How Many Packs to Pull Ultra Ball from Sun & Moon
| Card | Ultra Ball — Sun & Moon #161 |
|---|---|
| Rarity tier | Secret Rare |
| Per-pack odds | 1 in 80 |
| Expected packs to pull | 80 |
| 50% confidence band | 56 packs |
| 95% confidence band | 239 packs |
| TCGplayer market | $32.48 |
| Pack-rip break-even | 6 packs @ $5 |
Ultra Ball chase methodology
| Formula | Specific-card odds = Secret Rare tier rate (5.00%) ÷ 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 Sun & Moon booster packs does it take to pull Ultra Ball #161? The numbers below come from the same per-rarity pull-rate model the PackRip Sun & Moon 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 80 per pack
Ultra Ball sits in the Secret Rare rare-slot pool for Sun & Moon. There are 4 Secret Rare cards in the Sun & Moon pool, and the Secret Rare slot fires with probability 5.00% 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 80 — approximately 1 in 80.
Pulls are independent and identically distributed, so the number of packs until you hit Ultra Ball follows a geometric distribution with parameter p = 0.012500. The expected number of packs is 1/p — that's ~80 packs on average. But "average" hides huge variance: the median pull lands faster than the mean (~56 packs at 50% confidence), and a long unlucky tail can stretch the wait dramatically. The 95% confidence band — 239 packs — is where 95% of pull-runs finish; the remaining 5% take even longer.
Concretely: if 100 collectors each opened Sun & Moon packs until they pulled Ultra Ball, roughly 50 of them would have it by pack 56, 95 of them would have it by pack 239, 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% | 9 packs | ~$45 sealed cost |
| 25% | 23 packs | ~$115 sealed cost |
| 50% | 56 packs | ~$280 sealed cost |
| 75% | 111 packs | ~$555 sealed cost |
| 90% | 184 packs | ~$920 sealed cost |
| 95% | 239 packs | ~$1,195 sealed cost |
| 99% | 367 packs | ~$1,835 sealed cost |
Read this table as "what fraction of openers have pulled Ultra Ball by pack N?". A 25% band of 23 packs means a quarter of openers hit it inside that window; 99% means almost everyone has hit it by pack 367. The dollar column anchors the variance to real-world sealed-pack cost at $5/pack.
Cheaper to buy Ultra Ball as a single?
Buying Ultra Ball as a single on TCGplayer (~$32.48) is dramatically cheaper than chasing it through packs — the expected pack-rip cost is roughly $400, well above the market price.
Pack-rip expected dollar cost for this specific card: ~$400 at $5 per Sun & Moon pack. Compare to $32.48 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 Ultra Ball plus the remaining 10 cards in every pack along the way — which is why the EV calculator at /ev/sm1 spreads the cost across the whole pack contents instead of pinning it to one card.
About Ultra Ball (Sun & Moon)
Ultra Ball is a Secret Rare card from Sun & Moon, the 2017 Pokémon TCG expansion. Sun & Moon (2017) opens the Alola era with 173 cards and brings the GX subtype into PackRip's catalog — 11 cards at rarity Rare Holo GX, drawn from an 11.1 percent slice of the rare slot. Above them sit 12 Rare Ultras and the first eight Rare Rainbow cards, which the engine treats as a much scarcer 2.8 percent tier. All six Secret Rares are Trainers or Energy rather than Pokemon. Fifty-seven illustrators contributed.
This specific card ranks as one of the top-3 most valuable pulls in Sun & Moon 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 Sun & Moon ranking shows where Ultra Ball sits relative to the rest of the chase pool.
Pull odds in context
For reference, a "1 in 80" 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 Sun & Moon opener uses the same exact RNG model, so you can stress-test the wait curve without spending real money.
Related chases
- Umbreon-GX — Full Art, $51.71 market
- Lillie — Full Art, $50.21 market
- All Ultra Ball printings across 15 sets
- All top-25 Sun & Moon chases
- Complete the Sun & Moon binder — full calculator
Open Sun & Moon free
Rip Sun & Moon packs free on PackRip's simulator with the same per-rarity pull rates this page is built from. The Hunt Pack mode boosts the Secret Rare slot if you specifically want to optimise for Ultra Ball-tier pulls. Coin economy is virtual — no real money on the line.
Strategy: optimising the Ultra Ball chase
Every experienced Sun & Moon 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 $32.48 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 ($400) 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 Sun & Moon (typically 36 packs for vintage sets), enjoy the experience, then if you didn't hit Ultra Ball in the box, buy the single for $32.48. A 36-pack box delivers a probability of 1 − (1 − p)36 ≈ 36.4% of pulling Ultra Ball at least once, where p is the per-pack hit rate of 0.012500. So a sealed box gives you roughly a 36% 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 Ultra Ball appears. The expected total cost is ~$400, but the 95th percentile pushes that to ~$1,195. 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 Sun & Moon, not just acquiring Ultra Ball, 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 Ultra Ball from Sun & Moon. Mathematically, you'd expect their results to cluster near the 80-pack expectation — but they won't. Roughly 5 will pull Ultra Ball within the first 56 packs and feel lucky. Roughly 3 will pull between 56 and 80 packs and feel "about average". And roughly 2 will be still pulling past pack 80, with one of them potentially stretching past the 95% bound of 239. 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 Ultra Ball compares to the broader Sun & Moon chase pool
Ultra Ball sits in the Secret Rare tier of Sun & Moon's rare-slot pool. 4 cards share this tier, and the tier itself fires roughly 5.00% of the time per pack. That means the per-pack chance of pulling any Secret Rare card (not just Ultra Ball) is 5.00%, which makes the expected wait for any Secret Rare 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 Sun & Moon" rather than "Ultra Ball specifically", the math gets dramatically friendlier — the wait drops to ~20 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 Ultra Ball is no exception.