The state for “unknown opposite polarization” can be written as: √(1/2) * ( [ A=(1 ; 0) ∧ B=(0 ; 1) ] - [ A=(0 ; 1) ∧ B=(1; 0) ] )
I don’t follow. I have no idea where this equation is coming from and how to interpret it. Can anyone make me understand this, please?
The concept of the map of alle possible chess positions and alle possible moves with little arrows indicating how good the relative strength of the Mr. Neumann’s move versus Mr Humman’s move is, is not the final representation. Because it leaves open how you rate the quality of a move. Theoretically, a move is either a winning move, a drawing move or a losing move, that’s all there is to it. Any more nuanced rating has to be relative the playing strength of the two players.
Like, it could be that the only game theoretically optimal move is one that leads to a very precise series of moves, where even one divergence is easily exploited even by a weak player. But there is another, theoretically losing move, that can only be exploited by a very precise series of moves, that no human player could be expected to play out in practice. What is the better move in that scenario?
Good players will also often play a “bad” move on purpose against a weaker player to turn a drawn position into a volatile position, because they expect their opponent to make mistakes and lose. Is that a good or a bad move?