Buying rare chests vs. winning rare chests

In the last couple of days I played a lot, won a lot of free rare chests (arena, daily stuff). Today I bought some rare chest - well not only "some" if you catch my drift. So anyway, I started to realize, that I have never ever seen 2000 or even 3500 feathers in a rare chest, that I won from the arena or the daily challenge. Also, very rarely I see 200 or 1000 gems in a rare chest (and by seeing I do not mean actually winning it, just seeing another card displaying those items). I just bough around 9-10 rare chest. In two of them I saw a card showing 3500 feathers, in 4 I saw 200 gems. This is a frequency of those high(er) rewards I definitely haven't noticed in in chests that I won from the arena or other sources. And this leads me to my question: is the drop chance for better rewards higher in those chests that you buy than in chests that you win? Has anybody ever experienced the same thing? If there are any of you who don't mind spending couple of gems on chests (I know there are some who don't care about 800 gems for example - me included), could you try to verify this? I know, some will propably call the conspiracy theory card again, but this feels real to me. Better rewards for buying those chest than for winning them seems to be very cheap.
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