How do the engines and the players say if a side is winning or not? What are the key factors they consider while assigning a score to each side?
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This is extremely simplified, but you can start by counting the “material value” of each position. Give each side 1 “point” for each pawn it has, 3 for each knight and bishop, 5 for each rook and 9 for each queen. Just counting that, every game starts out at 39-39, and now the engine can see that moves that lead to captures are better than moves that don’t, other things being equal.
Of course, mates are the object of the game so you make any position that contains mate worth +200 or -200, so that mates override any considerations of material.
There are a gazillion ways you can refine this, but basically after that you have the software create a list of legal moves from your position, and calculate the value of each of those moves. If you do that once, you’ve got a “1-ply” engine; if it searches two moves ahead you have a “2-ply engine”, and so forth. In general an engine that searches 5-8 moves ahead and always selects its strongest move is a strong enough opponent for 99% of humans.
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