While Velociraptor would have beaten T. rex in a game of chess - because its cerebrum, the brain's "thinking" part, was relatively larger - T. rex still was no dummy. It's entire brain was the largest by volume of any dinosaur's, and it had the capacity to rule the Cretaceous (with its tiny arms tied behind its back). Here are the facts:
Smell: A dog's "smelling part" of its brain takes up about one-fourth of the brain case, and it's our Excellent Smeller model. A T. rex's smelling part? More than half of its brain capacity! In Jurassic Park, remember when the kid was told to stand still so the can't-see-a-non-moving-boy T. rex wouldn't eat him? Even if that T. rex was blind, he would have smelled that boy, not to mention being able to identify what he'd had for dinner an hour earlier. One boy = one "smelly" appetizer.
Sight: T. rex had an eye about the size of a softball, one of the largest eyes ever developed in the animal kingdom - past or present. This would have included plenty of space for black-and-white and color receptors; since its ancestors (crocs) and its descendants (birds) see in color, scientists think T. rex did, too. Also, it's optic nerve was huge (2 cm), which meant that eyesight was keen - not to mention binocular. That is, since T. rex eyes faced forward, it had three-dimensional depth perception. Distance, size, shape, color, depth, and motion - a two-story-tall eagle.
Hearing: Although T. rex hearing hardware (including a long stapes) seems to closely resemble that of living birds and crocodiles, this sense is harder to pin down. Large internal chambers near the inner ear would have amplified low-frequency sounds...but not much more has been documented. With everything else going on in T. rex senses, even moderate hearing would have been enough for this hunter to ferret out its dinner!