Author: Sune Fischer
Date: 12:35:28 02/06/02
Go up one level in this thread
On February 06, 2002 at 13:09:27, William H Rogers wrote: >On February 06, 2002 at 10:37:19, Sune Fischer wrote: > >>On February 06, 2002 at 10:19:29, William H Rogers wrote: >> >>>So it would seem, but the search is exponential and not linear. >>>I think you should not consider the "depth" but rather the number of nodes >>>searched. >>>If you go one ply deeper then (assuming your branch factor (BF) is not too depth >>>dependent) you a factor of BF more nodes, this ratio is fairly constant so I'd >>>go with Uri's definition. >>> >>>The diminishing returns issue is probably an effect of converging towards the >>>ideal move as often as possible. >>> >>>-S. >>> >>>I vote for your analisis. Just for an example lets say that a program can only >>>search to a level of 10 plys and it thinks that it has found its very best move, >>>then lets assume that we can search 2 to 4 plys deeper and it discovers that >>>there is a better move that can help it win the game. This happens all of the >>>time in chess and in other zero-sum games. The deeper you search the better you >>>game will be, of course it really depends on your evaluation routine is >>>basically sound in the first place. >>>Bill >> >>I agree, if we forget about chess programs and just study chess, then we can >>ask: >> >>A:) What is the percentage of ideal moves that can be found at ply 0 ? >>B:) What is the percentage of ideal moves that can be found at ply 1 ? >>C:) What is the percentage of ideal moves that can be found at ply 2 ? >>D:) What is the percentage of ideal moves that can be found at ply 3 ? >>E:) What is the percentage of ideal moves that can be found at ply 4 ? >>etc... >> >>Now obviously this percentage cannot be constant since it must sum to 1, so it >>has to be descending which means diminshing returns. >>Exactly what type of function that is I do not know, but it would interesseting >>to find out :) >> >>-S. > >I think that there might be many different moves based upon which opening that >was used by white, otherwise white might say e4 and mate in 58 moves. We have >not reached that point in computer chess yet, but we certainly headed that way. >Last year a major tournement was won by a program that never left its opening >book. >Bill Well I don't disagree with that, but suppose in any position we knew what the best move(s) was. Now how often would a n-ply search find the correct move(s)? This will give some kind of probability distribution on the plies. I'm sure this is directly related to the diminishing returns at the higher plies. -S.
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