How is the expected number of attempts calculated?

Each enchant attempt is treated as an independent trial with a fixed success probability p (a geometric distribution). The expected number of attempts to the first success is 1 ÷ p. So a 25% success rate averages 4 attempts.

Why does the success rate fall as the enchant level rises?

Higher enchant levels are harder to reach, so the calculator subtracts a fixed penalty per level above +1 from the tier's base rate. The result is floored at 1% so you never see an impossible zero.

What does the chance within 5 tries mean?

It is the cumulative probability of at least one success across five independent attempts, computed as 1 − (1 − p)^5. Even a high cumulative chance is never a guarantee — each attempt is still independent.

How is the expected cost worked out?

Expected cost equals the expected number of attempts multiplied by your cost per attempt (mora plus materials). Enter your real per-attempt cost to get a realistic budget for reaching the target level.

Are the base rates the exact in-game numbers?

No — Genshin Impact does not publish a single fixed enchant table, so the tier base rates and per-level penalty are sensible illustrative defaults. The probability maths itself (geometric distribution) is exact for any rate you choose.

Genshin Impact Enchant & Gear Score Calculator

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This calculator turns Genshin Impact gear-upgrade gambling into clear numbers. Pick a tier and a target enchant level and it tells you the per-attempt success chance, how many attempts you should expect on average, the expected total cost, and your cumulative odds within the first few tries.

How it works

Each enchant attempt is modelled as an independent Bernoulli trial with a fixed success probability p. This is the classic geometric distribution.

Per-attempt rate. The chosen tier sets a base success rate. Each enchant level above +1 subtracts a fixed penalty, floored at 1%.
Expected attempts. The mean number of attempts to the first success is 1 / p. A 20% rate averages 5 attempts.
Cumulative odds. The chance of at least one success in n tries is 1 - (1 - p)^n. This is why your odds within 5 tries are much higher than a single attempt, yet still never reach 100%.

Worked example

Suppose you are taking a Rare (blue) item to +3. The base rate is 55%, minus a penalty of 12 points for the two levels above +1, giving a 43% per-attempt chance.

p = 0.43
Expected attempts = 1 / 0.43 ≈ 2.33
Chance within 3 tries = 1 - (1 - 0.43)^3 ≈ 81.5%

At a cost of 1,200 mora per attempt, the expected cost to land the upgrade is about 2.33 × 1,200 ≈ 2,800 mora.

Tips and notes

Because attempts are independent, a long streak of failures does not make the next attempt more likely — the per-attempt rate is the same every time.
Use the cumulative columns to decide how much currency to reserve before you start.
Replace the per-attempt cost with your real mora-plus-material value for an accurate budget. Everything runs locally in your browser.