Robert Allgeuer wrote:What I meant is that the static score from one leaf position evaluation will eventually be propagated down to the search root as overall score of the search. Depending on whether this specific line was searched to an even or an odd depth this score will have the right to move bonus added or subtracted. One could see the right to move bonus as a modulation of the root score according to whether the best line is searched to odd or even depth.
I think this leads to an effect that the program prefers to play into lines that end in (quiet) positions with its own right to move, i.e. into lines that are searched to odd depths. It may prefer such lines over lines that would trigger another extension and thus evaluate one ply deeper up to an even depth, essentially even losing search depth in the PV. Whether this is good or not I do not know, but at least it would not be obvious to me like this, why this were a desirable effect.
The above analysis is correct only if the side to move bonus is too big. One of the properties of a good and well-tuned evaluation function is that in a quiescent position, the strongest move shouldn't change the evaluation much. If the strongest move increases the static evaluation function a lot, it means that the position before the move was made was evaluated too lowly.
Now consider an evaluation function without a side to move bonus. In most positions, there will be at least one move which improves the static eval (unless the side to move is in zugzwang). This means that the evaluation function doesn't satisfy the property described in the preceding paragraph. The correct value of the side to move bonus is the amount by which the best move will typically improve the static eval for an evaluation function without such a bonus.
In fact, one could argue that one of the main points of a side to move bonus is to
avoid the type of effect you describe. A program without a side to move bonus often
will prefer lines of odd depth rather than even depth. This is most obvious when analysing relatively quiet and highly symmetrical positions, like the initial position. Without a side to move bonus, a chess program's eval will typically alternate between high and low from one iteration to the next. A 1-ply search will give white a big plus after 1. e4, while a 2-ply search will return zero with a PV like 1. e4 e5. At 3 plies we are at 1. e4 e5 2. Nf3, with a clear plus for white again, and so on. With a well chosen side to move bonus, the result should be a slight plus score for white at all depths, which is what most strong chess players would consider the correct assesment.
Tord