The rule of thumb I hear a lot is that each piece
should have two eyes. I always assumed one was for the plant, and the other for the
root, but I never asked.
I have always cut my seed potatoes unless there were more than I had space to plant.
Theoretically, the more starch available, the more the plant can grow without need for external food, but I have never noticed much of a difference in yield or plant size. Perhaps beyond a certain point, the starches are simply utilised by something else in the soil.
You could, perhaps, do a small-scale trial. Divide only what seed potatoes are necessary for the amount of space available to plant, and plant some uncut. Just keep track of which are where, and take note of the comparative plant growth rates, size, and yield, and get back to us at the end of the season.
Otherwise, let us know how you proceed, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein