01 · THE MODEL
First, describe the gear's current state
Overload gear has three line slots. For each slot, the calculator records whether a line is present, which effect it has, its Tier, and whether the slot is permanently locked. You can choose one to three target effects and optionally set a minimum Tier for each.
For example, your goals could be Attack at T10 or higher and Max Ammo at T7 or higher. A target effect below its Tier requirement is not complete. If you choose no minimum Tier, the effect only needs to appear. The calculation stops when every goal is met.
AEffectsWhether a target line appears and which slot it occupies.
BValuesWhether each target line's Tier meets its threshold.
CLocksWhich slots are kept for the next action, and what that costs.
If you start with gear that has not been Overloaded, the model includes the initial cost of 1 Custom Module and assumes that every line appearing on the first Overload is T11. If you enter existing gear, the estimate starts from that state and excludes resources spent in the past.
02 · PROBABILITIES AND RESOURCES
How does each reroll work in the model?
When changing effects, the chance of a line appearing depends on its slot: 100% for slot 1, 50% for slot 2, and 30% for slot 3. Effects already present on the same piece are excluded. The remaining effects are sampled according to their 10% or 12% weights, renormalized over the eligible effects. So a 10% weight does not always mean a 10% chance on a particular roll.
Slot 1100%
Slot 250%
Slot 330%
The configured Tier probabilities are 12% each for T1–T5, 7% each for T6–T10, and 1% each for T11–T15. When Change Effects rolls the same effect back into the same slot, its previous Tier is excluded and the remaining probabilities are renormalized. Reset Attributes also excludes the previous Tier in every rerolled slot.
Costs are part of every decision- Each Change Effects or Reset Attributes action has a base cost of 1 module.
- Each locked slot adds 1 module to that action's cost.
- Adding the first permanent lock costs 2 more modules; adding a second costs 3 more. Up to two slots can be locked.
- Unlocking does not refund its cost, and reroll costs already paid are not refunded if you keep the old result.
Change Effects rerolls the effects, Tiers, and whether a line appears in each unlocked slot. Reset Attributes keeps the effects and only rerolls Tiers on unlocked slots that already have a line. Empty slots stay empty.
03 · FINDING A STRATEGY
Compare the remaining journey, not just the next roll
One action may cost more now but preserve lines that are close to your goal. Another may be cheaper now but lead to many more rolls later. Looking only at the next cost or hit chance can therefore lead to a poor choice. The solver accounts for every possible next state. Breaking a long process into states and reusing each state's best future result is called dynamic programming.
The solver lists the available actions and locking choices for each state, then calculates the possible outcomes and their probabilities. For each outcome, it compares keeping the old lines with adopting the new result. It chooses the action with the lowest total expected cost.
1List the states
Record the three effects, relevant target Tier categories, and locked slots.
2List available actions
Consider changing effects or resetting values, and which slots to lock, retain, or unlock first.
3Calculate all possible outcomes
Use slot rates, effect weights, Tier probabilities, and costs to calculate expected remaining spend.
4Choose the lowest-cost action
The result is a policy indexed by state. After the gear changes, look up the recommendation for the new state.
The implementation uses modified policy iteration to find the policy. It estimates the future cost of the current recommendations, improves actions that reduce that cost, and repeats until the estimates stabilize. This is the numerical method used to solve the model; the probability-weighted equation above describes how each state's cost is compared.
That is why Pro's keep-or-adopt rule is not based on whether the new lines look better. It compares their expected future costs. If the new state is not cheaper than keeping the old lines, the model recommends keeping them. If costs tie, the simulator adopts the new result.
Why compare two strategies?
The calculator compares an interleaved strategy with a two-stage baseline. The interleaved strategy can choose between changing effects and resetting values in each state, so it may improve the Tier of an existing target before all target effects are present. The baseline first obtains all target effects and only then resets values. Comparing them shows how much expected cost the more flexible strategy may save.
04 · SIMULATION AND INTERPRETATION
The average is not anyone's guaranteed bill
Expected cost is a long-run average calculated from the probability model. It does not mean every run will cost the same. A real sequence may reach the goal quickly or encounter many unfavorable rolls.
To show the range of possible costs, the tool uses Monte Carlo simulation: it repeatedly samples complete reroll journeys using the recommended policy and records each run's cost. P50 is the median, so about half the simulated runs cost no more than this value. About 90% are at or below P90, and about 95% are at or below P95. The Quick Estimate page rounds the interleaved strategy's simulated P90 up to a whole module as a budget guide, not a guarantee.
Expected valueThe model's average total cost, not a prediction for one run.
P50The median simulated cost, a typical point in the distribution.
P90 / P95More conservative budget guides; a few runs can still exceed them.
A simulation mean close to the expected value calculated by the state-policy model is a useful cross-check. A difference may simply come from sampling variation when the number of runs is finite. The Pro page shows the standard error and other details to help interpret the comparison. A fixed random seed makes the same simulation reproducible; it does not make actual in-game rolls predictable.
05 · SCOPE AND LIMITATIONS
The estimate depends on the model inputs
The estimate answers: “Given the probabilities, costs, and actions listed here, how many Custom Modules should I expect to spend if I follow the lowest-expected-cost strategy?” It is not an official guarantee of game outcomes and cannot account for probabilities that are undisclosed or have changed.
- For existing gear, resources spent before the entered starting state are excluded.
- The model supports up to three target effects, three slots, and two permanent locks.
- To reduce computation, non-target effects are grouped by their 10% or 12% weight. Names within a group do not affect modeled draw weights or available actions; actual simulation and display still retain each effect's identity.
- The model excludes Custom Lock alternatives, material acquisition rates, farming time, and joint optimization across multiple pieces of gear.
- The interleaved solver is limited by the state space the browser can handle. If the limit is exceeded, the interface says so and provides an estimate using the two-stage baseline; that result is not an interleaved solution.
REFERENCE · TERMS AND SOURCES
Terms and implementation details
- Expected value
- Multiply each possible outcome by its probability, then add the results. Here it means the average resources needed to complete the goals.
- Dynamic programming
- Break a long process into states, calculate the best future cost from each state, and reuse those results to make current decisions.
- Markov decision process (MDP)
- A mathematical model of states, available actions, random outcomes, and costs. Rerolling can be represented this way.
- Bellman equation
- A recursive relationship used in dynamic programming: the best current cost is the immediate cost plus the probability-weighted future cost, minimized over available actions.
- Modified policy iteration
- An iterative solver that evaluates a policy and improves its actions in repeated rounds until the result converges. It is used by the interleaved solver.
- Monte Carlo simulation
- Repeatedly sample outcomes from the specified probabilities to observe a cost distribution. Here it estimates percentiles and cross-checks the theoretical mean.
- State compression
- Merge states that have identical probabilities and goal checks for the strategy, reducing the combinations the browser must process. The Wikipedia link provides background on state spaces; this calculator's compression is implementation-specific.
Theoretical background: Richard Bellman, Dynamic Programming (1957); Ronald A. Howard, Dynamic Programming and Markov Processes (1960). Bibliographic record
