@Wiggum: By "log", do you mean the chat box in the top right? It would be possible, though I'll have to give it some thought to ensure it doesn't drown out other information. A checkbox in the options menu could toggle this, and there's plenty of request for better roll information overall so I'll have to see if that might make this unnecessary.
I think I could quickly pop in a message on screen for new turns. In the chatbox I think there's already a line saying "a new round begins" and it just says "time passes" if the final end turn hasn't been pulled yet. Also the last end turn counter in the cup will say "TURN" instead of "END TURN" with a circular arrow, but I guess it's not the most straightforward thing. Perhaps I could revisit this alongside the cup chit improvements.
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To address the fate idea a couple posts above, there have been similar suggestions, I'll keep this in mind when I get around to it. Pausing the game like that would only be possible in single player mode, however.