I've heard lots of people say that your visualization abilities get better 'naturally' as you get better. Many say once you get to 1800 or 2000 or whatever random rating you want, you can play blindfold. Maybe not play well, but you can do it. I have not found this to be the case.
If I stare at the board, I can mentally move the pieces several moves, especially if it is forced. If you don't give me a board, I've got almost nothing. Interestingly, you can give me an empty board and I calculate much better.
I spent several weeks working with the ChessEye visualization software, and though I can name all the colours of every square, it had only a small effect on my visualization. All said, though, I may be the worst tactical player rated over 2000 on chess.com, so I may not be the best example of a 'good player'.
So Slemmen, MuensterChess and @chuddog , you guys are actually visualizing the entire board, along with each and every piece on the board? When you make moves, you are still memorizing/visualizing the entire board and pieces as you go?
(I estimate that I've played 1000 games of chess in my life, and that power is not with me yet. Probably about 800 hours of chess) I still lose track of where pieces are at this stage)
Yes, again, the entire position. Otherwise the calculations, long or short, have no value. If you're missing parts of the board in your mind, you're almost certainly missing things in your calculations.
Imagine if you were a quarterback, and you said, "I can throw long and accurately. But... I can only see 2 of my receivers and can't see where the defensive backs are." You'd be laughed off the field.