Markov Chain Reroll Solver: Expected Masterpiece Costs

Markov Chain Reroll Solver: Expected Masterpiece Costs

Rerolling gear to Masterpiece quality is a mathematical optimization problem. This guide outlines how to use our Reroll Solver to minimize your costs and maximize your returns.

The Optimal Reroll Strategy

Rerolling is highly profitable for high-tier artifact gear (like T8 Avalonian weapons) where the price difference between Excellent and Masterpiece is tens of millions of silver. Do not waste silver rerolling low-tier flat gear (like T4 swords), as the cost of the reroll click will easily exceed the value increase of the item.

Mathematical Formulation

Using the Item Value (IV) equation, the cost of a reroll click increases with the item's tier, slot, and enchantment. Let C_i be the cost of rerolling at quality i:

C_i = IV * 3.97 * qualityMultiplier_i

Our Markov Chain Solver computes the expected total silver cost to transition from your starting quality to your target quality (usually Excellent or Masterpiece) using transition probabilities.