A different kind of random reward
Drops decide whether you find something. Upgrades and crafting decide whether you improve something you already have. The mechanism is similar, a roll against a success chance, but the structure is different: the process is often a ladder of stages, each with its own chance, and each attempt typically consumes materials, currency or the item itself.
Because the stages are linked, the chances compound. That is why a series of individually reasonable percentages can add up to something far more expensive than expected.
Chances multiply across stages
Suppose an item is enhanced through five stages with success chances of 90, 80, 70, 60 and 50 percent. Any single stage looks fine. The chance of getting through all five without a single failure is the product:
0.9 x 0.8 = 0.72, then x 0.7 = 0.504, then x 0.6 = 0.3024, then x 0.5 = 0.1512.
So only about 15 percent of attempts at the whole ladder succeed on a first run. That is the kind of figure that rarely appears on a screen, where players see one stage at a time.
The cost depends on what failure does
How expensive the whole ladder is depends heavily on the failure rule. Here are three common versions, using the same five stages.
Safe failure. A failed attempt costs materials but does not change the item’s level. Each stage is then an independent wait, and the average number of attempts per stage is 1 divided by its chance:
1/0.9 = 1.11, 1/0.8 = 1.25, 1/0.7 = 1.43, 1/0.6 = 1.67, 1/0.5 = 2.00.
The total is about 7.5 attempts for the whole ladder.
Reset on failure. Any failure sends the item back to the start. The average number of attempts for each stage can be built up step by step. If E is the expected attempts to reach a stage, the next stage needs (E + 1) divided by that stage’s chance:
- stage 1: 1 / 0.9 = 1.11
- stage 2: (1.11 + 1) / 0.8 = 2.64
- stage 3: (2.64 + 1) / 0.7 = 5.20
- stage 4: (5.20 + 1) / 0.6 = 10.33
- stage 5: (10.33 + 1) / 0.5 = 22.66
That is roughly 22.7 attempts, about three times the safe-failure figure for the same chances.
Partial loss. A failure drops the item one level, which sits between the two cases above. The exact calculation is more involved, but the cost generally lands between those extremes, depending on how often you slip back.
A further variant destroys the item on failure, in which case the cost must include rebuilding the base item each time. The right figure then depends on what the base item is worth.
Why late stages dominate
In the reset example, the final stage accounts for a large part of the burden: the total reaches about 22.7 attempts, and the last stage alone adds about 12 of them (22.66 minus 10.33), because a 50 percent chance means every earlier stage must be repeated about twice on average. More generally, in a reset system the cost grows quickly as chances fall toward the end of the ladder, since every failure erases the progress made earlier. This is why many games add protective items for late stages.
Average versus spread
As with drops, the average conceals large variation. The chance of completing the ladder on the first run is about 15 percent, while some players will need many runs. The same long right tail described for rare drops, covered in the article on expected attempts, applies here. Budgeting to the average therefore leaves a substantial chance of running short.
Protections and modifiers
Games often include tools that change these numbers:
- Protection items that prevent a level drop or destruction.
- Bonus chance items or events that raise a stage’s rate for a time.
- Counters that increase the next chance after a failure, or guarantee success after a set count, in the manner of pity timers.
- Catch-up mechanics that make repeated failures easier to recover from.
When evaluating one, compare the cost of the protection against the expected loss it prevents. A protection that costs more than the average loss it prevents may still be worth buying for the reduced variance, but that is a personal judgment about risk.
Reading the real cost
A practical way to assess an upgrade path:
- List the success chance of each stage.
- Multiply them for the chance of a clean run.
- Work out what failure does at each stage.
- Compute expected attempts, as above, and multiply by the cost per attempt.
- Check the resource sources for your inputs. Currency that is hard to obtain makes the reset cost heavier, a theme in resource scarcity.
Designers use these structures partly to create long-term goals and partly to move resources out of the game, and failing attempts act as one of the currency sinks that keep an economy from filling with surplus. That is a legitimate design purpose, though it can feel punishing when failure rates are not communicated clearly.
Summary of the core point
Individual stage percentages are not the cost. The cost comes from multiplying the stages and from what happens when one fails. Any single attempt is still uncertain, and the figures above are long-run averages rather than predictions.