Loot Drop Probability Calculator

ANA›Life Services Authority›National Calculator Authority›Loot Drop Probability Calculator

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Loot Drop Probability Calculator

Calculate the probability of obtaining a specific loot item at least once given a base drop rate and number of attempts (kills/runs/chests).

Base Drop Rate (%)

Probability of the item dropping on a single attempt (0.0001% – 100%)

Number of Attempts

Total kills, runs, or chests opened (1 – 1,000,000)

Pity Timer (optional)

Guaranteed drop every N attempts (leave blank if no pity system)

Target Probability (%)

Desired probability — calculates attempts needed to reach this chance (1% – 99.9999%)

Calculate Results will appear here.

function looCalc() { const resultDiv = document.getElementById('loo-result');

const dropRateInput = document.getElementById('loo-drop-rate').value.trim(); const attemptsInput = document.getElementById('loo-attempts').value.trim(); const pityInput = document.getElementById('loo-pity').value.trim(); const targetInput = document.getElementById('loo-target-prob').value.trim();

// Validate drop rate if (dropRateInput === '') { resultDiv.innerHTML = 'Please enter a base drop rate.'; return; } const dropRate = parseFloat(dropRateInput); if (isNaN(dropRate) || dropRate 100) { resultDiv.innerHTML = 'Drop rate must be between 0.0001% and 100%.'; return; } const p = dropRate / 100; // probability per attempt

// Validate attempts (optional if target prob is given) let attempts = null; if (attemptsInput !== '') { attempts = parseInt(attemptsInput, 10); if (isNaN(attempts) || attempts 1000000) { resultDiv.innerHTML = 'Attempts must be between 1 and 1,000,000.'; return; } }

// Validate pity (optional) let pity = null; if (pityInput !== '') { pity = parseInt(pityInput, 10); if (isNaN(pity) || pity 1000000) { resultDiv.innerHTML = 'Pity timer must be between 1 and 1,000,000.'; return; } }

// Validate target probability (optional) let targetProb = null; if (targetInput !== '') { targetProb = parseFloat(targetInput); if (isNaN(targetProb) || targetProb = 100) { resultDiv.innerHTML = 'Target probability must be between 1% and 99.9999%.'; return; } }

if (attempts === null && targetProb === null) { resultDiv.innerHTML = 'Please enter either Number of Attempts or a Target Probability (or both).'; return; }

// ── Helper: probability of at least one drop in n attempts WITH pity ── // With pity every K attempts, guaranteed drop occurs at attempt K, 2K, 3K, ... // P(at least one drop in n attempts with pity) uses inclusion-exclusion approximation: // The model treats it as: probability of NOT getting a drop in a full pity cycle of K attempts // = (1-p)^K BUT pity guarantees a drop at attempt K, so P(no drop in cycle) = 0 // More precisely: P(no drop in n attempts with pity) = 0 if n >= pity // For n = pityK) { return 1.0; // pity guarantees at least one drop } // Standard geometric: P(at least one) = 1 - (1-p)^n return 1 - Math.pow(1 - dropP, n); }

// ── Helper: attempts needed to reach target probability (no pity) ── // 1 - (1-p)^n >= T => n >= log(1-T) / log(1-p) function attemptsForTarget(T, dropP) { return Math.ceil(Math.log(1 - T) / Math.log(1 - dropP)); }

// ── Helper: expected attempts to first drop ── // E[X] = 1/p (geometric distribution) // With pity K: E[X] = sum_{k=1}^{K} k * P(first drop at k) // P(first drop at k) = (1-p)^(k-1) * p for k '; const rowStyle = 'style="padding:8px;border-bottom:1px solid #ddd;"';

// Expected attempts to first drop const expAttempts = expectedAttempts(p, pity); html += 'Expected Attempts for First Drop'; html += '' + expAttempts.toFixed(2) + ' attempts';

// Expected drops per 100 attempts
const expDropsPer100 = pity !== null
? (100 / expAttempts).toFixed(4)
(100 * p).toFixed(4); html += 'Expected Drops per 100 Attempts'; html += '' + expDropsPer100 + '';

// Probability over given attempts if (attempts !== null) { const prob = probAtLeastOne(attempts, p, pity); const probPct = (prob * 100).toFixed(4); html += 'Probability in ' + attempts.toLocaleString() + ' Attempts'; html += '' + probPct + '%';

// Expected number of drops in n attempts
const expDrops = pity !== null
? (attempts / expAttempts).toFixed(4)
(attempts * p).toFixed(4); html += 'Expected Drops in ' + attempts.toLocaleString() + ' Attempts'; html += '' + expDrops + ''; }

// Attempts needed for target probability if (targetProb !== null) { const T = targetProb / 100; let needed; if (pity !== null && T >= 1.0) { needed = pity; } else if (pity !== null) { // With pity: if target = probAtPity) { needed = pity; } else { needed = attemptsForTarget(T, p); needed = Math.min(needed, pity); } } else { needed = attemptsForTarget(T, p); } html += 'Attempts Needed for ' + targetProb + '% Chance'; html += '' + needed.toLocaleString() + ' attempts'; }

// Milestone probabilities (25%, 50%, 75%, 90%, 99%) html += 'Milestone Attempts (no pity)'; const milestones = [25, 50, 75, 90, 99]; milestones.forEach(function(m) { const n = attemptsForTarget(m / 100, p); html += '' + m + '% chance'; html += '' + n.toLocaleString() + ' attempts'; });

html += ''; resultDiv.innerHTML = html; }

#### Formulas Used

Probability of at least one drop in n attempts: P(X ≥ 1) = 1 − (1 − p)n

where p = drop rate per attempt (e.g. 5% → p = 0.05).

Attempts needed to reach target probability T: n = ⌈ log(1 − T) / log(1 − p) ⌉

Expected attempts to first drop (no pity): E[X] = 1 / p   (Geometric distribution)

Expected attempts to first drop (with pity K): E[X] = Σk=1K−1 k · (1−p)k−1 · p  +  K · (1−p)K−1

The pity term adds K × P(no drop in first K−1 attempts), guaranteeing a drop at attempt K.

#### Assumptions & References

More Calculators

References

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