How do I increase my portrait options on Wordscapes?

It seems there is no way to speed up the acquisition of portraits other than to keep playing. In particular the last few portraits you need to complete a set seem to be programmed to not come easy. I have had situations where I completed a set in one or two sessions. In other cases I played several days to get one remaining portrait. It is a bit frustrating and very annoying to say the least. But it is a game so keep trying or give up whenever you wish