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[Pio Korinth]

Hi Joona and Ma Chao!

The big problem as I see it, trying to minimize the absolute value of difference between a shallow and a deep search, is that doing so IMO will lead to a simplification of the evaluation function. IMO It might help though if you can determine if the deeper search is a win, draw or a loss.

The reason why I think it will lead to a simplification of the evaluation is that having an evaluation function f such that f(position) = 0 if the position is neither a win nor a loss, f(position) = 0.01 if the position is win for you and f(position) = -0.01 if the position is a win for the opponent, will look like a great function since the absolute value of the difference between a deep and shallow search will always be small.

Joona, if I am guessing right, your try failed because the evaluation function you ended up with decimated all the values that tended to fluctuate, for example king safety and maybe mobility. Am I right? I am really curious if my thought experiment is right. Also I do not understand the logic by using the absolute value of the difference as a meassure of error??

An interesting idea I have thought about is trying to improve the search and evaluation endgame parameters of an engine by using an endgame tablebase as an oracle. What you could do then is to set up lots of positions and meassure the fitness of the evaluation as a function of how many solutions (mates and draws) you could find in a fixed number of moves searched. I think you should also give a bonus for finding the solutions in fewer steps than the fixed number and also a bonus if the function is close to the true value and of course a penalty if it is not close to the true value. Why not try the same method for other positions that can be proven as check mates or draws in the opening and middle stage of the game.

Joona, I am not surprised if you mathematically could prove (assuming the leaf nodes has some error distribution from their true values (1 , 0, -1)) that a deeper search will lead to a worse result than a shallow search. I think it has a lot to do with the branching factor and conditional probabilities of the game tree. A low branching factor would propegate the errors a lot more IMO. If the search is deep enough the argument is wrong since you will now find the true value

Ma Chao, thank you for a really interesting topic . I think your questions are really good.