Methodology & sources

Published rules and statistical models

Published base rates, hard-pity limits and rate-up rules are rule inputs. A complete per-pull soft-pity table is generally not a published rule. Genshin and Star Rail estimates combine published rules with statistical soft-pity models; statistical references are not official confirmation. The Genshin weapon model uses a 77-pull cap as a statistical modeling choice, rather than replacing the official description.

ZZZ uses verified base rates, hard pity and rate-up guarantees in a simplified model, without a complete soft-pity curve. A published consolidated probability is not a fixed probability for every pull. This approximation is not the complete official mechanism.

Pity, paths and special states

Pity is separate across banner types. Carry-over, guarantees and special banner states follow each game configuration. Genshin Capturing Radiance depends on the toggle and initial counter; weapon Fate Points do not carry into the next phase. Check your own game history.

Preview targets with unannounced rank, phase or dates may use explicitly labeled planning assumptions. Being selectable does not mean that the rank, lineup or deadline is officially confirmed.

Shared budgets and income timing

Targets share one budget and are attempted in order. Each target does not receive the same balance again. Stage results describe progress through that order; average pull cost is not a guaranteed cost.

Your game server determines deadlines, daily resets and claimable income days. Display time zones only convert specific times. Extra income is credited under your selected amounts and claim dates; put already claimed rewards in your balance to avoid double counting. Projected dates and future rewards remain assumptions.

Added top-ups use the selected region, quantity and configured regular rewards, excluding first-purchase doubling. This is a scenario comparison, not a purchase recommendation. Refund exchanges enter the simulation only when enabled; do not manually count the same refund again.

Sampling error and high probabilities

Complex plans use seeded Monte Carlo simulation with actual sample counts, model versions and precision states. A run-time budget can reduce samples for long plans. Sampling intervals describe simulation uncertainty, not errors in rules, income or date assumptions.

Every sampled run succeeding does not prove certainty. Without a hard-pity proof, finite all-success samples alone do not establish a guaranteed 100%. Check the sample count, result state and assumptions together.

Sources and maintenance

The links below provide game rules and statistical references. Data check dates come from current game configurations. Recorded announcements, confirmed lineups and projected content are labeled separately. Maintenance is manual, without a promise of real-time updates.

A source link does not prove that every rule on the page was verified. Official community sites can also host player content. Check each calendar’s source notes for evidence and unknowns. Report discrepancies with announcement links or in-game rule screenshots.

Game data and models