Author: James Swafford
Date: 09:53:49 10/14/02
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On October 14, 2002 at 10:18:36, Vincent Diepeveen wrote: >On October 14, 2002 at 10:01:47, Vincent Diepeveen wrote: > >>On October 14, 2002 at 08:59:37, James Swafford wrote: > >You asked why 3.8 is not possible. > >That is because the minimal tree which you have to search, >as proven on paper by Knuth, is roughly: > >2 * squareroot(number of possibilities) > >Now that 2 is a constant number so not interesting. >I leave it always away. Just like the 1 node reduction >you get. Agreed. [snip] > >Crucial to know is how many possibilities a chess position has in order >to know what the theoretical smallest tree is without hashtables and >without nullmove. Right. > >So i measured in diep using a huge search from openings position >(18 ply), but i wasn't stupid lucky. > >I measured 2 different things > a) number of possibilities when in check > b) number of possibilities when not in check. > >As we all know, when in check , all chessprograms extend the search >by 1 ply. So they do not count for the tree. Agreed? Yes. > >The average number of possibilities i measured for b) was >40. I was very surprised, but it answered a quesetion of me. > >If each ply deeper there is 40 more possibilities, that means >automatically that your minimal tree without hashtable grows >with: > squareroot(40) = 6.32 I have never measured this myself, so I won't comment much on this but to say the accepted number is 35. It doesn't matter anyway. [snip] If it's true that they didn't use hashing (effectively) or any form of pruning, then I concede it would be _very_ difficult to achieve 18 ply in a typical position. That said, I still believe 12(6) means: 12 ply brute force, and _up to_ another 6 ply in hardware. Note that's not the same as "18 ply". As you have pointed out, that would be very hard to do. But that doesn't mean it's simply "12 ply" always. -- James
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