I had a free few minutes, so I decided to take stats on the gambling game on an alternate device. I already had a few of the items from the free drops, so I wasn't testing to the full amount from 0.
Owls: Average: 1.08 per chest, would take 56 total chests if starting from 0 (55.56)
Hats: Average: 0.74 per chest, would take 55 total chests if starting from 0 (54.05)
With what I already had, it would have taken 49 chests and cost 735 gems for me to max out (i.e. not from 0). The hats increased once I had all the owls, up to a 1.63 average.
I was just curious, but maybe somebody will find these numbers useful if considering going for it. As for me, I am back to low single digits of each, though I may do another run-through tomorrow if I have time.