FMCheck

The idea. A buyer won't pay more than it would cost to make an item at least this good themselves, the cheapest way they can, and a seller won't take much less. So the estimate is that cost, plus what the open slots are worth.

1. Cheapest way to make one (M)

The goal: a clean item with these stats that gains at least the same stat points, within the same number of used slots (so it keeps as many open slots), using the scrolls you entered. The maker picks the best scroll for each step, stops once the goal is reached, and drops an item that can't reach it anymore (or that a Chaos scroll destroyed) and starts again with a new clean item.

M = clean price + C(used slots, points gained)

C(s, 0) = 0
  goal reached
C(s, n) = M
  if n points can't be reached in s slots:
  drop it, start over
C(s, n) = the smaller of M and,
  over every scroll t:
    price_t
  + p_t × C(s − 1, n − gain_t)
      it passes
  + (1 − p_t) × (1 − boom_t) × C(s − 1, n)
      it fails, item kept
  + (1 − p_t) × boom_t × M
      it fails and destroys the item

s = slots left to use, n = points still missing, p = success chance, gain = points one pass adds, boom = chance a failure destroys the item. M appears on both sides, so it's solved by repeating until it settles.

2. Open slots

per stat point = (M − clean price) ÷ points gained

per open slot = the best scroll's
    p × gain × per stat point
  − price
  − (1 − p) × boom × M
  (never below 0)

open slots = per open slot × open slots

Chance of an item like this (doesn't need prices)

clean roll = (max − value + 1) ÷ (max − min + 1)
  for the main stat; range = base ± min(ceil(10% of base), 5)

scrolls = for each scroll you entered:
  sum over k ≥ passed of
    C(used, k) × p^k × ((1 − p) × (1 − boom))^(used − k)
  failed slots go to the scrolls most likely to have failed

chance = clean roll × scrolls

When nothing passed (only failed slots)

A clean item's price is mostly what its slots can still become, so each failed slot takes its share. The base stats keep a small part even when every slot failed.

value = clean price × (10% + 90% × slots left ÷ all slots)

3. Estimate

estimate = M + open slots

It's worked out once with every "from" price and once with every "to" price, which gives the range.

Scroll rates in MapleStory Classic: Lesser 100% (+1), Intermediate 60% (+2), Greater 10% (+3; +4 weapon attack), Chaos 10% (+4; +5 weapon attack) and half of Chaos failures destroy the item. Exact gains per scroll come from the game data.

Assumptions. A failed scroll uses up its slot (checked in game). Dropped or destroyed items count as worth nothing, so the estimate leans a little high. The clean price you enter already covers how good the clean roll is. Real sales can land above or below this: treat it as a ballpark and check what similar items sold for.

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