This page defines mathematical relationships; it is not a game-data table. Numeric examples are explicitly labeled as what-if arithmetic. A game-specific rate, guarantee, reset, threshold, price, or eligibility rule belongs in a calculator only when an authoritative source supports it or the interface asks the user to enter the current value. See the methodology and evidence policy.
A modifier applied to encounters or items that changes difficulty or value.
Some affixes slow clear speed, reducing GPH even when EV per run is unchanged.
Affixes can indirectly change time/cost assumptions rather than drop rates.
Count of successes in n independent trials with constant probability p.
Exactly k: C(n,k)·p^k·(1−p)^(n−k). Any-unique: 1−(1−p)^n.
If p changes each trial (pity, buffs), use ∏(1−p_i) and its complements instead of a single p.
The chance of seeing an event at least once across N attempts: P(≥1) = 1 − (1 − p)^N.
What-if example: with constant p=1/16 and 20 independent runs, P(at least one)=1−(15/16)^20.
This shortcut requires a constant probability and independent attempts. Changing rates, guarantees, eligibility, or without-replacement draws require a different model.
An interval produced by a stated statistical procedure whose long-run coverage is the named confidence level under that procedure's assumptions.
What-if example: after 200 defined observations, report the estimator, interval method, and 95% confidence interval instead of presenting one sample rate as truth.
The interval is about the procedure, not a guarantee that this one realized interval has a stated probability of containing the parameter. Small samples and changing conditions need special care.
The probability that a defined event occurs in one defined attempt, conditional on the stated eligibility, version, and setup. It may be written as a percentage or 1-in-N.
What-if example: if p=5% is constant and 20 attempts are independent, P(at least one)=1−(1−0.05)^20.
Do not infer a rate from an item name, rarity label, or old patch. Preserve the source and exact attempt boundary.
A pattern where each additional unit of effort yields smaller gains (e.g., scaling penalties or caps).
If a buff stacks with diminishing returns, EV per run increases slower at higher stacks.
Some games apply DR to stats or currencies; not always relevant to drop odds.
A long series of attempts with no desired drop despite p>0.
What-if example: at constant p=5% over 60 independent tries, P(zero hits)=0.95^60≈4.6%.
Avoid gambler's fallacy: odds are not 'due'. Evaluate EV and pacing instead.
Average reward per attempt: EV = Σ(outcome value × probability). Neutral to time; pair with GPH for time efficiency.
What-if example: if the outcome distribution stays fixed, reducing run time changes value per hour but not EV per run.
EV is an average, not a guarantee. High variance may hide long dry streaks despite good EV.
EV translated by your average run time and costs to estimate net profit per hour.
What-if example: 50,000 value per run at 90 seconds per complete run is about 40 runs/hour and 2,000,000 gross value/hour before costs.
Use one complete, repeatable time boundary and the same value unit throughout. Travel, loading, failures, and direct costs belong inside that boundary when applicable.
A guarantee the target rarity drops by a fixed maximum number of attempts.
If an authoritative rule guarantees success by boundary G, reaching G without the guaranteed outcome is a diagnostic state—not evidence that a new cycle should be inferred.
A guarantee bounds the worst case but does not supply the probability of earlier attempts. Reset and eligibility rules must be separately documented.
Repeated drop checks where one outcome does not affect the next.
What-if example: for two independent 2% checks, P(any)=1−0.98²≈3.96%.
Independence must come from the rule or be labeled as a scenario assumption. Pity, lockouts, shared slots, and without-replacement draws can break it.
Attempts whose success chance is unaffected by past outcomes.
What-if example: with constant p=6% over 20 independent trials, P(any)=1−(1−0.06)^20≈71.0%.
If p varies by setup/time, treat as non-identical trials and use the mixed-p formula.
The defined set of outcomes and their probabilities or weights used to generate rewards.
Before calculating, identify the exact edition, version, table path, eligible pool, rolls, conditions, functions, and target entry.
A label or screenshot is not a complete table. Complex nested tables should be resolved from the versioned source before entering a final probability.
Events are mutually exclusive when they cannot occur together in the same defined trial or slot. For mutually exclusive outcomes, P(any)=Σp_i because every pairwise intersection is zero.
What-if example: if one slot can produce A with 2% probability or B with 3% probability, but never both, P(A or B)=2%+3%=5%.
The independent complement product 1−Π(1−p_i) is not the same-slot formula. If a reward has several slots or stages, establish their dependence before combining them.
The 50th percentile: half the outcomes lie at or below it.
Median GPH is robust to jackpots. Compare with EV to understand skew.
In skewed loot, EV ≠ median; players often feel closer to median in short sessions.
A documented stateful rule that changes a future outcome or guarantees one based on prior eligible attempts.
Record the exact eligible counter shown by the game and the published rule. Do not infer a reset, rate curve, or qualifying attempt type that the source does not define.
A guarantee, an increasing conditional rate, and a reward-exchange counter are different mechanisms even when players call all three pity.
A documented hard boundary that guarantees the defined outcome after a fixed number of eligible attempts without that outcome.
At the documented boundary, show a guarantee diagnostic. Do not use modulo arithmetic or assume the next counter state when the user reports a contradictory outcome.
A near-certain rate is not a cap. Eligibility, pause, carry-over, and reset behavior need their own source support.
A cut-point at a chosen probability (e.g., 90th percentile).
What-if example: a 90th-percentile session value describes a distribution cut-point, not a guaranteed personal outcome.
Needs the full distribution (or a good approximation); tails need more data.
The outcome-generation process used for events such as drops or affixes. A probability model describes the distribution; it does not reveal or reproduce a game's implementation.
Two players with the same EV can see different short-term results because RNG streaks are normal in small samples.
Implementations, state, seeds, and server-side rules may be private. Do not claim a calculator predicts individual random outcomes.
A bad-luck protection mechanic where drop probability increases after many misses.
Model only a published per-attempt schedule or values the user can verify. The no-hit probability is the product of each applicable conditional miss probability.
Soft pity changes p across attempts, so a single constant-p binomial shortcut is not valid. Do not invent the curve from community anecdotes.
The square root of variance. It summarizes the root-mean-square deviation from the mean in the same unit as the measured outcome.
If GPH has a large standard deviation, comparing two routes requires longer testing to be confident.
Useful for confidence intervals and A/B comparisons of routes.
The number of observed runs. Larger samples reduce variance of the estimate and tighten confidence intervals.
Comparing two routes with similar EVs requires enough runs to overcome randomness.
Small samples can be misleading, especially with rare, high-value drops.
A named content period that may have its own balance, tables, currencies, and thresholds.
Record the exact season or patch as provenance. Changing a season label must not silently load rates, prices, or thresholds.
LootCalc does not assume a label proves current numeric rules; verify the live UI or an authoritative versioned source.
A boundary where a documented state or output changes, such as a progress slot or track milestone.
Enter the live thresholds you can verify, keep them strictly ordered, and calculate progress without inferring unlisted rewards.
Reset timing, threshold values, and reward consequences are separate facts; do not copy them across versions.
Probability that at least one of several events occurs.
For mutually exclusive events, add their probabilities. For independent events, P(any)=1−∏(1−p_i). In general, use inclusion–exclusion with the actual intersections.
Never choose the complement product merely because it is convenient; the event relationship is part of the model contract.
A measure of the spread of outcomes around the average (EV). Higher variance means wider swings run to run.
Activities with rare, high-value uniques have high variance: long dry streaks followed by spikes.
Variance explains why results can be far from EV in the short term while converging in the long term.
Average where components contribute per weight (time share, frequency, or value).
What-if example: a portfolio average can be Σ(component value × normalized share), provided every value uses the same unit and boundary.
Weights can be any non-negative proportions; normalize if they don't sum to 1.
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