Stropping on cardboard was an educational eye-opener for me. It made me realize, for the first time, just how much the substrate affects results, and not just the compound itself. Also made me realize that the simplest and cheapest of materials can work well, and one doesn't need to spend a lot on fancier strops, if anything at all. Subtle differences in the cardboard itself, and how they 'play' with a particular compound, can make big differences in results. And some steels seem to respond well to it, while others may not. With cardboard over a hard backing (usually wood), I've noticed pretty good results in stropping middle-of-the-road stainless steels like VG-10, 420HC that can be tenaciously burr-prone. White rouge and similar aluminum oxide compounds seem to be a good fit for it. I've used the inside face of Kleenex boxes and cracker boxes to good effect with these compounds in particular. Didn't pick those for any particular functional advantage; it's just that they were conveniently handy in my house.
The main thing to look for, in any stropping substrate, is something that compresses as minimally as possible, and also holds the compound well. Meet those two criteria first, and it becomes much easier to make a strop perform pretty well, if not even excellently.
David