The chance of penetration for Puma varies wildly depending on range. At max range, vs the Centaur you should have a 50% chance of penetration. At point-blank range the chance becomes 100%. You need 6 penetrating hits (with the Puma) to kill the centaur. Thus, your estimate was entirely correct!
Alternatively, you could use your superior mobility/range/sight and try to flank the Centaur a bit to the side/rear, where you have an almost-guaranteed chance to penetrate.
Thanks for the feedback. Would you build a Puma against a centaur?