✨ Trait Reroll Calculator
Calculate expected reroll attempts and gem costs to get your desired trait.
Data Source:youtube_guides•Updated: 2025-12-17•Confidence: A
Input
RulerMythic
+100% Damage, One Placement
The most powerful damage trait. Doubles all damage dealt by the unit. Reduces placement limit to 1 but massively increases power. Also called 'Monarch' in some translations.
📊 Results
Expected Attempts (E = 1/p)
1,000
≈ 50,000 gems
Percentile Thresholds
50% chance
693 attempts(34,650 gems)
75% chance
1,386 attempts
90% chance
2,302 attempts(115,100 gems)
95% chance
2,995 attempts(149,750 gems)
99% chance
4,603 attempts
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 | Rarity | Probability | Expected | Effect |
|---|---|---|---|---|
Ruler | Mythic | 0.10% | 1,000 | +100% Damage, One Placement |
Duelist | Legendary | 0.80% | 125 | +25% Crit Chance, +15% Range, +20% Boss Damage |
Sacred | Legendary | 0.30% | 333 | +75% Damage |
Scarred | Legendary | 0.30% | 333 | +25% Damage, -15% Cooldown, +25% Range |
Wizard | Epic | 2.00% | 50 | +35% Damage, +15% Range |
Fortunate | Epic | 2.00% | 50 | +30% Damage, +20% Coin Bonus |
Prodigy | Epic | 2.00% | 50 | +XP Bonus |
Agile | Rare | 5.00% | 20 | +Movement Speed, +Attack Speed |
Swift | Rare | 5.00% | 20 | +40% Attack Speed |
Mighty | Rare | 5.00% | 20 | +25% Damage |
Sturdy | Rare | 5.00% | 20 | +50% Health |
Keen | Common | 10.00% | 10 | +15% Damage, +10% Range |