You can write down an equation for evaluating a ray-traced picture with perfect mathematical precision, you just cannot evaluate the integral for any scene that

You can write down an equation for evaluating a ray-traced picture with perfect mathematical precision, you just cannot evaluate the integral for any scene that is non-trivial. MC is the integration technique for it. Edit: so you know exactly what you get, if you keep it simple - the gotchas start if you try to be clever and use fewer samples (biased MC)