e4, back to chess fundamentals

Chess is a bit of a philosophical paradox, simple in the basics (piece movements, rules) but intractably complex in gameplay. Every game, whether by rank amateur or grandmaster, is as unique as a snowflake (unless both players intentionally follow a previous published game or theory line all the way to the end). And yet at any given point during any game, the allowed moves are quite definite, of finite number (averaging something like 20 or 25 per move over the course of a game), and known to both players at all times.

The basic reason for the complexity is of course "combinatorial explosion", the exponential increase in the number of prospective positions as more than one move into the future is considered. For example, assuming for simplicity 20 choices at each move, while the player "on move" has to decide between only 20, the player waiting has 400 different decisions to consider (until the first player moves), and the first player wishing to consider a mere two-move combination has to consider 8000 different move sequences. Of course "shortcuts" like rules of thumb and preemptive elimination of "obviously bad" moves are absolutely necessary for practical play, but shortcuts are just as obviously suscepible to error (exceptions). Even computers cannot deal completely effectively with the complexities.