H. G. Muller wrote on Tue, Dec 15, 2015 08:26 PM UTC:
Well, I am not exactly sure what you mean by turn here, but if you mean the number that counts up in the analysis output of an engine, which counts 'nominal search depth' in half-moves, you should realize that all strong engines lie about their depth. This is just the length of the principal variation, and virtually all branches of the tree are not even searched half as deep. So if the effective branching factor, which is the factor that the number of searched position goes up for every half-move of nominal search depth, is around 3, it does not mean that the engine searches a tree with three moves in every node all to the nominal depth.
Of course you also have to take account of the fact that in the bulk of the tree on every other level only a single move has to be searched, to refute the previous move. Engines are pretty clever at picking the right move for that, based on the search of the previous depth. This means that for a game with 36 moves per position, the effective branching factor would only be sqrt(36) = 6 per half-move, without any selectivity whatsoever.
Through simple-minded depth reduction (2 or 3 half-moves) in positions where the opponent proves unable to exploit a turn pass, this can already be brought down to around 4. Conditionally reducing the non-captures (i.e. reducing their search depth 1 or 2 half-moves until this reduced search proves that the move is worthwile score-wise), the EBF falls to around 3. By sorting the moves somewhat cleverly based on the statistics of their success as refutations in the entire tree, and reducing the moves late in that sorting even more, you get branching factors like that of Stockfish, which ly around 2.
Up to that point, no knowledge about the game has been used at all to guide the search. Of course the engine needs knowledge to play strong, but it is all in the static evaluation. It is not needed to get the EBF low.
Of course you also have to take account of the fact that in the bulk of the tree on every other level only a single move has to be searched, to refute the previous move. Engines are pretty clever at picking the right move for that, based on the search of the previous depth. This means that for a game with 36 moves per position, the effective branching factor would only be sqrt(36) = 6 per half-move, without any selectivity whatsoever.
Through simple-minded depth reduction (2 or 3 half-moves) in positions where the opponent proves unable to exploit a turn pass, this can already be brought down to around 4. Conditionally reducing the non-captures (i.e. reducing their search depth 1 or 2 half-moves until this reduced search proves that the move is worthwile score-wise), the EBF falls to around 3. By sorting the moves somewhat cleverly based on the statistics of their success as refutations in the entire tree, and reducing the moves late in that sorting even more, you get branching factors like that of Stockfish, which ly around 2.
Up to that point, no knowledge about the game has been used at all to guide the search. Of course the engine needs knowledge to play strong, but it is all in the static evaluation. It is not needed to get the EBF low.