As stated before it is very random. I've gotten party pieces after barely beating the red king and then gotten coins after getting to the levels with multiple kings. It can be very frustrating indeed.
This is exactly the reason I hate Infinity time and never play it even once! so I won't waste 1 hour of your life for 20K coins!
I just bought 2 upgrade party packs ($10 + $10) for 4 party characters that only cost around 30 min of my working hours which is much more efficient and practical way to invest your precious time.
Another quirk with the infinite infinity chest, or whatever it's called, is that it sometimes will give both stickers for a party character at once. Though I have to say that this is something I heard first hand several times when the game was newer, but have not heard anyone mention it recently.
