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I read in a magazine that fish use the ice to trap the bait they are eating. To a point i think that could be very true, can see where if bait was running close to shore they could use where the lake bottom and the ice meet to make a dead end for the bait fish. If you get what i mean, not sure if i explained it the best. but if that was true, then very shallow water lines could work well.
the fish you see below were all caught in about 4'-6' , works for me!
theres no such thing as too shallow!
I think 2 feet is too shallow