How Many Packs to Pull Infernape LV.X from Diamond & Pearl
| Card | Infernape LV.X — Diamond & Pearl #121 |
|---|---|
| Rarity tier | Lv.X |
| Per-pack odds | 1 in 35 |
| Expected packs to pull | 36 |
| 50% confidence band | 24 packs |
| 95% confidence band | 104 packs |
| TCGplayer market | $124.37 |
| Pack-rip break-even | 25 packs @ $5 |
Infernape LV.X chase methodology
| Formula | Specific-card odds = Lv.X tier rate (8.56%) ÷ 3 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 Diamond & Pearl booster packs does it take to pull Infernape LV.X #121? The numbers below come from the same per-rarity pull-rate model the PackRip Diamond & Pearl 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 35 per pack
Infernape LV.X sits in the Lv.X rare-slot pool for Diamond & Pearl. There are 3 Lv.X cards in the Diamond & Pearl pool, and the Lv.X slot fires with probability 8.56% 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 35 — approximately 1 in 35.
Pulls are independent and identically distributed, so the number of packs until you hit Infernape LV.X follows a geometric distribution with parameter p = 0.028533. The expected number of packs is 1/p — that's ~36 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~24 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 104 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.
Concretely: if 100 collectors each opened Diamond & Pearl packs until they pulled Infernape LV.X, roughly 50 of them would have it by pack 24, 95 of them would have it by pack 104, 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% | 4 packs | ~$20 sealed cost |
| 25% | 10 packs | ~$50 sealed cost |
| 50% | 24 packs | ~$120 sealed cost |
| 75% | 48 packs | ~$240 sealed cost |
| 90% | 80 packs | ~$400 sealed cost |
| 95% | 104 packs | ~$520 sealed cost |
| 99% | 160 packs | ~$800 sealed cost |
Read this table as "what fraction of openers have pulled Infernape LV.X by pack N?". A 25% band of 10 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 160. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.
Cheaper to buy Infernape LV.X as a single?
Buying Infernape LV.X as a single (~$124.37) edges out pack-ripping on raw cost. Pack-rip expected value is ~$175 for this specific pull.
Pack-rip expected dollar cost for this specific card: ~$175 at $5 per Diamond & Pearl pack. Compare to $124.37 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 Infernape LV.X plus the remaining 9 cards in every pack along the way — which is why the EV calculator at /ev/dp1 spreads the cost across the whole pack contents instead of pinning it to one card.
About Infernape LV.X (Diamond & Pearl)
Infernape LV.X is a Lv.X card from Diamond & Pearl, the 2007 Pokémon TCG expansion. Diamond & Pearl (2007) opens the Sinnoh era with 130 cards and introduces the Level-Up subtype to PackRip's catalog. Three cards carry the Rare Holo LV.X rarity — Empoleon LV.X #120, Infernape LV.X #121 and Torterra LV.X #122, the three Sinnoh starters. The engine draws Lv.X cards from a 5.56 percent slice of the rare slot, roughly one pack in eighteen. Ken Sugimori illustrates 40 of the 130.
This specific card ranks as one of the top-3 most valuable pulls in Diamond & Pearl 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 Diamond & Pearl ranking shows where Infernape LV.X sits relative to the rest of the chase pool.
Pull odds in context
For reference, a "1 in 35" 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 Diamond & Pearl opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.
Related chases
- Torterra LV.X — Lv.X, $95.79 market
- Empoleon LV.X — Lv.X, $66.00 market
- All Infernape LV.X printings across 2 sets
- All top-25 Diamond & Pearl chases
- Complete the Diamond & Pearl binder — full calculator
Open Diamond & Pearl free
Rip Diamond & Pearl 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 Infernape LV.X-tier pulls. Coin economy is virtual — no real money on the line.
Strategy: optimising the Infernape LV.X chase
Every experienced Diamond & Pearl 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 $124.37 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 ($175) 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 Diamond & Pearl (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Infernape LV.X in the box, buy the single for $124.37. A 36-pack box delivers a probability of 1 − (1 − p)36 ≈ 64.7% of pulling Infernape LV.X at least once, where p is the per-pack hit rate of 0.028533. So a sealed box gives you roughly a 65% 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 Infernape LV.X appears. The expected total cost is ~$175, but the 95th percentile pushes that to ~$520. 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 Diamond & Pearl, not just acquiring Infernape 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 Infernape LV.X from Diamond & Pearl. Mathematically, you'd expect their results to cluster near the 36-pack expectation — but they won't. Roughly 5 will pull Infernape LV.X within the first 24 packs and feel lucky. Roughly 3 will pull between 24 and 36 packs and feel "about average". And roughly 2 will be still pulling past pack 36, with one of them potentially stretching past the 95% bound of 104. 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 Infernape LV.X compares to the broader Diamond & Pearl chase pool
Infernape LV.X sits in the Lv.X tier of Diamond & Pearl's rare-slot pool. 3 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 Infernape 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 Diamond & Pearl" rather than "Infernape 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 Infernape LV.X is no exception.