Author: Robert Hyatt
Date: 07:06:01 09/12/01
Go up one level in this thread
On September 12, 2001 at 05:04:55, Uri Blass wrote: >On September 12, 2001 at 00:49:38, Robert Hyatt wrote: > >>On September 12, 2001 at 00:00:21, Uri Blass wrote: >> >>> >>>1)The size of the tree is not enormous. >>>If it was so big humans had no chance to prove the draw or equal material by a >>>tree. >> >>First, the size of the tree _is_ enormous. It took many humans, searching >>all night long, to find the draw in game 2. > >No >It took me with the help of Genius3(p100) and no help from >other humans few hours to see a draw evaluation >(I proved at that time by a tree >that black can force draw evaluation when I consider numbers like >+0.2 also as a draw) OK.. Before we proceed, we need to come to a standard definition of "draw". That is (to a computer) an evaluation of "draw_score" which is typically 0.00. If you start making wild assumptions, such as "any score < .3 is a draw" then none of this analysis matters. Because to a computer, .2 is _not_ a draw at all, and considering it such is an invalid condition to test under. > >I needed some hours because the hardware was slow at that time and >today 30 minutes are enough. If you didn't know the position was a draw from the beginning, I don't believe you would prove that it is, within 30 minutes. If you could, you are better than a _bunch_ of GM/IM + computer operators on ICC and FICS. > >I did not publish my analysis at that time but I know that there was >no need for many humans+many hours to > > >Crafty also can see the draw if you continue >some plies down in the tree. So what? You have to see it from the _beginning_ to prove it is really a draw. Not based on some human analysis that is hardly perfect in what is searched and what is excluded. > > >The hardest line for computers after Ra6 Qe3 is the following line: >I used * for obvious singular moves > >45.Qxd6 Re8* 46.h4 h5 47.Bf3* Qc1+* 48.Kf2* Qd2+* 49.Be2* Qf4+* >50.Kg1* Qe3+ 51.Kh2* Qf4+* 52.Kh3* Qxf5+* 53.Kh2* Qf4+* > >Here even Crafty can see 0.00 at depth 12 Again, you miss the point here. Crafty doesn't necessarily _prove_ that this position is a draw. It proves that its evaluation suggests that one side has an advantage, and the other side will therefore try to repeat. It is not a "proof" that this is a draw, in the same way that a mate score definitely proves that the position is a mate. Because for mates there are no positional decisions like "OK, he has a pawn on a3 that I don't think I can stop so I am going to perp him rather than letting it promote". A few plies deeper might show that "hey, I can let the pawn promote because I can mate him anyway..." So 0.00 scores do not _prove_ that a position is a draw. It only proves that one side of the tree search believes it should repeat to avoid something that looks worse, but which might not be worse at all on deeper analysis. I have seen _many_ cases in a game where Crafty would say 0.00, and then drop negative or jump positive on a deeper search. > >New position >[D]4r3/5kp1/R2Q1p2/1p1Pp2p/1Pp2q1P/2P5/4B1PK/8 w - - 0 1 > >Analysis by Crafty 18.10: > >54.g3 > +- (2.97) Depth: 1/3 00:00:00 >54.g3 Qf2+ 55.Kh3 Qxe2 > -+ (-1.68) Depth: 2/3 00:00:00 >54.Kh3 > µ (-1.28) Depth: 2/3 00:00:00 >54.Kh3 Qe3+ 55.Bf3 Qxc3 > +- (1.62) Depth: 2/3 00:00:00 >54.Kg1 Qxh4 > +- (1.79) Depth: 2/3 00:00:00 >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qxh4+ > +- (2.14) Depth: 3/6 00:00:00 >54.Kg1 Qe3+ 55.Kf1 Qc1+ 56.Kf2 Qf4+ 57.Bf3 Qxh4+ > +- (2.21) Depth: 4/8 00:00:00 >54.Kg1 Qe3+ 55.Kf1 Qc1+ 56.Kf2 Qf4+ 57.Bf3 Qxh4+ 58.Ke3 > +- (2.51) Depth: 5/11 00:00:00 >54.Kg1 Qe3+ 55.Kf1 Qc1+ 56.Kf2 Qf4+ 57.Bf3 Qxh4+ 58.g3 Qg5 > +- (2.24) Depth: 6/15 00:00:00 21kN >54.Kg1 Qe3+ 55.Kf1 Qc1+ 56.Kf2 Qf4+ 57.Bf3 Qxh4+ 58.Ke2 e4 59.Qd7+ Re7 > +- (2.29) Depth: 7/16 00:00:00 55kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Kf1 Qd3+ 59.Be2 Qf5+ 60.Ke1 >e4 > ± (0.78) Depth: 8/17 00:00:01 185kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Kf1 Qc1 59.Ke2 Qb2+ 60.Kf1 >Qc1 > ± (1.16) Depth: 9/23 00:00:01 350kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Kf1 Qc1 59.Ra7+ Kg6 60.Ke2 >Qb2+ 61.Kf3 c3 > ± (1.17) Depth: 10/23 00:00:02 660kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qe3+ 58.Kf1 Qf4+ 59.Kg1 Qc1 60.Ra7+ >Kg6 61.Qd7 Qxd1+ 62.Kh2 Rb8 63.Qxg7+ > ² (0.35) Depth: 11/25 00:00:03 1633kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Ke2 Qd3+ 59.Ke1 Qc3+ > = (0.00) Depth: 12/29 00:00:09 4227kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Ke2 Qd3+ 59.Ke1 Qc3+ > = (0.00) Depth: 13/34 00:00:29 13389kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Ke2 Qd3+ 59.Ke1 Qc3+ > = (0.00) Depth: 14/35 00:00:39 18185kN >54.Kg1 Qe3+ 55.Kf1 Qf4+ 56.Ke1 Qc1+ 57.Bd1 Qxc3+ 58.Ke2 Qd3+ 59.Ke1 Qc3+ > = (0.00) Depth: 15/38 00:01:04 29538kN > >(Blass, Tel-aviv 12.09.2001) > > >The number of non singular moves in that line is at most 6 plies from >Deeper blue's point of view(I count also the first 2 plies Ra6 Qe3 >as non singular(Deeper blue did not expect Qe3 when it played Ra6 so >it is clear that Qe3 was not singular from it's point of view and >I assume that Ra6 was also not singular. > >Here is part of Deep blue logfile from that position > >12(6) #[Ra6](162)[TIMEOUT] 162 T=192 >ra8a6 Qb6c6q pd5c6Q Rb8c8 be4d5 Kf7e7 ra6a5 Bd6c7 ra5b5P Ke7d6 bd5f3 Kd6e7 rb5c5 >Rc8a8 bf3d5 Ke7d6 >--------------------------------------- >--> 45. Ra6 <-- 15/75:45 > >You can see that deeper blue could search depth 18 so >6 non singular moves mean that the remaining depth from the position >that Crafty see 0.00 is 12 and depth 12 +singular extension is >clearly bigger than depth 12 of Crafty. > >It seems to me that something is wrong in your assumptions about >deeper blue(maybe depth 12(6) is not depth 18 and maybe >deeper blue did not extend a full ply for every singular move. > It didn't extend a full ply for _every_ singular move. I gave the one constraint that they used, namely that two consecutive plies were limited to 2 plies of extensions, max. But your analysis of a forced draw, based on a 0.00 score by a computer, is flawed. Try other programs in the same position and see if _all_ of them say 0.00... >Uri
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