Universal Tower Defense Trait Reroll Calculator
Calculate expected reroll attempts and gem costs to get your desired trait in Universal Tower Defense on Roblox.
Input
Enter a probability percentage (e.g., 0.1 for 0.1%)
Results
Percentile Thresholds
Formula & Assumptions
This calculator uses the Geometric Distribution to model trait rerolling:
- Expected Value (E): E = 1/p, where p is the probability
- Percentile (k attempts for X% chance): k = ⌈log(1-X) / log(1-p)⌉
Assumptions: Each reroll is independent, probabilities are accurate, and RNG is fair.
Example: For p=0.1% (Ruler), expected attempts = 1,000. For 90% confidence, you need ~2,302 attempts.
All Traits Reference
| Trait | Probability |
|---|---|
RulerMythic +100% Damage, One Placement | 0.1% |
DuelistLegendary +25% Crit Chance, +15% Range, +20% Boss Damage | 0.8% |
SacredLegendary +75% Damage | 0.3% |
ScarredLegendary +25% Damage, -15% Cooldown, +25% Range | 0.3% |
WizardEpic +35% Damage, +15% Range | 2% |
FortunateEpic +30% Damage, +20% Coin Bonus | 2% |
ProdigyEpic +XP Bonus | 2% |
AgileRare +Movement Speed, +Attack Speed | 5% |
SwiftRare +40% Attack Speed | 5% |
MightyRare +25% Damage | 5% |
SturdyRare +50% Health | 5% |
KeenCommon +15% Damage, +10% Range | 10% |
BasicCommon No special effects | 62.5% |
How to Use the Trait Reroll Calculator
Step 1: Select Your Target Trait
Choose the trait you want to obtain from the dropdown menu. The calculator includes all available traits from Mythic (Ruler) to Common (Basic), each with their respective probability rates. You can also enter a custom probability percentage if needed.
Step 2: Set Gems Per Reroll
Enter the number of gems required for each trait reroll attempt. The default is 50 gems per reroll, but you can adjust this value based on your current game settings or any discounts you might have.
Step 3: Review Your Results
The calculator will display the expected number of attempts needed, total gem cost, and percentile thresholds (50%, 75%, 90%, 95%, 99%) to help you understand the probability distribution and plan your gem spending accordingly.
Understanding Percentile Thresholds
Percentile thresholds show you how many attempts you need for different confidence levels. For example, a 90% threshold means you have a 90% chance of getting your desired trait within that many attempts. This helps you set realistic expectations and budget your gems wisely.
Calculator Features
📊 Accurate Probability Calculations
Uses geometric distribution formulas to calculate expected attempts and percentile thresholds. All calculations are based on official game probability rates, ensuring accurate results for planning your trait reroll strategy.
💎 Gem Cost Estimation
Instantly calculates the total gem cost based on your expected attempts and gems per reroll. This helps you budget your resources and decide whether it's worth pursuing a specific trait.
🎯 Complete Trait Reference
Includes all available traits with their rarity, probability rates, and effects. Click on any trait in the reference table to quickly select it in the calculator.
⚡ Real-time Updates
All calculations update instantly as you change your selections. See how different traits and gem costs affect your expected attempts and total spending in real-time.
Best Practices for Trait Rerolling
Plan Your Gem Budget: Use the percentile thresholds to understand the range of attempts you might need. For rare traits like Ruler (0.1%), prepare for potentially thousands of attempts. Set a gem budget before starting to avoid overspending.
Consider Trait Value: Evaluate whether the trait is worth the gem cost. Mythic traits like Ruler provide massive damage bonuses but require significant investment. Epic and Rare traits offer good value with more reasonable costs.
Use Percentile Thresholds: Don't just look at the expected value. Check the 90% and 95% thresholds to understand worst-case scenarios. This helps you prepare for the possibility of needing more attempts than average.
Track Your Attempts: Keep track of how many rerolls you've done. If you're approaching the 99% threshold without success, consider whether to continue or save gems for other upgrades.
Frequently Asked Questions
How accurate are these calculations?
The calculator uses geometric distribution formulas based on the official game probability rates. The calculations are mathematically accurate, but remember that probability doesn't guarantee results - you might get lucky with fewer attempts or need more than expected.
What does "expected attempts" mean?
Expected attempts (E = 1/p) is the average number of attempts you would need over many tries. It's not a guarantee - you might get the trait on your first try or need many more attempts. The percentile thresholds give you a better picture of the probability distribution.
Should I reroll for Mythic traits?
Mythic traits like Ruler are extremely powerful but very rare (0.1% chance). They require significant gem investment (50,000+ gems on average). Consider your gem budget and whether the trait's benefits justify the cost for your playstyle and goals.
Can I use custom probabilities?
Yes! If you know the exact probability for a trait that's not in the list, or if the game rates have changed, you can enter a custom probability percentage. The calculator will use your custom value for all calculations.
What if the gem cost per reroll changes?
Simply update the "Gems Per Reroll" field with the current cost. The calculator will automatically recalculate all gem costs based on your new value. This is useful if there are discounts, events, or game updates that change reroll costs.