TCGplayer (~$138.26) is dramatically cheaper than chasing it through packs — the expected pack-rip cost is roughly $234, well above the market price.
Pack-rip expected dollar cost for this specific card: ~$234 at $5 per Great Encounters pack. Compare to $138.26 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 Darkrai LV.X plus the remaining 9 cards in every pack along the way — which is why the EV calculator at /ev/dp4 spreads the cost across the whole pack contents instead of pinning it to one card.
About Darkrai LV.X (Great Encounters)
Darkrai LV.X is a Lv.X card from Great Encounters, the 2008 Pokémon TCG expansion. Great Encounters (2008) is a 106-card set with only six Trainers and no Energy at all. Four Lv.X cards close the numbering — Cresselia #103, Darkrai #104, Dialga #105 and Palkia #106 — and there are no Secret Rares. Water is the widest type at 24 cards, just ahead of Colorless at 23.
This specific card ranks as one of the top-3 most valuable pulls in Great Encounters 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 Great Encounters ranking shows where Darkrai LV.X 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 Great Encounters opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.
Related chases
- Dialga LV.X — Lv.X, $249.99 market
- Palkia LV.X — Lv.X, $140.00 market
- All Darkrai LV.X printings across 2 sets
- All top-25 Great Encounters chases
- Complete the Great Encounters binder — full calculator
Open Great Encounters free
Rip Great Encounters packs free on PackRip's simulator with the same per-rarity pull rates this page is built from. The Hunt Pack mode boosts the Lv.X slot if you specifically want to optimise for Darkrai LV.X-tier pulls. Coin economy is virtual — no real money on the line.
Strategy: optimising the Darkrai LV.X chase
Every experienced Great Encounters 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 $138.26 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 Great Encounters (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Darkrai LV.X in the box, buy the single for $138.26. A 36-pack box delivers a probability of 1 − (1 − p)36 ≈ 54.1% of pulling Darkrai LV.X 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 Darkrai LV.X 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 Great Encounters, not just acquiring Darkrai LV.X, 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 Darkrai LV.X from Great Encounters. Mathematically, you'd expect their results to cluster near the 47-pack expectation — but they won't. Roughly 5 will pull Darkrai LV.X 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 Darkrai LV.X compares to the broader Great Encounters chase pool
Darkrai LV.X sits in the Lv.X tier of Great Encounters'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 Lv.X card (not just Darkrai LV.X) is 8.56%, which makes the expected wait for any Lv.X 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 Great Encounters" rather than "Darkrai LV.X 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 Darkrai LV.X is no exception.