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.

What is the Dota 2 Enchant & Gear Score Calculator?

Set an item tier, base success rate and decay to see per-level enchant probabilities, the average number of attempts, and the expected total cost to reach your target enchant level using geometric-trial math. It runs free in your browser on Gera Tools, with nothing uploaded.

Dota 2 Enchant & Gear Score Calculator

Name: Dota 2 Enchant & Gear Score Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

Understanding the decay curve

The per-level decay models the common game design pattern where early enchant levels are easy and later ones are punishing. If the base rate is 95% and the decay is 12% per level, the rate at each level looks like:

Enchant level	Success rate
0 → 1	95.0%
1 → 2	83.6%
2 → 3	73.6%
3 → 4	64.8%
4 → 5	57.0%
5 → 6	50.2%
6 → 7	44.2%
7 → 8	38.9%
8 → 9	34.2%
9 → 10	30.1%

Notice that the last level takes an average of about 3.3 attempts, while the first level takes barely more than 1. With 100 gold per attempt, the first level costs on average 105 gold but the tenth costs about 332 gold. Set the floor so the rate never drops below a meaningful minimum — without a floor, the decay formula can reach values like 0.1%, meaning thousands of attempts per level.

Worked cost example

Going from level 0 to 5 with the settings above (95% base, 12% decay, 5% floor, 100 gold per attempt):

Level 0→1: 1/0.950 ≈ 1.05 attempts × 100 = 105 gold
Level 1→2: 1/0.836 ≈ 1.20 × 100 = 120 gold
Level 2→3: 1/0.736 ≈ 1.36 × 100 = 136 gold
Level 3→4: 1/0.648 ≈ 1.54 × 100 = 154 gold
Level 4→5: 1/0.570 ≈ 1.75 × 100 = 175 gold
Total average cost: approximately 690 gold for 0→5

Extending from level 5 to 10 costs significantly more than 0 to 5 because the rates are lower throughout. This is why the total is often dominated by the final few levels.

Budgeting strategy

The expected total is an average — individual runs can be much cheaper or much more expensive. Key principles:

Budget toward the expected total, not the best case. The geometric distribution has no upper bound; rare but real runs can cost 5–10× the average.
Consider diminishing returns. If the stat bonus per enchant level decreases as the level rises but the cost per level increases, there is a crossover point where further enchanting is not worth it.
Stop loss. Decide in advance how much you are willing to spend. If the item is lost or becomes obsolete, that gold is gone.
Materials first. For crafting systems where enchant materials must be farmed, compute the total expected material cost before farming so you know what session length to plan for.