I recall that the client display some complexity nummer for every game you play. Unfortunately, I don't have computer access ATM so I'm not able to run the Java app (it's probably doable on Android, but meh..). I believe most of the worlds abstract strategy games are in the database/library, so you can just check them out.
I also found this: https://boardgamegeek.com/geeklist/284017/estimating-abstract-game-complexity-using-ludii