Author: Carmelo Calzerano
Date: 05:17:10 10/10/02
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On October 10, 2002 at 07:16:27, Nagendra Singh Tomar wrote: >In ur example; you should note that when we are searching for the opponent's >best reply for d4 we always have alpha and beta (calculated till the first >subtree e5 is fully evaluated)in hand. If we find any of the opponent's reply to >be better than e5 (and asusming that e4 was THE best move), the score of the >reply WILL be more than the beta set by e4 hence it will fail-high and we will >not update PV. IF at any point in time we get a move that lies between alpha and >beta we know that the move lies on the PV based on the tree calculation till >that time. >IOW if at any point in ply 'x+1' we update the PV, this updation WILL percolate >all the way upto the top, updating the PV moves of all the plies <= x. That's a wrong assumption. Think a minute about it: even if, at ply N, your current search score lies between alpha and beta, you cannot possibly assume that at ply N-1 a move not yet analyzed will cause a fail high, rejecting the move at ply N-2. For instance, just add one ply at your own example and it won't work anymore: The current PV is 1. e4 e5 2. Nf3, and we are now analyzing 1. d4 d5. We try 2. c4 at first, and we find a score lying in the alpha-beta window. Thus, our PV become [1. d4] d5 2. c4 and we lost all the information about the move 2. Nf3. Note that the analysis of 1. d4 is not finished yet, so in our PV array we actually have [e4][d5][c4]. Now we analyze 1. d4 Nf6, and let's suppose Nf6 fails high: the 1. d4 move is rejected. The correct PV should be still 1. e4 e5 2. Nf3, but you actually lost it: your PV array is in an unconsistent state! That's why you CANNOT assume that a score lying between alpha and beta will propagate up to the tree, because at the tips you have no idea how many moves are left that could possibly reject the whole variation. >beta is there to say that the opponent has got means to stop u from playing a >move, so score>beta cannot lie on PV. For a move for which alpha < score < beta, >the opponent has got no means to stop us from playing this move. Unfortunately that's not true... ;-) Regards, Carmelo
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