Apparently, alotta Houdini’s stuff was real-er-than-real magic, as in most of his accomplishments were legit as opposed to a clever illusion. He did grow up learning “magic”, but if it looked as if he was doing something practically superhuman, it was probably because he really was.
What’s more, the show wasn’t even the end game. When he was a kid his mom got scammed by some mystic or something, so after each show he’d then go out in the streets and expose the manipulative tactics that these guys would use to prey upon the superstitious. In fact, he was friends with the guy who wrote the Sherlock Holmes books, but when that guy’s wife fell sick and he turned to a mystic in hopes he could do something, he got into a disagreement with Houdini because, well, you do the math. So that friendship kinda just ended.
Also Houdini was able to utilize his skills for espionage in cooperation with the Scotland Yard or something.