The Wooden, Golden, and Magical Chests are all available starting with Village 3. The Small Lucky Chest is available at Village 4, Small Easter Chest at Village 10, Big Easter Chest and Emerald Chest at Village 20, Valentine’s Chest and Big Lucky Chest at Village 30, Saphire Chest after Village 70, and the Ruby Chest at Village 110.
These are the official probabilities according to Moon Active, the developer behind Coin Master:
TYPE # OF CARDS 1 STAR CARD 2 STAR CARD 3 STAR CARD 4 STAR CARD 5 STAR CARD JOKER CARD
Wooden Chest 2 86% 48% 18% 15% 2% 0%
Golden Chest 4 60.4% 77.74% 99.5% 35.87% 5.95% 0%
Magical Chest 8 79.21% 94.29% 99.5% 99.5% 23.6% 0%
Mystery Chest 6 0.5% 98.33% 98.33% 99.5% 99.5% 10%
Emerald Chest 4 63.71% 56.13% 80.69% 70.84% 27.1% 0%
Saphire Chest 6 71.78% 79.16% 90.49% 99.5% 38.04% 0%
Ruby Chest 8 56.2% 82.47% 97.19% 99.5% 61.14% 1.9%
Valentine's Chest 6 0.5% 98% 98% 99% 99% 4%
Small Lucky Chest 6 0.01% 98% 98% 99.5% 99.5% 1.4%
Big Lucky Chest 8 55% 82% 96% 99% 60% 14%
Small Easter Chest 6 0.01% 99.5% 99.5% 99.5% 99.5% 2.4%
Big Easter Chest 8 56% 83% 97% 99% 61% 6%