Original air date: March 27, 1989
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 planet’s 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 don’t show any life signs, and they act as though they’re in some cheesy crime novel. Worf quickly makes the reasonable guess that they’re simulations, but Data says that’s 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 he’d 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 they’re 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 Fermat’s Last Theorem, it’s 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!"
- The '80s: The hotel appears to be from this era, probably because that's when this episode was filmed.
- Failed Future Forecast: Picard says that Fermat's Last Theorem has gone unproven for 800 years. In real life, 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.
- Fate Worse than Death: Living within the simulation of "The Royale", an extremely lousy novel, with the plot apparently playing on a permanent loop, made Colonel Richey believe he was suffering this. The final entry of his journal (found next to his remains) makes clear that he was eager to die.
- Fictional Flag: The crew discover the body of an American astronaut with fifty-two stars on his flag patch, indicating he came from some time in the early 21st century.
- 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: Rita, 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 Colonel Richey 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. As he notes in his diary:"I hold no malice toward my benefactors. They could not possibly know the hell they have put me through, for it was such a badly written book, filled with endless cliché and shallow characters. I shall welcome death when it comes."
- 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.
- In the Back: The Love Triangle between the Bellboy, Mickey D (the gangster) and Rita ends with Mickey D shooting the Bellboy in the back while he's walking to the door.
- It Was a Dark and Stormy Night: The opening line of the novel, as Picard is dismayed to learn.Picard: It's not a promising beginning.
Troi: It may get better.
- 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.
- Meaningful Name: The ship that Col. Richey was in is the Charybdis. In mythology, Charybdis was a giant whirlpool that swallowed ships that ventured too close.
- 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.
- Taking the Fight Outside: The assistant manager of the Royale suggests that Mickey D and the Bellboy go outside to resolve their problems. Both of them agree, only for Mickey D to shoot the Bellboy In the Back.
- 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.
- We Will All Be History Buffs in the Future: The away team finds an old astronaut's spacesuit that has the United States flag on it with 52 stars. It is Riker who instantly tells the years when that number of stars was in use, even though Data is accompanying him. The reason is that Riker was born and raised in the United States (more specifically, Alaska), so he probably got US history classes at school.
- 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 the dealer's 10, hitting is the mathematically favored move.
- Your Door Was Open: When Riker, Data and Worf find Col. Richey's room in The Royale, the door is unlocked. While hotel guests normally lock their rooms while they sleep (Richey died in bed), he would have known that the patrons are literary characters and there would be no one who would want to rob his room.