If we can define a simplified version that removes this branching factor
altogether, we would be able to skip this problem and focus on many other important research problems that are right now impossible to work on because of the branching factor
On synthetic search-tree models we explore the influence of three important factors on the occurrence of pathological behaviour: the granularity g of the heuristic, the branching factor b of the game tree and the similarity s of the nearby nodes.
They extended the original puzzle to allow additional diagonal moves and thus obtain a different branching factor for the search trees.
The paper shows the interplay between the lookahead pathology and three factors that affect it: the dependence of the sibling nodes in the search tree, the branching factor and the granularity of the heuristic function.
In the following section we investigate the influence of three factors on the quality of the search in synthetic search trees: the granularity g of the heuristic function (the number of possible heuristic values returned), the branching factor b of the search tree (the number of successors of each node), and the similarity s of the search tree (the similarity among values of sibling nodes).
where b is the branching factor of the tree and [DELTA]d is the depth from the node x to the terminal node t.
The performance of the maximax algorithm was estimated by observing how the degree of pathology is influenced by three factors: the branching factor b, the granularity g, and the similarity s.
In the first experiment we observed how the quality of the search is influenced by the branching factor and the granularity in independent trees.
In the next experiment we computed the required granularity to avoid situations where a deeper search is inefficient, as a function of the branching factor b and the local similarity s.
The degree of pathology decreases with the increased granularity g and the local similarity s and increases with the branching factor b.
Deep Blue's branching factor
at each move (or ply) averages perhaps four or five, after allowing for various procedures, like the alpha-beta algorithm and special continuations that are selectively incorporated into the search.