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You’ll find that most paintings of players playing chess have a cat somewhere in the scene. This one has a wooden lion and a spider.
Chess skills are most helpful when you are playing chess. However, when you climb & jump on rocks, your entire brain & body are put to work.
The board & pieces are all the material, but the METAGAME dynamic is certainly a factor in competition. The Royal Game by Stefan Zweig is about losing the battle to a weaker player who uses a novel psychology.
That’s me at the board, on the right, maybe 20 years ago.