Computer Chess Club Archives


Search

Terms

Messages

Subject: Re: Never Say "Impossible"

Author: J. Wesley Cleveland

Date: 10:16:52 05/16/01

Go up one level in this thread


On May 15, 2001 at 14:21:22, Uri Blass wrote:

>On May 15, 2001 at 12:18:43, J. Wesley Cleveland wrote:
>
>>On May 14, 2001 at 15:47:47, Robert Hyatt wrote:
>>
>>>On May 14, 2001 at 14:51:16, J. Wesley Cleveland wrote:
>>>
>>>>On May 13, 2001 at 22:42:00, Robert Hyatt wrote:
>>>>
>>>>>On May 13, 2001 at 19:48:59, J. Wesley Cleveland wrote:
>>>>>
>>>>>>On May 12, 2001 at 20:41:23, Robert Hyatt wrote:
>>>>>>
>>>>>>>On May 11, 2001 at 16:50:28, J. Wesley Cleveland wrote:
>>>>>>>
>>>>>>>>Okay. With exact results, you only need the number of plies to the next capture
>>>>>>>>or pawn move stored with each position to solve the 50 move rule problem.
>>>>>>>>Repititions are a non-problem, i.e. if from position A, you know that position B
>>>>>>>>is a forced win, *but* the win leads back through A, you would never choose to
>>>>>>>>move to B, because you would already know there is a shorter win from A.
>>>>>>>
>>>>>>>
>>>>>>>How would you _know_ that either of those positions were forced wins if you
>>>>>>>don't save _everything_ as you search?
>>>>>>>
>>>>>>You know because you have a string of positions in the hash table, each of which
>>>>>>is one ply closer to mate. There *can't* be a repitition, or it would be a
>>>>>>different string. It is just like endgame tablebases, which do not need any
>>>>>>history of positions.
>>>>>
>>>>>
>>>>>I'm not sure I follow.  Endgame tables have _all_ positions available during
>>>>>their creation.  That is how the algorithm works.. find a position that is
>>>>>marked as "unknown" by backtracking from a position marked as "known".  Then
>>>>>you can mark the unknown entry as mate in one more move than the known entry.
>>>>>But you must have _all_ positions stored during the creation... _every_ one.
>>>>
>>>>I thought that is what we were discussing. If you have a hash table large enough
>>>>to store every position found in the search, then you do not need total path
>>>>information with each position, which means you could solve chess by considering
>>>>"only" about 10^25 positions. So, if Moore's law holds up, we could solve chess
>>>>by the end of the century, rather than by the end of the universe.
>>>
>>>
>>>First, how do you conclude 10^25?  assuming alpha/beta and sqrt(N)?
>>
>>It is a classic alpha-beta search with a transposition table large enough to
>>hold *all* positions found in the search. I'm guessing at the number of
>>positions, but I feel that the same logic should hold, as only positions with
>>one side playing perfectly would be seen.
>
>By this logic you can get sqrt(n) for the following position
>
>[D]8/4b2B/k7/6n1/8/8/4K1R1/8 w - - 0 1
>
>It means that programs should be able to solve it without tablebases because
> n<(2^5)*(2^5)*(2^6)*(2^6)*(2^6)*(2^6)=2^34 so sqrt(n)<2^17 but I do not know
>about a program that can solve it without tablebases inspite of the fact that
>hash tables of 128 Mbytes are more than enough to remember 2^17 positions even
>if every position is 32 bytes and positions in the endgame can be stored by less
>bytes if the program is smart enough.
>

My estimate (guess) assumes perfect move ordering. I suspect that move ordering
is pretty bad here, as evaluating positions that don't involve material loss is
pretty hard.



This page took 0 seconds to execute

Last modified: Thu, 15 Apr 21 08:11:13 -0700

Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.