conditions:
• "The two seem to match perfectly."
• no fountain breeding boost
results:
• 96,000 PD used as a deposit
• 325 eggs in total
• 17 event eggs
• 308 normal eggs

My event egg research has concluded. The math should be correct, someone good at math has helped me.
Keep in mind that these are odds and not guaranteed.

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A produced egg has a 5% chance to be an event egg, in other words every 20th egg is an event egg.
(17 event eggs in 325 eggs;  17÷325=0.05)

With a perfect pair, the amount of eggs per day is ~8.
(325 eggs in 40 days; 325÷40=8)

That makes a chance of 28% for one event egg in one day.
(0.05^1×0.95^7×8=0.28)

That being said, the chance for 3 event eggs in one day, the occurrence that brought this research to life, is about 0.5%.
(0.05^3×0.95^5×56=0.0054)(56 is the amount of possibilities that the 3 event eggs can appear in in 8 eggs)

I mainly want to know what difference the breeding boost makes. How likely a message is to appear is interesting too.

16 times thrown a coin into Emera Fountain

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4 "Did you know that coins from the fountain are donated to charity on a regular basis? You have done a good deed! (Nothing happened)"
1 Where did it go? (Nothing happened)
1 Your lucky number today is __ (Nothing happened)

2 Your coin and the one next to it look so similar! (Slightly increased breeding chance)
• eggs: 14
• 38 hours (not using the fountain at 0:00)
1Your coin and the one next to it look alike! (Increased breeding chance)
• eggs: 5
• 22 hours

2 Your coin looks a bit larger than the others! (Slightly increased mega-able chance)
3 Your coin looks much larger than the all others! (Increased mega-able chance)

1Your coin is shining bright in the water! (Slightly increased shiny chance)
1 Your coin is shining much brighter than all the other coins! (Increased shiny chance)

Pecha Berry natures: docile, naive, timid, serious, bashful, jolly, quirky, hasty
Gems: Mystery Boxes, Golden Game Slot, Royal Tunnel, Treasure hunt, Bulletin Board, Emera Beach, Dream World Shop, Rumbling