"The Royale" starts off as a TNG sci-fi mystery but ends up more of a lighthearted comedy piece. The episode does not really cash in either the mystery or comedy direction particularly strong but it is a fun time with the Enterprise crew.
It all begins when the Enterprise finds NASA debris and a lone casino/hotel in a pocket of breathable air on an uninhabitable planet. Riker, Data, and Worf investigate, only to become trapped in the casino/hotel once they pass through the casino's antique revolving door. Once there, they unravel the casino/hotel's mystery as Data and Worf engage in some actually funny business.
"The Royale" offers some unintentional laughs as well: such as Riker, Data, and Worf's supposedly being stuck in the hotel, when it is clear that the actors are simply walking through *full* revolving door rotations, and the 24th Century Picard remarking that "Fermat's last theorem" has been unproven for 800 years, when it was actually proven in 1995 (six years after this episode was aired).