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The probability and astronomy calculators run deterministic math in the browser. Img23D sends the source image to the project DeepSeek endpoint for procedural Three.js generation; preview and GLB/STL export run in the browser.

The HoYoverse Gacha Calculator uses a discrete Markov chain over (pity, guarantee, Fate Points, copies) state — the same mathematical approach as hsrwarpcalc.com and the community-standard Python paimon.moe pity simulators, but solved exactly rather than sampled.

Frequently asked questions

What is soft pity in HoYoverse games?
Soft pity is a per-pull rate ramp that kicks in near the end of a banner cycle. On Genshin Impact and Honkai: Star Rail character banners, the base 0.6% rate begins increasing by roughly +6 percentage points per pull starting at pity 74, until the hard-pity guarantee at pull 90. On weapon and light cone banners with hard pity 80, soft pity starts around pull 63–65 with a +7% per-pull ramp.
Does the calculator model Genshin's Epitomized Path (Fate Points)?
Yes. The Genshin weapon banner uses a Markov chain over (pity, Fate Points ∈ {0,1,2}, copies gained). Each 5★ pull that is not your chosen weapon grants one Fate Point (capped at 2). At 2 Fate Points, the next 5★ is guaranteed to be your chosen weapon. The calculator exposes 0/1/2 FP as a toggle.
How accurate are the odds?
The math is exact — a discrete Markov chain, not a Monte Carlo simulation. The uncertainty is entirely in the input constants. Base rates and hard-pity thresholds are officially published by HoYoverse and exact. Soft-pity start pull (74 for characters, 63–65 for weapons) and slope (+6% / +7% per pull) come from community sampling and typically vary by ±1–2 pulls across sources. Advanced overrides let you tune these to match any specific data source.
Does Zenless Zone Zero's Bangboo channel have a 50/50?
No. The Bangboo channel is the only ZZZ banner without a 50/50 — every S-rank Bangboo drawn is guaranteed to be the featured Bangboo. Base rate is 1.0%, hard pity at pull 80. Agent and W-Engine channels use 50/50 and 75/25 respectively.
What is TLE and what does the decoder show?
A Two-Line Element (TLE) set is NORAD's standard format for encoding a satellite's orbit in two 69-character lines. Our decoder parses inclination, eccentricity, right ascension of ascending node, argument of perigee, mean anomaly, and mean motion, then propagates the current sub-satellite point (latitude/longitude) using SGP4.
How is the moon phase computed?
The Moon Phase calculator uses Jean Meeus's algorithm from Astronomical Algorithms (chapter 47). It computes the Moon's mean elongation D from the Sun, then derives the illuminated fraction as (1 − cos D) / 2. Accuracy is approximately 1% between years 1900 and 2100.
Do any of these tools require signup or send data to a server?
The gacha, Kepler, TLE, and moon-phase calculators run their calculations in the browser. Img23D sends the selected source image to the project DeepSeek endpoint; its interactive preview and GLB/STL export run in the browser.