ZZZ Pity Calculator

Three inputs drive the whole result. Channel changes the formula entirely since each has its own cap and rates: the Agent channel (standard + limited), the W-Engine channel, and the Star-Studded Cast (standard/stable) channel. Current pity is how many pulls in a row you've made without an S-rank — it counts from your last S-rank and resets to 0 whenever you hit one. The guarantee switch only applies to the limited channel: flip it on if your last S-rank was NOT the featured unit (you lost the 50/50), because your next S-rank there is then guaranteed to be the one you want.

Read the output in order: the chance of the exact target within budget, the chance of any S-rank (including off-banner), the average pulls needed to hit it, and the worst-case safety net. The distribution chart shows cumulative probability climbing pull by pull — it steepens sharply around the soft pity zone and goes nearly vertical at the hard cap. The odds-by-milestone table lets you compare a few budget scenarios at a glance without re-entering numbers.

Each channel has its own separate hard cap: the Agent channel (both standard and limited) guarantees an S-rank within 90 pulls; the W-Engine channel guarantees one within 80 pulls. These are the in-game published figures, not estimates — hit the cap and it's 100% guaranteed, even though the base rate per pull sits around 0.6% (Agents) or around 1% (W-Engines, the highest weapon base rate among HoYo games).

The Star-Studded Cast channel — home to permanent Agents and W-Engines — has its own separate milestone: reach 300 pulls there and you freely SELECT a standard S-rank Agent, no luck involved. The rule that every 10 pulls in a row guarantees at least one A-rank or better is a SHARED mechanic across every channel (Agent, W-Engine and Star-Studded Cast alike), not a perk unique to this one — so on any channel you rarely go a long stretch empty-handed of A-rank.

When you land an S-rank on the limited Agent channel, there's a 50% chance it's the featured unit and a 50% chance it's a random standard Agent. Lose that coin flip and the guarantee kicks in: your next S-rank on that channel is then 100% guaranteed to be the featured one. So the worst case to secure a limited Agent is 90 pulls (loss) plus 90 more (guaranteed win) — 180 pulls, or 28,800 Polychrome.

The W-Engine channel is much friendlier: the featured W-Engine lands at 75% right on the first S-rank (75/25 instead of 50/50), so the worst case is still 80 plus 80 for 160 pulls, but the odds of ever needing that full stretch are far lower since the first-try win rate is already high. The tool automatically switches to the right guarantee math when you change channels, so you never have to remember which is 50/50 and which is 75/25.

If the S-rank rate stayed at a flat 0.6% from pull 1 to pull 90, most players would rarely feel close to the hard cap since cumulative odds would already be decent early on. In practice the game uses a rising curve called "soft pity": starting around pull 74-75, the per-pull S-rank rate jumps in steps instead of staying at the base rate, climbing faster the closer you get to 90 until it hits a guaranteed 100%. That's why most players actually land their S-rank somewhere around pull 75-85, rarely needing to reach the literal 90th pull.

The exact soft pity onset isn't officially published — community measurements put it somewhere around pull 74 to 75 depending on sample size, with the rate climbing roughly 2% per pull past that point. This is a large-sample community statistic, not a figure from official documentation, so the tool flags it as a community estimate rather than an absolute claim — transparency over false precision.

To know how much to save before a new banner drops, work backward from the worst case: multiply the pulls needed (up to 180 for a limited Agent starting at 0 pity with no guarantee) by 160 Polychrome per pull. But most players don't need to bank the full worst case — plug in your actual pity and guarantee status, check the probability at a few budget milestones (say 30, 60, 90 pulls), and decide how much risk you're comfortable carrying.

Three practical saving tips: if you already hold the guarantee (you lost the 50/50 last time), the upcoming limited banner is nearly a sure thing at the cap — prioritize saving for that one first. If the tool already shows 80-90%+ at your current budget, saving further adds very little for a lot more farming. And don't forget: switching between "how many pulls" and "how much Polychrome" is just a display toggle in the tool — both modes describe the same odds, just a different unit to track your wallet.

Hand-counting with "on average 1 in 0.6% pulls gets an S" only holds if the rate never changes — but since soft pity spikes the rate after pull 74-75, the real average pull count is well below the naive 1/0.6% ≈ 167 figure. That's why community-measured averages vary quite a bit — some report roughly 62 pulls counting from 0 pity including a possible loss-then-guaranteed-win, others report 75-80 pulls if only averaging near-cap outcomes — the gap comes from how each source defines "average," not a calculation error.

The tool uses a closed-form probability model: it computes the entire soft-pity curve plus guarantee state exactly with math, rather than running tens of thousands of trials and averaging like some Monte-Carlo simulators do. That approach gives stable results — feed it the same numbers and it returns the exact same probability every time, with no simulation noise.

Beyond the three main channels, Zenless Zone Zero has a fourth, less-discussed one: the Bangboo channel (Bangboo signal search). It has a hard cap of 80 pulls guaranteeing an S-rank Bangboo, but its biggest difference is that it has NO 50/50 mechanic: you pre-select the Bangboo you want, so when an S-rank drops it is 100% guaranteed to be that exact one — there is no coin flip to lose.

The Bangboo channel also isn't pulled with Polychrome bought using real money — it uses Boopon, tickets earned through normal play. That makes it the gentlest channel: no 50/50 risk, no spending of paid currency. The tool focuses on the Agent / W-Engine / Star-Studded Cast channels because those are where you weigh a real budget, but if you're after a specific Bangboo, just remember the number 80 and rest assured it always lands the one you designated.

The Star-Studded Cast's 300-pull milestone lets you freely choose an S-rank Agent, but only from a fixed list of six standard-pool characters, not every S-rank in the game: Nekomata, Koleda, Soldier 11, Lycaon, Grace Howard, and Rina. These are the channel's permanent six; once you reach 300 pulls you file a selection ticket for one of them, no luck involved.

This channel also has a perk for newcomers: the very FIRST time you pull on the Star-Studded Cast, you are guaranteed at least one S-rank Agent within the first 50 pulls — a beginner's insurance so you aren't left empty-handed by bad luck right at the start. Note this insurance triggers only once, for the account's first 50 pulls; pulls after that revert to the normal 90 hard cap and 300 milestone.

Every pull on a tape channel (Master/Encrypted Tape) generates some Residual Signal, which you take to a dedicated shop to exchange for Master Tape, Encrypted Tape, Boopon and various upgrade materials. In other words no pull is a total loss — even an A-rank or a duplicate still banks signal toward resources.

The amount depends on the result: an A-rank W-Engine = 10, an S-rank W-Engine = 50. For characters the first six copies count differently from later ones: a duplicate A-rank Agent (copies 1-6) gives 10 signal + 1 character profile, and from the 7th copy on 15; a duplicate S-rank Agent (copies 1-6) gives 50 + a profile, and from the 7th 75. The Bangboo channel uses a separate exchange currency called En-Nies (A-rank Bangboo = 10, S-rank = 50). Thanks to this system, the more you pull the bigger your "refund fund," easing the sting of not hitting your target.

A very common question: should you pull a few dozen extra times to "pre-build" pity on a banner you don't actually need, hoping to save on the next one? Many sources say NO. The reason: Agent-channel pity does carry with you across limited banners, but if you land an S-rank along the way while on a 50/50 state, you can easily lose the coin flip and get a character you didn't want — wasting resources AND resetting your pity, entirely counterproductive.

The safer approach is to bank enough tape and then commit it to the banner you genuinely want. To be 100% certain of securing a limited character even in the worst case, budget for two hard pities (about 180 pulls): one lost 50/50 followed by a guaranteed win. If you haven't saved that much and your desired banner isn't up yet, don't waste pulls idly "building" pity — hold your resources, enter your current pity into the tool, and only pull once the odds of hitting your target are high enough for your risk appetite.