Gacha Pity Counter Expected Cost
Compute remaining finite hard-pity acquisition expectation from caller conditional per-pull schedule and known failures, not fixed independent geometric chance; no banner/reset guarantee or monetary return claim.
Description
A conditional pity schedule gives success probability after each failure count.
A conditional pity schedule gives success probability after each failure count. Certainty at the final step bounds the remaining wait.1
Enter 1–1000 probabilities 0–1 ending exactly 1, failure count 0–length−1 and nonnegative draw cost. Earlier guaranteed-success entries before the declared failures are inconsistent input. Return expected remaining draws/cost and maximum remaining draws.
When to use Gacha Pity Counter Expected Cost
Use Gacha Pity Counter Expected Cost when you need to evaluate the supplied records under the calculation and evidence rules below. No independent fixed-probability assumption, multi-item guarantee or history verification is supplied.
Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
How to use Gacha Pity Counter Expected Cost and understand its results
- Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
- Enter conditionalSuccessProbabilityByPull, alreadyFailedPullCount, callerCostPerPull using the field table and calculation rules, then run the tool.
- Read expectedAdditionalPulls, expectedAdditionalCost, maximumAdditionalPulls. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| conditionalSuccessProbabilityByPull | Conditional success probability by pull | list of number | Required |
| alreadyFailedPullCount | Already failed pull count | number | Required |
| callerCostPerPull | Caller cost per pull | number | Required |
Enter 1–1000 probabilities 0–1 ending exactly 1, failure count 0–length−1 and nonnegative draw cost. Earlier guaranteed-success entries before the declared failures are inconsistent input. Return expected remaining draws/cost and maximum remaining draws.
expectedDraws=sum(remaining-step survival probabilities) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| expectedAdditionalPulls | Expected additional pulls | number |
| expectedAdditionalCost | Expected additional cost | number |
| maximumAdditionalPulls | Maximum additional pulls | number |
{
"input": {
"conditionalSuccessProbabilityByPull": [
0.5,
1
],
"alreadyFailedPullCount": 0,
"callerCostPerPull": 2
},
"output": {
"expectedAdditionalPulls": 1.5,
"expectedAdditionalCost": 3,
"maximumAdditionalPulls": 2
}
}Limitations and assumptions
No independent fixed-probability assumption, multi-item guarantee or history verification is supplied.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 10,000 entries; string lists to 128 strings of at most 128 characters each. The rules above may impose smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Loot Box Expected Cost Per Item: Collecting all missing items takes longer when draws repeat owned items. A subset expectation accounts for unequal item probabilities. For a complementary task, use Drop Rate Geometric Attempts To Success: A geometric waiting model assumes an independent fixed success probability on every attempt. A confidence target asks for a minimum whole draw count.
References
-
Gacha Pity Counter Expected Cost — tool.io
Similar or alternative tools
- Loot Box Expected Cost Per Item
Collecting all missing items takes longer when draws repeat owned items. A subset expectation accounts for unequal item probabilities.
- Drop Rate Geometric Attempts To Success
A geometric waiting model assumes an independent fixed success probability on every attempt. A confidence target asks for a minimum whole draw count.