Markov Chain Quality Reroll Solver: Probability Math of Masterpiece Gear
Rerolling gear quality at the repair station can turn a cheap Outstanding item into an expensive Masterpiece. However, random clicks can drain your silver quickly. To determine if rerolling is profitable, we model the quality transition as a discrete-time Markov Chain.
Probability State Transitions
The base transition probabilities from any state to a higher quality are:
- Masterpiece: 0.1%
- Excellent: 0.9%
- Outstanding: 9.0%
- Good: 30.0%
- Normal: 60.0%
The expected click cost from a current quality state to your target quality state (e.g. Outstanding to Masterpiece) is calculated using the expected value equation. If the difference between the target market price and your purchase price exceeds the expected reroll cost, the run is profitable.
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