Rerolling item quality at the repair station can turn a cheap Outstanding item into an extremely expensive Masterpiece. But because the quality roll is a game of chance, many players fall into "reroll traps," spending millions of silver without getting the upgrade. In this guide, we will analyze the exact Markov Chain math behind quality upgrades so you can determine if rerolling is actually profitable.
The Upgrade Probabilities
Every time you click the "Reroll" button, the game rolls a random number. The probabilities for upgrading to a higher quality tier are:
- Good (Q2): 30.0% chance
- Outstanding (Q3): 9.0% chance
- Excellent (Q4): 0.9% chance
- Masterpiece (Q5): 0.1% chance
- Normal/No Change (Q1): 60.0% chance
The Click Cost Formula
The cost per reroll click depends entirely on the item's Item Value (IV). The formula is:
IV = (Base IV + Artifact Offset) * 2^enchantment
Click cost = IV * 3.97 * Quality Multiplier. The quality multipliers are Normal = 1.0, Good = 1.25, Outstanding = 1.5, and Excellent = 6.24. This means clicking an Excellent item to roll for Masterpiece is 6.24 times more expensive per click than rolling a Normal item!
Solving the Markov Chain
To find the expected silver cost, we model quality upgrades as an absorbing Markov chain. The expected clicks $E(i)$ from state $i$ to target $T$ is:
E(i) = (Click Cost + sum_{j > i} (P_{i -> j} * E(j))) / (1 - P_{i -> i})
For example, if you have a Tier 8 flat (.0) weapon, the expected silver cost to hit Masterpiece from Normal is approximately 2,500 clicks, which translates to roughly 3.8 million silver. If the price difference between Normal and Masterpiece on the market is 6 million silver, then rerolling is highly profitable! If the difference is only 2 million silver, you will lose silver on average.
Use ScanAlbion's Markov Chain Reroll Solver to instantly calculate the break-even math before wasting silver at the repair station!