Hi, Yes, in the combinatorial game theory we assume that all the moves are optimal. That’s exactly the reason why we defined N and P positions the way we did.
Sorry sir I didn't understand, if I am in a winning position I'm reaching a P-Position moving from an N-Position, instead if I move from an N-position to another N I'm still in a loosing position?
Moving from N to N is not an optimal move, because it gives the opponent the ability to put you in a P position (and win). We are making the assumption that players make optimal moves for themselves.
