Why can a chess move improve the chance of winning, according to the computer? When watching the Sinquefield cup on http://grandchesstour.org/, it is possible to try different moves qnd see how the computer evaluates the position after your suggested move. 

Most moves will impair your position if it is not considered the best move by the computer. But for some moves (quite often) you instantly get an increased chance of winning, perhaps half a pawns advantage. I don't understand this: If a single move has a potential for significantly improving the players position, should this not already be reflected in the current standing before the move? 

In my mind, any move not considered the best move by the computer, should lead to an impaired position, while the best move should just at best keep the standing even, not actually improve the players position. Logically, if the computer knows this move will improve the players position, then shouldn't it already appear at the current position to improve the players position, saying that "with the best play, you are half a pawn up"? Alternatively, is this just a result of how the website is implemented at grandchesstour.org?
If the computer was capable of evaluating every line of play right to the end of the game, the evaluation would never change. Indeed, the evaluation of every move would be either "win", "lose" or "draw". This is essentially what happens in endgame tablebases.* If computers could do this for every position, every game against a computer would consist of the computer either resigning without making a move, offering you a draw in the initial position or being annoyed that you hadn't resigned or accepted that draw offer.

However, computers cannot evaluate that far because it would take impossibly long, both because games can be very long (hundreds of moves, in principle) and because there are many possibilities at each move.  So, computers have to take a number of shortcuts. This includes trying to figure out quickly what the most important candidate moves are (taking an unprotected piece is probably a great move; hanging your queen is probably an awful move; ...) and also stopping the search after several moves and using some heuristics instead of more searching to try to figure out if the resulting position looks good or not.

The problem is that these shortcuts can go wrong.  The computer might decide that hanging a piece is bad when it's actually a genius sacrifice. It might decide that a position has stabilized when really it hasn't. It might just not have enough power to see far enough into the future to see the real point of a particular move.

Here's a simple example, though it's no longer very realistic.  Suppose you're about to checkmate me but I have a series of ten checks I can make to delay you.  If I only look ten moves in advance, I'll think I'm doing OK: maybe I'm even a pawn up, so my evaluation is "After ten moves, I'm still a pawn up, so I'm good. Score&nbsp;+1" I play my first check, you respond, and now I see that it's mate in ten and resign. This is the so-called "horizon effect" which modern programs try to avoid (e.g., by looking deeper along lines that have a lot of forced moves) but it illustrates the general principle.

If the engine can see, say, ten moves into the future, then it's seeing farther into the game as each move is made.  At the initial position, it can see what the board will look like at move 10; after one move, it can see to move 11 and so on. (Again, this is a simplification, since computers don't, these days, look a fixed distance into the future, but it gives you the general idea.)

The example you've given is just a less dramatic version of the examples I've given. As more moves are made, the computer can see deeper into the game, so it can give a more accurate evaluation.  Another way to see this is in terms of information: as more moves are played, the computer has more information. It used to be guessing about what your response to 1.e4 would be, but now it knows that you've play the Sicilian, and so on.



* There's a slight nuance here in that you actually need to count the number of moves to the win to avoid repeating positions. For example, consider the endgame of KQ vs&nbsp;K. Every move that doesn't stalemate or surrender the queen wins, so you need a mechanism to drive towards checkmate, rather than just randomly moving and saying, "Wow, I'm totally going to win this&nbsp;&ndash; almost every move wins!"