Good sense suggests new tires, perfectly mounted and balanced with pressure dialed in to within 1 or 2 psi. And inspected frequently for anything unusual like subtle odd wear patterns and protruding 3 inch deck screws!!
Having said the sensible and cautious, I run old rear tires, usually down to the first sight of the cord. But my bikes are generally under 50 HP and pretty light weight, and I ride smoothly when I can. I haven't lost the gamble yet, but I'm due. I have come to the tentative conclusion that tires are built with great strength and safety margins.
So, in the end, financial principles apply, in this case the principle is the risk reward ratio. Choose, or invest, as you see fit.
