In the current Carnival Event, I played the random chest for the SOK prize. That way I get a chance at some other prizes too. Here are the statistics from my 4 main worlds of A, D, E & K. (The format was great in mail, not so readable in forums. If you care, you can always copy to a spreadsheet).
SOK SOA SOI WF VT Attempts
A 0 2 1 3 6 12
D 2 0 0 1 5 8
E 1 2 1 2 7 13
K 5 0 0 2 5 12
--- -- -- -- -- -- --
total 8 4 2 8 23 45
% 18% 9% 4% 18% 51% 100%
It's clear the Victory Tower(VT) was NOT the posted 35%, however I did get a serious bonus of 4 SOK on K-world so I'm not complaining too much!
You probably know the abbreviations, but:
SOK = Shrine of Knowledgem gives a forge point
SOA = Shrine of Awe, gives medals
SOI = Shrine of Inspriation, gives blueprint of your age or under
WF = Watchfire, gives small city protection
VT = gives small medals once per week, NOT daily