Rerolling item quality at the repair station can turn a cheap Outstanding item into a highly priced Masterpiece. However, quality rolling is a probabilistic game. To decide if a reroll is profitable, we use a Markov Chain model to solve the expected silver cost.

Quality Upgrade Probabilities

When you click the reroll button, the item has a probability of upgrading to a higher quality tier:

• Good (Q2): 30.0%
• Outstanding (Q3): 9.0%
• Excellent (Q4): 0.9%
• Masterpiece (Q5): 0.1%
• Normal/No Change (Q1): 60.0%

Item Value (IV) & Click Cost

The silver cost per click is directly determined by the item's Item Value (IV). The formula for IV is:

IV = (Base IV + Artifact Offset) * 2^enchantment

Where Base IV = 16 * 3^(tier - 4). Runes add +50, Souls +100, Relics +150, and Avalonian items add +200 to the base value before scaling. The cost per click scales with quality multipliers (Normal = 1.0, Good = 1.25, Outstanding = 1.5, Excellent = 6.24).

Markov Chain Expected Cost Formula

The expected total clicks E(i) from a current quality i to target quality T is solved using the recurrence relations of absorbing Markov chains:

E(i) = (Click Cost + sum_{j > i} (P_{i -> j} * E(j))) / (1 - P_{i -> i})

ScanAlbion's Reroll Solver uses this exact algorithm to let you input item tier, enchantment, artifact type, and current quality, displaying the exact expected silver budget you must prepare to reach your target quality.