Why does a three legged support work better than a four legged one?

Three points determine a plane. To put it another way, a plane can always contact any set of three points. So the tips of the legs of a 3-legged support always contact the floor. A 4-legged support has four possible sets of three legs, i.e. four possible planes that it can contact. Unless all four legs are exactly the same length, their ends don't all lie in the same plane. When set down on a single plane ... like the floor ... the support winds up wobbling among different sets of three points.