This episode is a nominee for the DITL "Worst of Trek" award.
Scanning the planet's inhospitable environment, the crew discover a strange 'stable spot', an area where an Earth-type environment exists within ammonia hurricanes. Riker leads Data and Worf down to the surface to investigate; they find a revolving door sitting in blackness. Passing through the crew find themselves within an Earth hotel, typical of the 20th century! All inside seem oblivious to anything strange about their situation, and politely refuse to believe any talk of other worlds. Worse, there seems to be no way out of the hotel; the doors simply lead back into it, whilst the walls prove unexpectedly phaser proof.
As they investigate they find the dessicated remains of Colonel Richey in a bedroom. A message written by him reveals that the crew of the Charybdis was killed in an encounter with an alien life form, an apparent accident. Seeking to make amends, the aliens created an environment for Richey to live in; with no knowledge of what would be suitable for him they based the environment on "Casino Royale", a book which was aboard the ship. Unfortunately the book is horribly written, and Richey's existence within it was a torture from which death was a merciful release.
Picard sets out to read the novel so as to get some idea of how the story concludes. On his advice Riker and Data win a huge sum at the gambling tables, buy the hotel out, and bring the story to its ending. They find themselves able to walk out of the front door and return to the Enterprise.
And a special note... I feel bad criticising Picard's waffle about Fermat's Last Theorem, because it seemed like an attempt to give a bit of airtime to a real life mystery, which is a good thing... but it just felt awkward and rather forced. It also seems to be a bit of a step too far in the development of "Picard, man of a thousand hobbies." I didn't like it. Neat to see holoprojectors in use, though.
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