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Originates from game theory, (the field of math, not the Youtube channel.) The 0 is replaceable with any number, usually no higher than k1. Describes how many "levels" of thinking someone exhibits. k0: I am going to play scissors. k1: I know Bob usually plays paper, so I'm going to play scissors. k2: Bob knows I usually play rock, so he will play paper, and to beat him I will play scissors. k3: Bob is aware that that I know he usually plays scissors, and that I'll play rock to beat him, so he will play paper. To beat that, I will play scissors. etc.
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