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I'm no chess genius, but surely he could explain the situation to Kasparov and politely ask him to lose on purpose. Is he a dickhead or something?
Assuming Kasparov doesn't remember each loop, I'd assume he's probably just going to think you're coming up with some excuse to either beat him or get out of having to playing the game.
Could also just leave out the supernatural part. I think he's going to figure out how to phrase it the right way long before he learns to play well or even plays Kasparov against himself.
Honestly just treat it like the first step of a magic trick, and then when he complies, you vanish from existence and that's actually a pretty sweet magic trick.
Then Kasparov is also released from the loop. He goes on with his life, never realizing that the only time he ever saw magic was the only time the conditions of his own imprisonment ended. He goes on to live the rest of his life, suspecting nothing, but always slightly haunted by that one day he can’t explain.
Oh yeah, don’t believe me? Your first sexual experience was in a kitchen. You like ketchup on your beans. Your favorite car is a …
Kasparov? Yeah, he's a huge dickhead actually.
Alright look mate here’s the deal. I’m stuck in a time loop and I don’t get out of it until I get a blowjob from your mom …