HAMBURG, Germany—Max Deutsch went through a month of training before he traveled across the ocean, sat down in a regal hotel suite at the appointed hour and waited for the arrival of the world’s greatest chess player.

Max was not very good at chess himself. He’s a 24-year-old entrepreneur who lives in San Francisco and plays the sport occasionally to amuse himself. He was a prototypical amateur. Now he was preparing himself for a match against chess royalty. And he believed he could win.

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