Okay, while this is a real newspaper advert from 1919 (which I recently nabbed on eBay), it is not advertising Nesbit and Houdini in person. These are their respective movies sharing the bill at the Empire Theater.
Nesbit's Woman, Woman was released on January 19, 1919, and this could be an ad for opening day. The reference to "Houdini" is actually The Master Mystery, his 15 part serial which was rolling out chapter by chapter at the Empire and, of course, would play second fiddle to a feature. Here's another Empire ad that makes this a little clearer.
Still, you have to think this kind of supporting player billing would rankle Houdini. It's probably why he went on to make feature films himself after entering the business with Mystery.
But this also makes for an interesting double bill. Although Evelyn Nesbit played fictional characters in her films (she's Alice Lindsay in Woman, Woman), her movies were really about showcasing her in films and situations that echoed her real-life infamy as temptress/victim/fallen woman. This is very similar to how Houdini's movies were really about selling the great escape artist in a fictional context. It's also worth pointing out that real movie fame eluded them both.
Houdini and Evelyn would travel side by side through the 20th Century as representatives of the Gilded Age. Both burst onto the scene in 1900; both had biopics made about their lives the 1950s -- Houdini with Tony Curtis in 1953 and The Girl In The Red Velvet Swing with Joan Collins in 1955 -- and both appeared as characters in the book, play, and film versions of E. L. Doctrow's Ragtime. However, Nesbit's name and fame is fading while Houdini has become a household word.
But lets give this one to Evelyn. At one point she was as famous a Houdini, and I've always had a bit of a thing for her...