But of course

Making them last more than one turn, however, is not the issue.
First, "Sea Mines" are not single mines, but fields of mines. That's why they should be persistent after each attack.
The way mines should work, but which cannot be done within the possibilities of the engine:
- Mine-fields should fade-out without the knowledge of either player. Often mines leaked, wiring corroded, the became unanchered or they had some other technical defect and simply ceased to function, unannounced to the owner. Because they were dangerous, you didn't just row out to perform a maintenance inspection. So after a while nobody knew how affective they would be.
- They should require a unit, possibly an engineer, to run the minefield. Minefields often did not have contact-detonators, which were unreliable, but were detonated manually by somebody on shore through a static-electrical charge, IIRC.
- They should have a high variance in effectiveness. Some ships were outright sunk and some only damaged.
- We'd need mine-sweepers; yes, they had mine-sweepers during the civil war

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Of course withing the possibilities of the engine you can mod to your heart's content
