Horrible:Meh:Adequate:
Good:Fantastic

The crew stumbles across some old debris, and it turns out to have "NASA" stamped on it, as well as the American flag. But if you think this is an episode about the old space program, it's not. Immediately after that first scene, it becomes something else entirely.
But first, Picard is musing in his ready room over an old math equation that happens to be based in our own reality. Fermat's Theorem is that
a to the
nth power plus
b to the
nth power equals
c to the
nth power cannot be solved where
n is greater than 2. The story is that this was found scrawled in the margin of one of Fermat's math books, and that he also noted that he had proof, but presumably didn't bother to write it down because it wouldn't have fit in the margin. This occurred in 1637, and for centuries people have been trying to come up with proof that the theorem is correct. Picard finds it intriguing because,
...it puts things into perspective. In our arrogance, we feel we are so advanced. And yet, we cannot unravel a simple knot tied by a part-time French mathematician working alone without a computer.
I think what Picard is saying is that it keeps us grounded as humans, but yet also proves that our simple humanity is still supreme over whatever technology we've created. I'm only going this far into dissecting this little exposition because it's fascinating to me that just a few years after this episode aired,
the theorem was proven. I don't understand the math of it, but it goes something like in order for the equation to be true,
this must be true, and
that must be true, and since those two things contradict each other, the equation can have no solution. It's just neat to me that for hundreds of years the equation was a puzzle, then Star Trek decided to use it as a metaphor, and it was immediately solved and forever messed with the timeline of the show.

But on to the story, on the horrible uninhabitable planet below, there is inexplicably a pocket of breathable air and a large building. Riker, Data, and Worf beam down to check it out. They enter the building, and find that it is a 20th century American casino swarming with people. But they have no life signs, so they're not really there. They waste some time trying to talk to people, but they seem to know nothing outside of the events at the casino. When the away team tries to exit the hotel, the revolving door dumps them right back inside. Oh and, communications are down, as are transporters, because of course they are.
They eventually get to the bottom of what's going on here. Somehow in 2037 the pre-warp NASA ship made it to this point in space, presumably with help from curious aliens. The crew died due to the alien interference, except Colonel Richey. The aliens felt bad about the accident, but didn't know what to do with Richey, so they attempted to make accommodations for him that he would enjoy. As a model for society, they used a cheesy novel that was on board the ship. So The Royale hotel operates exactly like the novel. The colonel lived in this phony reality for 38 years, until he died in his sleep.

With the only other idea being to slice into the habitable section and hope to beam the trio out before the planet consumes them deemed too risky, they set about an alternative way to exit the hotel. In the novel, the casino gets bought out by foreign investors who then leave town. They figure that if they can take on the role of the foreigners and acquire the hotel, then they will be able to leave. So basically it becomes a video game that they have to beat. Data fixes some dice and in short order raises the millions needed to buy the joint, and they walk out the door and get beamed back to the ship. There Picard says that like Fermat's Theorem, the exact events surrounding the missing ship and the aliens may never be explained. But that's since been solved, so can we dive a bit deeper here?

I have questions. First, why were they trapped in the hotel? This question is directly raised in conversation, but then they go on to finding a technobabble solution rather than answering the actual question of why it was the intent of the aliens that Richey not be able to leave. And why can they beam through the planet's goings-on but not through the hotel? Was Richey ever able to solve the puzzle? I guess that without a ship waiting to beam him up there was no reason for him to exit the hotel. Was the story just looping over and over for him the whole time, or was it one long and drawn out version of the novel? More importantly, why didn't the crew of the Enterprise attempt to extract the remains of Richey and give him a proper burial? Or destroy the hotel so that no one else gets trapped? Is there a follow-up to incidences like this where later a team of scientists come in to clean up? What happened to the aliens? So many loose ends...

The video game premise of this episode is repeated (in much better fashion in my opinion) in DS9's "Badda-Bing Badda Bang." It's almost identical. There's a casino, a takeover, and the crew must find a way to cheat the system and prevent the buyout. The strange habitable bubble on a wasteland planet idea is also later recycled in TNG's own "The Survivors." There an alien accidentally destroys everything, and sets up an ideal little world for himself to live in. I guess this proves that "The Royale," though certainly flawed, is a high-concept with enough meat to make it a very
Good episode of Trek. There's the lost NASA explorer, the mystery of the hotel, the absent alien overlords, and the good old-fashioned solution that lets them escape the casino. Perhaps that's the better parallel to draw with the long-unsolved equation. It's not that it means that some things we will just never know. Rather, it means that sometimes a solution can be found rather quickly with a fresh set of eyes. In 38 years, Richey found no way of escaping or even stopping the insipid events of the characters going on around him. But in under a day, our heroes bought the hotel and stopped the whole thing.
Published April 20, 2018
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