The Enterprise is investigating an unexplored planet way out in the back woods of the galaxy, where the Klingons have reported seeing the remains of a vessel floating around. Picard and Riker muse on the as-yet-unsolved Fermat's Last Theorem before the ship beams over a piece of the debris from the planets atmosphere to find that it is puzzlingly marked with the NASA emblem from the mid-21st century.
In another crazy twist, even though the planet is basically an ice cube covered by poison gas, Wesley locates a building on the surface surrounded by breathable air. Having nowhere else to look for clues, Riker, Worf, and Data beam down to it to see if they can figure out just what the hell is going on. They find nothing but a revolving door in the middle of nowhere. When they walk through it, they find themselves suddenly inside a glitzy, 20th century hotel casino. The people around them dont show any life signs, and they act as though theyre in some cheesy crime novel. Worf quickly makes the reasonable guess that theyre simulations, but Data says thats not it. Riker's amused by the whole thing until he realizes that they're stuck inside the fake casino.
Eventually they find the long-decayed remains of one of the astronauts from the ship they found in one of the hotel rooms, and in his bedside table they find a novel titled Hotel Royale as well as a journal with only one entry. The journal explains that the astronauts' ship encountered an alien life form that accidentally contaminated the ship and killed his shipmates. Then, in an attempt to make amends, they built a place for him to live based on the book hed had with him. He laments that the book was awful enough that his being trapped in it makes him pray for death.
Armed with these revelations, Riker figures out that people can leave the hotel when the book says theyre supposed to, and comes up with the idea of playing along with the story. He, Worf, and Data take the roles of the foreign investors who buy the hotel at the end of the novel and then leave. Data adjusts the craps dice to his favor and breaks the bank. Once the away team has "bought" the casino, they are allowed to leave, and they safely return to the ship. Riker admits that they're leaving the planet with more questions than they started. Picard tells him that, like Fermats Last Theorem, its a puzzle that might never be solved. (See, about that...)
- Artistic License Physics: The planet is stated to have an average surface temperature of −291°C. This is colder than Absolute Zero (−273°C), which is physically impossible.
- Brainless Beauty: One of the denizens of the casino is an attractive, squeaky-voiced and rather dim young woman who can't seem to handle playing blackjack on her own. Texas is clearly smitten with her.
- Casino Episode: Takes place at an alien casino.
- Cliché Storm: The novel, In-Universe.
- Deliberate Values Dissonance: Upon hearing that the astronaut died peacefully in his sleep, Worf mutters, "What a terrible way to die!"
- Dewey Defeats Truman: Picard says that Fermat's Last Theorem has gone unproven for 800 years. IRL, Princeton mathematician Andrew Wiles came out with his own proof five years after the episode aired, leading the franchise to Retcon this in Star Trek: Deep Space Nine's "Facets", when Dax says one of her previous hosts had the best approach to proving it since Wiles.
- The '80s: The hotel appears to be from this era, probably because that's when this episode was filmed.
- Fixing the Game: Data uses his strength to "reload" the dice at the craps table in their favor — which Data notes were already fixed to favor the house.
- A Form You Are Comfortable With: The aliens needed a place that the human they found could live in, so they created an environment based on a book he had. Too bad it was terrible.
- The Gambling Addict: Texas, though even he bets against Data on the final roll of the dice.
- The Ghost: The woman over whom the bellhop and gangster are feuding in the casino story never makes an appearance.
- Gone Horribly Wrong: The aliens honestly wanted to give the poor guy a place where he'd live out his life happily, and it's just bad luck that all they had to go on was a hack novel.
- Heart Is an Awesome Power: A rare, thoughtful example of Troi's empath abilities helping out. When the away team enters the structure, they fall off the Enterprise's sensors and their communicators stop working. But Troi can still sense Riker; she relays his moods to Picard so the captain has some clue about the situation planetside.
- Idiot Ball: This is essentially a Holodeck Malfunction episode, which makes Riker, Data and Worf's confusion about their environment a little surprising. Since this kind of LARP is a popular form of entertainment in their time, it's odd that it took them so long to figure out what was going on. Or rather, trying to figure out not what it is, but why it's there (which they don't learn until later).
- It Was a Dark and Stormy Night: The opening line of the novel, as Picard is dismayed to learn.
- Looks Worth Killing For: Mickey D namechecks the trope after killing a lovestruck bellboy.Mickey D: You shoulda listened to me, kid. No woman's worth dying for. Killing for. Not dying for.
- Off-the-Shelf FX: The patch for the Charybdis mission is an unaltered Apollo 17 patch. The remastered version changed the text to something more appropriate.
- Railroading: The away team can't leave the hotel by normal means, and their phasers do nothing to the walls. Picard skips to the end of the book and reads that the casino is eventually bought out by "foreign investors," which means the only way for Riker, Data and Worf to escape is to win enough money to "break the bank."
- Screw This, I'm Outta Here!: After listening to the Royale's terrible dialogue over the communicator for a while, Troi can't take any more, and requests Picard's permission to leave the room.
- Stylistic Suck: The acting and dialogue of the denizens of The Royale is pretty hack and clichéd, but then, they live inside a hacky, clichéd novel.
- Suckiness Is Painful: The poor astronaut is forced to spend year after year in the living hell played out in the re-creation of what he describes as a bad novel. He welcomes the death that comes in his sleep.
- Unnaturally Looping Location: The landing party tries to exit the Royale through the revolving door, only to find themselves walking into a different room of the hotel.
- What Year Is This?: A variation. The crew identify the debris of the Charybdis as coming from between 2033 and 2079, as it bears an American flag with 52 stars.
- Win to Exit: In order to leave the hotel, the team has to finish the novel by winning enough money to buy the place.
- Writers Cannot Do Math: A very subtle example. It's a minor plot point when a woman isn't sure whether to hit or stay in blackjack; the man hitting on her advises her to hit, but Data states that the odds favor staying. However, with a hard 13 against dealer's 10, hitting is the mathematically favored move.