The wandering monster tracking is great, but not quite perfect:
Currently, the counter sticks around after fighting the monster, with a new one getting set the next time you spent an adventure (which might be immediately IF it's not one of the free ones, I haven't fought any of those yet today).
Since mafia does know that you fought the monster on that turn already, could the timer be removed to indicate that you already fought the monster on that turn, rather than pointing you to try and fight him again?