Vanechka
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If it's just a hobby, then I don't know.
If we're talking about digging in external taverns or allied cities, you can use a ballista-killer simultaneously with the digger, but it's simpler to just use a digger with the city number set to "0".
Then you:
1. Launch the digger.
2. Manually search for the tavern/allied city with the mouse, enter the tavern...
...and the digger completes one cycle there. Then the procedure is repeated.
It's still faster than doing it manually.
Again, all manual operations can be replaced with a ballista-killer, but the process is time-consuming, and you need to make sure that the killer doesn't eliminate too much extra after the hero is found.