As stated, your chances of running into a mine is highly unlikely. Trying to find one would be like looking for a needle in a haystack. There is a minefield in the Tsuyama Strait that if you look hard enough, you'll find them. If they put mines in the stock game, they are very rare to find.
You can find more mines with the supermods. I know TMO has several minefields. I just happened to be looking at my sub when I found this one, but it was too late. You can see the chain and the mine is rubbing near the front of the con tower.
I'm fairly certain mines in TMO are set where you will not hit them running on the surface, just periscope depth only, so you're fairly safe anyway.
Your not going to see mines floating on the top of the water.
Also with TMO there is a sonar mod that detects mines and subnets. Your chances of hitting a subnet is fairly good in many area's...
Still, you don't want to see a mine anyway...or hit one. If you just want to see mines, there are single missions full of them. This one blew, but I made it back to base.
