I don't think it is that much of a mystery. The thesis uses a tree model where the probability that a node is a win or a loss is independent for all nodes. This leads to a rather high fraction of singular moves. E.g. to have 1 out of every 16 nodes a loss for the side to move requires a branching ratio b = ln(1/16)/ln(15/16) = 43 (which is reasonable for Chess). But the fraction of won positions where the winning move is singular is b*(1/15)^2 = 19%.Michel wrote:Why minimax search works so well in chess like games remains somewhat of a mystery (not solved in this thesis AFAICS).
In Chess singular moves are much rarer than that. One factor contributing to this is that the the probability that a node is a win is not independent. The game-theoretical result of especially sibbling nodes will be highly correlated. Many positions are quiet, and most moves then won't affect the result much, so that many of the daughter nodes will inherit the result from the parent.
When you refine the model by assuming that there are two kind of nodes, independently chosen, where one kind has daughters with a large probability to be wins, while for the other this is a low probability, you create an extra degree of freedom that decouples the fraction of singular moves from the fraction of lost positions. For a given branching ratio you can then always tune the singular-move probability so low that each level of minimax will actually help to improve the accuracy.