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What is the significance of the chess game in the film 2001: A Space Odyssey?

Stanley Kubrick was himself quite the chess fan, and so he picked an actual chess game to feature in 2001, rather than a completely senseless position as so many other films and shows have done. The game he chose was Roesch – Schlage, Hamburg 1910. The position in 2001 is White to move after 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. Qe2 b5 6. Bb3 Be7 7. c3 O-O 8. O-O d5 9. exd5 Nxd5 10. Nxe5 Nf4 11. Qe4 Nxe5 12. Qxa8 Qd3 13. Bd1 Bh3.

Position after 13. … Bh3

Your assessment is correct: White’s development is atrocious and Black’s control of the center and kingside is absolutely brutal. Here White has no options: his best chance to delay immediate mate is 14. Qb7, although even then 14. … Bxg2 15. Qxg2 Nxg2 16. Kxg2 Ng6 should win shortly for Black.

Here’s where the dialogue kicks in in the movie. Frank Poole, playing White, opts for 14. Qxa6. “Anyway, Queen takes pawn,” he says.

“Bishop takes knight’s pawn,” HAL drones. 14. … Bxg2

“Huh, lousy move,” Frank remarks (although based on the opening, he’s not exactly Vishy Anand himself). “Rook to king one.” 15. Re1. The slowest way to stave off mate at this point, though Frank is doomed regardless.

HAL announces forced mate in two: “I’m sorry, Frank–I think you missed it. Queen to bishop three, bishop takes queen, knight takes bishop, mate.” 15. … Qf3 16. Bxf3 Nxf3#.

The funny part about this scene in the movie is that while Frank is indeed correct to resign due to imminent mate, HAL screws up his analysis, twice.

First, HAL says his winning 15th move is “Queen to bishop three”–not actually a legal move on the position in the English notation system that was standard at the time. The move he actually makes would be read as “Queen to bishop six.”

Second, while HAL is right about forced mate, he’s wrong about the number of moves it takes. Frank can in fact hold out for an extra two moves by playing, instead of HAL’s 16. Bxf3, 16. Qh6 gxh6 17. h4 Nh3+ 18. Kh2 Ng4#. HAL still mates, but for HAL–touted as “foolproof and incapable of error”–it’s quite a large oversight.

Now, you can read this as Kubrick screwing up, or–and this is more likely, knowing what a perfectionist Kubrick was–you can read it as very subtly foreshadowing HAL’s later breakdown in the movie. I think the latter’s more interesting.

“Huh. Yeah, looks like you’re right,” Frank admits after a few seconds’ thought. “I resign.”