I would like to do this with Joker80, because I cannot be sure that ChassV uses correct piece values, which might affect its opinion on some opening lines very much. I am still thinking how I should modify Joker to get the information we want.

One way to do it might be like this: In stead of narrowing the search window by delimiting it with the scores of the best two variations found by either side, it should discount the scores by a margin of, say, 50 centiPawn, and only narrow the window if that discounted score is better than the current window setting. Then a single reply on an alternative move, which would make the score come out, say, 30 cP lower, would not immediately be considered a refutattion of that alternative move. In stead the search of replies would continue until either one was found that refuted the move by a margin of more than 50 cP, or all moves would be search to make it sure what the best reply is, so we would get an exact score for the alternative move. (Which would the ly closer to the score of the best move than 50 cP.)

The margin sets how much score we are willing to sacrifice to create variation so that the opponent cannot use a well-prepared variation against us. (i.e. this depends on how much weaker in terms of a centi-Pawn score odds we estimate the difference between a well-prepared opponent and someone who would have to find the moves behind the board.) I guess this means the margin should decrease as we get deeper into the game, based on how much branching we already created: If at move 6 we have already selected a 1-out-of-100 path, the preparation of the opponent on this particular position will necessarily on average be 100 times worse than his preparation from the standard opening, so throwing in more variation to make him totally unprepared will not bring much further gain. So we should have an idea of how common the current position will be.

We can obtain this 'rareness factor' by multiplying the move choices along the branch. If on ply 1 we had 3 playable moves (within the score margin), on ply 3 we had 2 and on ply 5 we have 4 moves, we are in a 1:3*2*4 = 1:24 position, and could shrink the margins accoringly. When we search the opening position through iterative deepening, the previous iteration will tell us how many playable moves there are, before searching each of them at the new, increased depth.

This is a bit complicated, though. So perhaps it would be better to simply do an iteratively deepened search where the search window will be kept open in every internal tree node to at least the margin around the root score of the previous iteration. That would mean that all positions in the tree within +/- margin from the previous root score would acquire exact scores. Only outside this window, positions would get upper or lower-bound scores, telling us that they should be considered refuted by one side or the other.

The main question is how to present any output from this process. Perhaps for every node in the tree that receives an exact score we should simply print out the entire branch leading up to that node, together with the score. I guess we would be happy if we have, say 10,000 lines, which should be easily doable. That would on average be a 1:100 choice for white as well as black, diluting any possile preparation efforts of the opponent 100-fold I guess that only after we have such an opening tree we could check if there are problems with the 'on average' notion, i.e. if the tree is robust in the sense that it could never be reduced by opponent move choice to a tree that is much smaller than the average.