What this tool does
This calculator models the probability of obtaining a target item from a gacha game's pull system, accounting for the pity mechanics that most modern gacha games use. Instead of treating each pull as a simple independent event, it factors in soft pity rate increases and hard pity guarantees to give you an accurate picture of your real odds.
Enter your game's pity parameters (or select a preset for Genshin Impact, Honkai: Star Rail, Wuthering Waves, or Zenless Zone Zero), specify how many pulls you have available, and instantly see your cumulative probability, expected pulls, and a full probability curve. You can also toggle the 50/50 featured character mechanic and estimate costs using your own currency-per-pull figure.
How it calculates
The calculator uses cumulative probability with a piecewise rate function that models soft pity ramp-up.
**Rate at each pull:** \`\`\` If pull < soft pity start: rate(pull) = base rate
If pull >= soft pity start: rate(pull) = base rate + (pull - soft pity start + 1) * soft pity increase
If pull >= hard pity: rate(pull) = 100% (guaranteed) \`\`\`
**Cumulative probability:** \`\`\` P(item by pull N) = 1 - product of (1 - rate(i)) for i = 1 to N \`\`\`
Each pull's failure probability compounds. Before soft pity, the rate is constant and low. Once soft pity begins, the rate climbs steeply each pull until hard pity guarantees the item.
**50/50 mechanic:** When enabled, the calculator convolves the single-pity distribution with itself. Winning the 50/50 gives you the featured item immediately. Losing it means your next 5-star is guaranteed to be the featured item, so you may need up to two full pity cycles.
**Expected pulls** are calculated as the sum of survival probabilities across all pulls, which equals the statistical average number of pulls needed. Percentile milestones (25th, 50th, 75th, 90th, 99th) show the pull counts where cumulative probability crosses each threshold.
Who should use this
- **Gacha gamers**: Know your real odds before spending pulls or currency on a banner. See whether your stockpile gives you a comfortable chance or if you should keep saving. - **Free-to-play players**: Plan your primogem, stellar jade, or astrite budget across multiple banners by understanding exactly how many pulls each target character requires on average. - **Content creators**: Generate accurate probability breakdowns for pull guides, banner analysis videos, or spending advice content. - **Curious players**: Understand why most players get their 5-star around pull 76-80 in Genshin Impact rather than at the hard pity of 90 — the soft pity ramp-up makes a dramatic difference.
How to use
1. Select a game preset (Genshin Impact, Honkai: Star Rail, Wuthering Waves, Zenless Zone Zero) or choose Custom to enter your own pity parameters 2. Review the pity system parameters — they auto-fill from the preset but you can edit them 3. Enter the number of pulls you have available or plan to make 4. Choose your 50/50 status: "On 50/50" if you haven't lost one yet, "Guaranteed" if your next 5-star is the featured character, or "No 50/50" for standard banners 5. Optionally toggle cost estimation and enter your cost per pull in any currency 6. View your results: the hero probability, expected pulls, probability milestones, cumulative probability curve, and detailed pull-by-pull breakdown
Understanding pity mechanics
Most gacha games use a three-phase pity system:
**Phase 1 — Base rate zone (pulls 1 to soft pity).** Every pull has the same low probability. In Genshin Impact, this is 0.6% per pull. Your cumulative odds grow slowly and linearly during this phase.
**Phase 2 — Soft pity zone (soft pity to hard pity - 1).** The game silently increases your pull rate each attempt. In Genshin Impact, starting at pull 74, each pull adds roughly 6% to your rate. By pull 80, your per-pull rate is over 36%, making it very likely you hit the 5-star before reaching hard pity.
**Phase 3 — Hard pity (guaranteed pull).** If you reach the hard pity count without winning, the game guarantees the item. In Genshin Impact this is pull 90, but due to the aggressive soft pity ramp, fewer than 1% of pity cycles actually reach pull 90.
**The 50/50 system** adds another layer. When you pull a 5-star on a featured banner, there is a 50% chance it is the featured character and a 50% chance it is a standard character. If you lose the 50/50, your next 5-star is guaranteed to be the featured character. This means getting a specific featured character can require up to two full pity cycles in the worst case.
FAQs
**Q: Why do most Genshin players get their 5-star around pull 76-80 instead of at pull 90?** A: Soft pity dramatically increases your per-pull rate starting at pull 74. By pull 78, your individual pull rate exceeds 30%, making it statistically very likely you win before reaching hard pity. The cumulative probability of getting a 5-star by pull 80 is around 65-70% for a fresh pity counter.
**Q: What does "On 50/50" vs "Guaranteed" mean?** A: "On 50/50" means you have not yet lost a 50/50 on this banner type — your next 5-star has a 50% chance of being the featured character. "Guaranteed" means you previously lost a 50/50, so your next 5-star is guaranteed to be the featured character. Choose "No 50/50" for standard banners or weapon banners that do not use this system.
**Q: Are the game presets accurate?** A: The presets use pity parameters that match community-tested and datamined values for each game. Soft pity thresholds and rate increases are based on large-scale statistical analysis by the gacha gaming community. However, game developers can change these values in updates, so always verify against the latest in-game details.
**Q: How does cost estimation work?** A: You enter the cost per pull in your own currency. The calculator multiplies this by your planned pulls and expected pulls to show total and average cost. It does not assume any specific real-world pricing, exchange rate, or top-up bonus — you provide the number that matches your situation.
**Q: Can I use this for weapon banners?** A: Yes, by using Custom mode. Weapon banners often have different pity thresholds. For example, Genshin Impact's weapon banner has a hard pity of 80 with the Epitomized Path system. Enter the specific parameters for your weapon banner and set the 50/50 mode accordingly.
**Q: What is the expected pulls number?** A: Expected pulls is the statistical average — if you repeated this process thousands of times, this is the average number of pulls it would take. Some attempts will be luckier (fewer pulls) and some unluckier (more pulls). The percentile milestones show you the full distribution.
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