I know some guys that fish for them with indicators in muddy water and it certainly is effective. I just love the sight fishing aspect of carp, so I seek them out in water that is clear enough to see them. When it is murky from feeding fish or just dirty water, I try to really move slow and zero in...you can usually see an outline or shape. I am certainly not against an indicator, I just enjoy targeting the fish without one more. The hunt is what gets me about carp...super addictive. One of the best things about carp is how adaptive they are, and the methods I have seen and used are ever evolving out there. I have caught them in 8 different states now and am still surprised by all the different ways they feed and eat flies. They are amazing creatures. It really comes down to the fish you chase. I say all the time that there is no one magic fly for all carp, but is probably one magic fly for your carp...they are just so varied in what they can use for a food source that a ton of methods can apply...just amazing fish!
For nymph/clam eaters, this is my go to fly, the hybrid:
I was shocked this year that the hybrid (small fly) actually worked on the goby eating carp of lake MI. From what I know of Great Lakes carp, they eat a ton of invasive gobies and crayfish...we go there every spring and fish two inch long bunny leeches that would scare carp on my home river the Columbia.