If you were to try and catch a full set of 18 shiny vivillon, and a full set of 18 Hundo vivillon, that would take approximately 52,000 catches to be 95% sure you catch all the Shiny’s. (You would likely have caught all the hundos before the shinys so the Hundo catches are irrelevant). Assuming you open the most number of gifts possible per day, that means it would take approximately 114 years to catch the full sets with consistent play. I thought it was interesting and decided to share my findings, that it is very nearly impossible to get a complete shiny set. And that is assuming you are able to consistently get postcards from each location.
Here is my math for anyone who would like to double check:
Shiny odds = 1/500
Hundo odds = 1/216 (postcard encounters, 10/10/10 IV floor)
Number of Scatterbug patterns = 18
Goal = 1 shiny + 1 hundo per pattern
Patterns are random
Average catches per day = 1.25 (Takes 15 gifts to get one scatterbug, typically can open 20 gifts per day)
• To have a 95% chance of getting all 18 shiny patterns (random), ~105 unique shinies are needed.
• At 1/500 odds, expected catches = 105 × 500 = ≈52,000 catches.
• Hundo odds = 1/216.
• By 52,000 total catches, expected hundos ≈ 52,000 ÷ 216 ≈ ~240 hundos.
• 240 hundos is more than enough to cover all 18 hundo patterns even with duplicates.
• Total catches needed ≈ 52,000
• Days ≈ 52,000 ÷ 1.25 ≈ 41,600 days
• Years ≈ 41,600 ÷ 365 ≈ ~113.9 years
Final result (95% confidence):
• Total catches ≈ 52,000
• Days ≈ 41,600
• Years ≈ 113.9
by Important_One7294