How is the expected number of attempts calculated?

Each attempt is an independent trial with success probability p, so the number of attempts to land one success follows a geometric distribution with mean 1 divided by p. The tool computes this per level and sums across the range you want to upgrade.

Why does the success rate fall as the level rises?

Most enchant systems make each step harder than the last. The tool models this with a per-level decay: the rate at level L is the base rate multiplied by the decay factor raised to L, clamped at a minimum floor so it never reaches zero.

Is the total cost a guarantee?

No. It is the statistical average. A single playthrough can finish well under or well over the total because each attempt is random. Budget toward the expected total rather than a lucky best case.

What does the floor rate do?

The floor is the minimum success chance an attempt can have no matter how high the level. It prevents the decay curve from driving the rate to an impossible value and keeps the expected attempts finite.

Can I model a system with no failure penalty?

Yes. This tool assumes a failed attempt only costs the attempt cost (materials or gold) and does not destroy the item. If your game downgrades or destroys gear on failure, treat the result as a lower bound on true cost.

Dota 2 Enchant & Gear Score Calculator

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Pushing an item to a high enchant level is rarely about a single lucky click — it is a string of probabilistic attempts whose cost compounds quickly. This simulator models the whole climb so you know the average attempts and total gold before you commit materials.

How it works

Each level has its own success rate, which decays as the level rises, and the average attempts per level come from the geometric distribution:

rate(L)       = clamp(base × (1 − decay)^L, floor, 1)
avgAttempts   = 1 / rate(L)
avgCost       = costPerAttempt / rate(L)
total         = Σ over each level from start to target

Summing per level gives the expected attempts and expected cost for the full upgrade path.

Example and tips

Going from level 0 to 10 with a 95% base rate, 12% decay per level, a 5% floor and 100 gold per attempt costs a few thousand gold on average, with the last levels dominating the bill because their rates are lowest. Stock materials toward the total, not the best case, and consider stopping one level short if the final step’s average cost is larger than the value it adds.