The percentage chance to get the item per single wish.
How many times you plan to wish or spawn.
Enter the number of wishes at which a drop is guaranteed (Hard Pity). Leave blank if none.
Success Probability (At least 1):0%
Expected Successful Spawns:0
Wishes for 50% Chance:0
Wishes for 99% Chance:0
Optimizing Your UDAE Strategy
In the world of UDAE (Universal Defenders / Dimensions: Anime Edition and related gacha-based ecosystems), managing your resources is the key to building a powerful team. Whether you are hunting for a Mythic unit or a limited-time character, understanding the mathematics behind the Wish Spawn Rate can save you valuable currency and frustration.
How the Calculator Works
This tool uses binomial probability principles to determine your likelihood of success. It takes your base spawn rate—often a very small percentage like 0.5% or 1%—and calculates the cumulative probability of obtaining at least one desired unit over a set number of attempts.
Key Metrics Explained:
Base Spawn Rate: The raw percentage chance defined by the game for a specific rarity tier (e.g., Legendary, Mythical).
Success Probability: The statistical chance that you will walk away with at least one copy of the item after spending your wishes.
Expected Spawns: The average number of items a player would get with your number of wishes over an infinite number of simulations.
Understanding "Gambler's Fallacy" in Spawns
One common misconception in UDAE wish mechanics is believing that past failures increase future chances (unless a hard pity system is explicitly active). Without a pity system, every wish is an independent event. If you have a 1% spawn rate, your 100th wish has the exact same 1% chance as your first wish.
However, cumulatively, the odds favor you the more you attempt. For example, with a 1% rate, 100 wishes gives you roughly a 63.4% chance of success, not 100%. This is why calculating the "Wishes for 99% Chance" is crucial for guaranteeing results in your planning.
Pity Systems and Hard Caps
Many modern gacha systems implement a "Pity" mechanic. This calculator includes a field for Hard Pity. If your number of wishes exceeds the Pity Threshold, the probability of success effectively becomes 100%. Knowing your distance from pity allows you to decide whether to spend currency now or save for a banner with better rates.
function calculateOdds() {
// Get input values
var rateInput = document.getElementById("baseRate").value;
var wishesInput = document.getElementById("totalWishes").value;
var pityInput = document.getElementById("pityCount").value;
// Parse values
var rate = parseFloat(rateInput);
var wishes = parseInt(wishesInput);
var pity = parseInt(pityInput);
// Validation
if (isNaN(rate) || rate < 0 || isNaN(wishes) || wishes = pity and pity is set (>0), success is 100%
if (!isNaN(pity) && pity > 0) {
if (wishes >= pity) {
probSuccess = 1; // Guaranteed
}
// Note: Accurate pity calculation involving soft pity ramps requires complex simulation.
// This calculator assumes standard probability until the hard pity cap is hit for the guarantee check.
}
// Expected Value (Average number of drops)
var expectedDrops = wishes * probabilityDecimal;
// Inverse calculation: How many wishes needed for X% confidence?
// n = log(1 – confidence) / log(1 – p)
var wishesFor50 = Math.ceil(Math.log(1 – 0.50) / Math.log(chanceOfFailure));
var wishesFor99 = Math.ceil(Math.log(1 – 0.99) / Math.log(chanceOfFailure));
// Edge case: if rate is 0
if (rate === 0) {
wishesFor50 = "Infinite";
wishesFor99 = "Infinite";
}
// Edge case: if rate is 100
if (rate >= 100) {
wishesFor50 = 1;
wishesFor99 = 1;
}
// Display Results
var resultDiv = document.getElementById("results");
resultDiv.style.display = "block";
document.getElementById("probResult").innerText = (probSuccess * 100).toFixed(4) + "%";
document.getElementById("expectedResult").innerText = expectedDrops.toFixed(2);
document.getElementById("wishes50").innerText = wishesFor50;
document.getElementById("wishes99").innerText = wishesFor99;
}