And the Houdini offer is a bit of a red herring. I couldn't beat Houdini if it gave me pawn odds. The Budapest is not as bad by any means as giving pawn odds. I might do okay in a 30 minute match if it gave me piece odds and draw odds. Or maybe f-and-g-pawn-odds with draw odds as well. But Budapest odds only, nope. You'd have to offer that as a centaur game.
The better challenge of the Budapest is a round robin centaur match, or just a head-to-head centaur match. Keep in mind in those cases you'll also be able to play the white side.
You don't think I can beat a Master playing the Budapest?