It was 30% for me (222 medals in 746 fates which is 29.7%). Sometimes I would go 20+ fates without anything, other times I would get 2-3 in a row. One time I got 5 in a row, I thought I was a god! Then I had nothing for ages :P

Other people posting seem to suggest that over the 222 medals it averages 30%, but as as low as 25% if you're unlucky, 35% if you're really lucky.