Analysing a chess game at different positions

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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.

There are lots of different things to look at, and there is no hard answer. The best indicator is to look at the amount of pieces on the board. If white have an extra piece over black they are almost always winning. If there is asymmetry in the number of pieces then we usually assign a point value to each piece, pawn being one point, bishops and knights being three points, rooks five points and the queen nine points. So say that white have a queen but black have two rooks then it is likely that black is slightly better then white.

But there are lots of other considerations you have to look at for a full analysis. How much space does each player control on the board, are the pieces developed to useful positions, is the king in a safe position, is there any strong attacks building up, is there a tactic in the position, etc. A computer will analyse all this and adjust the points from counting the pieces to get a score in the same scale. A human will typically not assign a score though and just tell which player is best.

A full answer to this question is pretty complicated. But two simple factors are:

* Material: who has more and stronger pieces on the board? A typical weighting system is pawn = 1, knight/bishop = 3, usually with the bishop weighted slightly more, rook = 5, and queen = 9, though this can vary. If I’ve traded one of my rooks for two of your knights, I am at a slight advantage: I’ve captured 6 points to your 5.

* Tempo: whose pieces are in a position to be more active? For example, a queen or bishop near the center of the board has more freedom of movement than one near the edge. A rook that is out in the open has more freedom than one walled behind pawns.

The obvious one is piece count. Whomever has the most pieces on the board is winning.

Roughly, pawns are worth 1, bishops and knights are worth 3, rooks 5, queens 9.

Then there’s positioning which is even rougher. Having pawns more forward is better. Having control of the center is better. Having more pieces more protected and threatening more is better. Having the king in a vulnerable position is real bad. If other pieces can put your king in check in 1 move, without instantly dying, that’ll mean trouble for you.

It depends, some computers can know things like “bishops that have long unobstructed paths in multiple directions and exist on the same coloured square as the king are valuable” and assign value to pieces based on meta analysis of game position based on a certain amount of data it has. They can advance the position several moves forward and use that analysis to focus on certain lines. For example the computer won’t deeply analyse the line of black opening h6/a6 pawn move because it has the data that it’s a bad move. The more powerful this type of computer is the farther along it can develop more lines (this is also why you sometimes see the evaluation bar randomly move as a very strange line that at first based on the rules the computer uses to prioritise lines it analyses is actually really strong).
The number is supposed to be pawns worth of value (1 for a pawn, 3 for a bishop etc). It’s not strictly material as positionally one can be ahead and the weighting that positioning can vary a little bit across analysis programs with the same position depending on the depth they analyse to (a 20 move deep analysis might see greater value in a piece than a 10 move deep)

They get stronger the larger the dataset they have is so that they can know what good positions look like so they prefer those. That’s how most analysis computers will work, as far as the super computers that far outstrip the masters go, they’re literally playing out millions of games to make their positions.