Potatoes - how deep?

I believe that you would get more potatoes earthing up which serves 3 purposes 1/gives frost protection 2/prevents the potatoes going green and 3/helps break up the soil, this is the reason people are advised to plant potatoes in a new garden (its not the potatoes that break up the soil) but I am not sure that you get a heavier harvest with earthing up, as for putting them on the ground and covering them with cardboard I think they would grow aas long as you keep the light off them, as for perforated plastic, yes you will get a crop any rain water will go through the perforations but so would light, whet I have done in the past is covered the ground with black plastic cut a X where I wanted the potatoes and placed them in a slight depression then left them as the shaws came through I covered them with newspapers when frost was forecasted, I did get a good harvest of nice clean potatoes, (remember if you have potatoes growing and they get caught by frost spray them with cold water and cover with newspapers to keep the sunlight off them) as for the last part of your question, I think I would put some compost into the depression to feed the plants and you would get a crop if you keep them covered with cardboard