![[us]](/mwf/v12/flags/us.png "United States")
I have begun the systematic project of evaluating each of the initial positions in Fischer-Random Chess. I post this here because it is of relevance to Rybka in reference to the recent tournament in Mainz and the idea that there might be some initial positions in which white has too much of an advantage. My method is using Hiarcs 10 in the Fritz 10 GUI in Chess960 mode and having it evaluate each position, starting from number 1 and going in order through to 960 (position 518 is the "normal" starting position for which many of our opening books have 25 million moves or more in the lines). I let it evaluate each position for 60 seconds. For the positions with higher evaluations (typically around +0.25 or more), I let it go for at least 10 minutes, typically if I'm going away from my computer for a short period. If I'm going away for a longer period, I let it evaluate the highest positions for an hour, and when going to bed, I let it evaluate the highest-evaluation position from that day and use the evaluation from after six hours. In all cases, I use the evaluation from the end of the depth at which it was evaluating after the end of the specified time period--thus, if it is evaluating the second move at depth 14 after 60 seconds, I let it continue until it reaches the end of depth 14 and then record that evaluation. Also, for the 60 second evaluations, I always make sure that it has evaluated at least through depth 14.
I am currently on position 247, so am just over a quarter of the way through. When I finish, I will list, in order, the positions with about the two dozen highest evaluations. Larry had been interested in those with the 10 highest--hopefully by then, I'll have at least 10-minute evaluations for all of the two dozen that I list, and I can list the top 10 out of those for the purpose of them being analyzed further by others.
Thus far, there are a few positions of interest. First, position number 13 has an evaluation of +0.30 after 60 seconds and an evaluation of +0.35 after 10 minutes. Second, position number 70 has an evaluation of +0.33 after 60 seconds, +0.42 after 10 minutes, and +0.44 after an hour. Third, position 120 has an evaluation of +0.37 after 60 seconds and +0.34 after 10 minutes. Fourth, position number 198 has an evaluation of +0.27 after 1 minute, +0.31 after 10 minutes, and +0.31 after an hour. Fifth, position 214 has an evaluation of +0.27 after 1 minute and +0.41 after 10 minutes.
Of course, we see lots of "funny" opening moves in the suggested lines--things like 1.e4 f6 or 1.h4 or 1.0-0-0 0-0-0 2.d4 d5, which I just had recently.
I will continue with this and will probably finish the 60-second analysis of all positions in five or six days. I'll post the results here.
I am currently on position 247, so am just over a quarter of the way through. When I finish, I will list, in order, the positions with about the two dozen highest evaluations. Larry had been interested in those with the 10 highest--hopefully by then, I'll have at least 10-minute evaluations for all of the two dozen that I list, and I can list the top 10 out of those for the purpose of them being analyzed further by others.
Thus far, there are a few positions of interest. First, position number 13 has an evaluation of +0.30 after 60 seconds and an evaluation of +0.35 after 10 minutes. Second, position number 70 has an evaluation of +0.33 after 60 seconds, +0.42 after 10 minutes, and +0.44 after an hour. Third, position 120 has an evaluation of +0.37 after 60 seconds and +0.34 after 10 minutes. Fourth, position number 198 has an evaluation of +0.27 after 1 minute, +0.31 after 10 minutes, and +0.31 after an hour. Fifth, position 214 has an evaluation of +0.27 after 1 minute and +0.41 after 10 minutes.
Of course, we see lots of "funny" opening moves in the suggested lines--things like 1.e4 f6 or 1.h4 or 1.0-0-0 0-0-0 2.d4 d5, which I just had recently.
I will continue with this and will probably finish the 60-second analysis of all positions in five or six days. I'll post the results here.
Thanks for doing this. Your method sounds quite reasonable given your circumstances. Based on your results so far, it seems unlikely that any of the positions you have checked are actually won for White, and almost surely none are proveably won for White. Vas and I had some discussions a few months ago about what constitutes a "won" position. I think I felt that 0.6-0.7 (with a clean extra pawn at the start being 1.0) was the threshold, while Vas thought it was somewhat higher (I recall Iweta agreed more with me on this). I believe Hiarcs uses fairly high eval numbers (try removing c7 as the most neutral pawn and compare the score to 1.0), unlike Rybka, so if no eval even reaches 0.5 on Hiarcs scale by the end of your research we can conclude that none of the starting positions would be considered "won" based on our understanding of chess. This of course does not mean that all positions are as fair as the normal one; for any really serious Chess960 event two game matches should be played from each position to eliminate the luck factor.
I doubt you'll find anything higher than 0.5
Our CCRL processing scripts for normal chess look for unfair openings. The criteria is something like, both engines evaluate 0.75 or greater out of the opening, the evaluations stay 0.75 or above for the whole game, and that engine goes on to win. Such games are automatically removed - there aren't many, about 80 out of 70,000 last time I looked. Testament to the quality of the neutral books that we use. Anyway, exactly the same scripts are used for FRC procesing, and having played 15,000 games so far, no such instances have occurred. Of course I can't guarantee every 960 position has been played, but it is fairly likely
The scripts also do exactly as above but with a 0.5 criteria, so that we can investigate manually if we wish (these games are NOT removed....) No games found there either !
So, I doubt you'll find anything higher than 0.5. It could be that there are some in our database that are initially higher but that the eval then dropped on subsequent moves
Our CCRL processing scripts for normal chess look for unfair openings. The criteria is something like, both engines evaluate 0.75 or greater out of the opening, the evaluations stay 0.75 or above for the whole game, and that engine goes on to win. Such games are automatically removed - there aren't many, about 80 out of 70,000 last time I looked. Testament to the quality of the neutral books that we use. Anyway, exactly the same scripts are used for FRC procesing, and having played 15,000 games so far, no such instances have occurred. Of course I can't guarantee every 960 position has been played, but it is fairly likely
The scripts also do exactly as above but with a 0.5 criteria, so that we can investigate manually if we wish (these games are NOT removed....) No games found there either !
So, I doubt you'll find anything higher than 0.5. It could be that there are some in our database that are initially higher but that the eval then dropped on subsequent moves
In that case, with 15,000 games, and thus each position having been played an average of 15 times, are there any statistics on winning percentages broken down by position?
At the moment, unfortunately not. On our normal chess list we do indeed have stats by ECO code, but no equivalent for FRC yet.
This method will not be valid for any matches involving Rybka, because the commercial versions of Rybka (so far) basically evaluate a clean pawn up in the opening as only about half a pawn up, on the grounds that two pawns up in the opening is roughly like one pawn up in th endgame. But I suppose you have enough non-Rybka games so that your conclusions are still valid.
![[de]](/mwf/v12/flags/de.png "Germany")
Thanks for doing this. Your method sounds quite reasonable given your circumstances. Based on your results so far, it seems unlikely that any of the positions you have checked are actually won for White,
if you think the rybka eval in a starting position is so reliable, that you can conclude, that there is no win in any of 2xx positions, you exaggerate quite much in my opinion.
and almost surely none are proveably won for White.
I wouldn't be so sure about that also.
Vas and I had some discussions a few months ago about what constitutes a "won" position. I think I felt that 0.6-0.7 (with a clean extra pawn at the start being 1.0) was the threshold, while Vas thought it was somewhat higher (I recall Iweta agreed more with me on this). I believe Hiarcs uses fairly high eval numbers (try removing c7 as the most neutral pawn and compare the score to 1.0), unlike Rybka, so if no eval even reaches 0.5 on Hiarcs scale by the end of your research we can conclude that none of the starting positions would be considered "won" based on our understanding of chess. This of course does not mean that all positions are as fair as the normal one; for any really serious Chess960 event two game matches should be played from each position to eliminate the luck factor.
what exactly are you taling about? what does that mean: "I feel, that +0.7 is won for white"? I'd say + infinite or mate in x is a win.
do you talk about how the rybka eval should be adjusted? so you talk about what eval for a given position suits the likings of the users most?
no I think you three pondered about what initial advantage is the threeshold for a win in an handicaped game.
it sounds weird to me to talk about numbers in this aspect. let's never forget, that every eval by a program is incorrect unless it shows 0.00 or mate in x.
but ok till now there's no better term than a number, which equals a probability of a win. this leeds to an important question: should rybkas eval really be considered like a winning percentage like + 0.7 for 60% chance for a win, +1.0 72%, +2 93% or such.
every program I use for analysis tends to show too high values in the very beginning of the game, relatively too slow values in the middlegame and too high values again in the endgame. this is pretty logical if you think about the search algorithm.
it's just the most succesful way of an eval algo for an engine, but has nothing to do with the exact eval of the position. we are used to interpret this eval according to the stage of the game and some other things and that's ok somehow. it will be very hard to make the engine show an eval of say +0.7 in the middlegame and +0.7 in the endgame, when both positions have the same chance to be won.
I just want to say, that the computer evals almost necessarily are flawed.
ok silly statement :-)
if you think the rybka eval in a starting position is so reliable, that you can conclude, that there is no win in any of 2xx positions, you exaggerate quite much in my opinion.
and almost surely none are proveably won for White.
I wouldn't be so sure about that also.
Vas and I had some discussions a few months ago about what constitutes a "won" position. I think I felt that 0.6-0.7 (with a clean extra pawn at the start being 1.0) was the threshold, while Vas thought it was somewhat higher (I recall Iweta agreed more with me on this). I believe Hiarcs uses fairly high eval numbers (try removing c7 as the most neutral pawn and compare the score to 1.0), unlike Rybka, so if no eval even reaches 0.5 on Hiarcs scale by the end of your research we can conclude that none of the starting positions would be considered "won" based on our understanding of chess. This of course does not mean that all positions are as fair as the normal one; for any really serious Chess960 event two game matches should be played from each position to eliminate the luck factor.
what exactly are you taling about? what does that mean: "I feel, that +0.7 is won for white"? I'd say + infinite or mate in x is a win.
do you talk about how the rybka eval should be adjusted? so you talk about what eval for a given position suits the likings of the users most?
no I think you three pondered about what initial advantage is the threeshold for a win in an handicaped game.
it sounds weird to me to talk about numbers in this aspect. let's never forget, that every eval by a program is incorrect unless it shows 0.00 or mate in x.
but ok till now there's no better term than a number, which equals a probability of a win. this leeds to an important question: should rybkas eval really be considered like a winning percentage like + 0.7 for 60% chance for a win, +1.0 72%, +2 93% or such.
every program I use for analysis tends to show too high values in the very beginning of the game, relatively too slow values in the middlegame and too high values again in the endgame. this is pretty logical if you think about the search algorithm.
it's just the most succesful way of an eval algo for an engine, but has nothing to do with the exact eval of the position. we are used to interpret this eval according to the stage of the game and some other things and that's ok somehow. it will be very hard to make the engine show an eval of say +0.7 in the middlegame and +0.7 in the endgame, when both positions have the same chance to be won.
I just want to say, that the computer evals almost necessarily are flawed.
ok silly statement :-)
![[nz]](/mwf/v12/flags/nz.png "New Zealand")
Of coarse no-one is saying that Rybka or any other engine evaluations are gospel truth, but they are the best that man can come up with at the current time for an automated process.The topic in this article is trying to find if such a position exists in 960 and if so what is it.When some suitable canidates show themselves then I would expect some closer inspection to take place.If the position is won for white then you would expect a program like Rybka to have a 100% score against any black player.For me that would just about prove that the position is infact won from the starting position.
![[il]](/mwf/v12/flags/il.png "Israel")
This is wrong.
Rybka is not a perfect player so claiming that if the position is won for white you can expect rybka to have 100% score for white is not correct.
Uri
Rybka is not a perfect player so claiming that if the position is won for white you can expect rybka to have 100% score for white is not correct.
Uri
Larry wrote:
"Based on your results so far, it seems unlikely that any of the positions you have checked are actually won for White"
I think that larry did not mean actually won in theoretical meaning but actually won in practical meaning that black has no chances at the high level of top programs.
Of course it is clearly possible that white can win one of the chess960 positions when the win is too deep for chess programs to see
but in that case you can also expects programs not to find the right moves so this possibility does not mean that games between programs are decided based on the opening position.
My opinion is the following
1)I believe that for every specific starting FRC position it is theoretically drawn that mean that for every specific FRC position if I have to bet about the theorethical result I am going to bet that it is a draw.
2)I believe that there is a starting FRC position that is not drawn that mean that if I have to bet about the question if all the positions are drawn my bet is no.
There is no contradiction because if you have 960 events that for every one of them there is 1% probability to happen then you can believe that one of them happens but you can also believe that every specific event out of them does not happen.
Uri
"Based on your results so far, it seems unlikely that any of the positions you have checked are actually won for White"
I think that larry did not mean actually won in theoretical meaning but actually won in practical meaning that black has no chances at the high level of top programs.
Of course it is clearly possible that white can win one of the chess960 positions when the win is too deep for chess programs to see
but in that case you can also expects programs not to find the right moves so this possibility does not mean that games between programs are decided based on the opening position.
My opinion is the following
1)I believe that for every specific starting FRC position it is theoretically drawn that mean that for every specific FRC position if I have to bet about the theorethical result I am going to bet that it is a draw.
2)I believe that there is a starting FRC position that is not drawn that mean that if I have to bet about the question if all the positions are drawn my bet is no.
There is no contradiction because if you have 960 events that for every one of them there is 1% probability to happen then you can believe that one of them happens but you can also believe that every specific event out of them does not happen.
Uri
As usual, your comments are very accurately worded and well thought out. My opinion is that before I would bet on any particular position to be theoretically won, a program should evaluate it at about 2/3 of the score that the same program would give to the opening position with c7 handicap. Clearly, none of the positions checked so far qualifies. Apparently only a small number are above even half of my threshold score, so I would be inclined to bet against even one of the 240 or so positions checked so far to be won, though of course I have no great confidence in this hypothetical bet. As to whether even one of the 960 positions is theoretically won, I'll wait until I see the rest of the data to comment. If we accept my 2/3 of a pawn rule as a valid guidline, then I would say that only FRC positions above 1/3 of a pawn (after a reasonable search) have even one chance in a thousand of being actually won, so we only need to check those above this margin more seriously. But I'll readily admit that my 2/3 of a pawn estimate could be seriously wrong; it's possible that even half a pawn or less in the opening position is a theoretical win. No one knows.
Things haven't really changed much lately--the position with the most promise remains position number 70, about which I wrote earlier, and I'm now through over the first 600 initial positions. There was some initial promise with position number 326, which was +0.45 after 1 minute and +0.48 after 10 minutes, but then came down to +0.30 after 1 hour and +0.27 after 6 hours.
Comparing this with how it evaluates the position with the usual initial setup with the c7-pawn missing, Hiarcs 10 gives a score of +1.32 after 10 minutes, and this score doesn't fluctuate much throughout the analysis. Interestingly, other engines give that same position the following evaluations after 10 minutes:
Rybka 2.3.2a: +0.54
Hiarcs 11.2: +1.07
Shredder 10: +1.45
Fritz 10: +1.26
Spike 1.2 Turin: +1.37
Fruit 05/11/03: +0.96
Ktulu 8: +1.15
Loop 10.32f: +1.20
Toga II 1.3.4: +1.08
I used Ktulu 8 specifically because I have good reason to believe that it plays the initial position in the opening stronger than any other engine, including Rybka, Shredder, and Spike. Next strongest is Loop 10.32f. More precisely, the initial position favors these two engines more than the other engines.
Comparing this with how it evaluates the position with the usual initial setup with the c7-pawn missing, Hiarcs 10 gives a score of +1.32 after 10 minutes, and this score doesn't fluctuate much throughout the analysis. Interestingly, other engines give that same position the following evaluations after 10 minutes:
Rybka 2.3.2a: +0.54
Hiarcs 11.2: +1.07
Shredder 10: +1.45
Fritz 10: +1.26
Spike 1.2 Turin: +1.37
Fruit 05/11/03: +0.96
Ktulu 8: +1.15
Loop 10.32f: +1.20
Toga II 1.3.4: +1.08
I used Ktulu 8 specifically because I have good reason to believe that it plays the initial position in the opening stronger than any other engine, including Rybka, Shredder, and Spike. Next strongest is Loop 10.32f. More precisely, the initial position favors these two engines more than the other engines.
Probably you know that the different evaluations in the opening position minus c7 are primarily cosmetic. It's not that the programs really disagree so much about that position, they merely disagree on the meaning of +1.00. Rybka considers that this number means roughly a pawn up in a typical endgame, and since it's less of an advantage in practice to be a pawn up in the opening, she gives a lower score. Some programs do the same thing by using 1.00 for the opening and a higher number for being a pawn up in the endgame, while still others may attempt to keep the 1.00 value as the average value of being a pawn up thruout the game. But none of this matters for our present purpose; just divide by the score without c7 to get a "true" value in terms of pawns for any FRC position. So, if Rybka 2.3.2a gave a score of 0.50 to any FRC position, that would be more than 90% of a pawn and hence probably won by my criterion. But I doubt that this is the case with any FRC position (of those you've checked) in view of your Hiarcs findings.
Yes, I often give a similar explanation to people concerning scores, especially in the endgame, where Shredder will give a score of around +2.5 in a position where Rybka gives a score of around +1, with both engines recommending the same lines.
I find rybka's score like the score of other programs as too optimistic in the endgame.
Based on experience even when rybka says +2 in the endgame I cannot be sure of winning and
you know that in the last world championship rybka against zappa had clearly more than +2 and could not win.
It had a tablebases won position but even in drawn position in the endgame it can say more than +2 and here is an example
from the final position of one of my correspondence games(all 5 piece tablebases are used):
878: Alfonsas Kupsys,B - Uri Blass, 2005
Analysis by Rybka 2.3.2a 32-bit :
62...Bc6-d5 63.g4-g5
+- (2.07) Depth: 5 00:00:00
62...Bc6-d5 63.Rb2-b8 Bd5-e6
+- (2.14) Depth: 6 00:00:00 3kN
62...f7-f6 63.Rb2-b6 Bc6-e4
+- (2.11) Depth: 6 00:00:00 3kN
62...f7-f5 63.g4-g5 f5-f4+ 64.Kg3-g4
+- (2.07) Depth: 6 00:00:00 4kN
62...f7-f5 63.g4-g5 f5-f4+ 64.Kg3-f2 Bc6-d5
+- (2.80) Depth: 7 00:00:00 6kN
62...f7-f6 63.Rb2-b6 Bc6-e4 64.Rb6-b8
+- (2.10) Depth: 7 00:00:00 6kN
62...f7-f6 63.Rb2-b6 Bc6-d5 64.Rb6-b8 Bd5-f7
+- (2.13) Depth: 8 00:00:00 8kN
62...f7-f6 63.Rb2-b8 Bc6-d7 64.Rb8-d8 Bd7-e6 65.Rd8-e8
+- (2.27) Depth: 9 00:00:00 10kN, tb=1
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3
+- (2.19) Depth: 9 00:00:00 12kN, tb=2
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6
+- (2.27) Depth: 10 00:00:00 14kN, tb=5
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3
+- (2.27) Depth: 11 00:00:00 16kN, tb=12
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5
+- (2.27) Depth: 12 00:00:00 19kN, tb=26
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.29) Depth: 13 00:00:00 25kN, tb=56
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.29) Depth: 14 00:00:00 33kN, tb=110
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.29) Depth: 15 00:00:01 40kN, tb=186
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.33) Depth: 16 00:00:02 61kN, tb=394
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.33) Depth: 17 00:00:03 79kN, tb=714
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.33) Depth: 18 00:00:04 99kN, tb=1190
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 19 00:00:06 147kN, tb=2283
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 20 00:00:09 204kN, tb=3559
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 21 00:00:14 295kN, tb=5321
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 22 00:00:21 399kN, tb=7763
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 23 00:00:36 569kN, tb=11238
(, 24.08.2007)
Note that it is not the only case when I find more than +2 by rybka in drawn position in analysis.
Rybka is simply not reliable when there are not many pawns in the board and I think that her scores should be smaller in these situations.
This problem cannot be solved by installing the 6 piece tablebases because I am sure that you can find positions with one more pawn when her score is not reliable(and I have in analysis of a different game that is not finished score of more than +2 when the position is drawn and there are 8 pieces in the board but fortunately I do not have to go to that position so I can win).
Uri
Based on experience even when rybka says +2 in the endgame I cannot be sure of winning and
you know that in the last world championship rybka against zappa had clearly more than +2 and could not win.
It had a tablebases won position but even in drawn position in the endgame it can say more than +2 and here is an example
from the final position of one of my correspondence games(all 5 piece tablebases are used):
878: Alfonsas Kupsys,B - Uri Blass, 2005
8/5p2/2b5/4k3/6P1/6K1/1R6/8 b - - 0 1
Analysis by Rybka 2.3.2a 32-bit :
62...Bc6-d5 63.g4-g5
+- (2.07) Depth: 5 00:00:00
62...Bc6-d5 63.Rb2-b8 Bd5-e6
+- (2.14) Depth: 6 00:00:00 3kN
62...f7-f6 63.Rb2-b6 Bc6-e4
+- (2.11) Depth: 6 00:00:00 3kN
62...f7-f5 63.g4-g5 f5-f4+ 64.Kg3-g4
+- (2.07) Depth: 6 00:00:00 4kN
62...f7-f5 63.g4-g5 f5-f4+ 64.Kg3-f2 Bc6-d5
+- (2.80) Depth: 7 00:00:00 6kN
62...f7-f6 63.Rb2-b6 Bc6-e4 64.Rb6-b8
+- (2.10) Depth: 7 00:00:00 6kN
62...f7-f6 63.Rb2-b6 Bc6-d5 64.Rb6-b8 Bd5-f7
+- (2.13) Depth: 8 00:00:00 8kN
62...f7-f6 63.Rb2-b8 Bc6-d7 64.Rb8-d8 Bd7-e6 65.Rd8-e8
+- (2.27) Depth: 9 00:00:00 10kN, tb=1
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3
+- (2.19) Depth: 9 00:00:00 12kN, tb=2
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6
+- (2.27) Depth: 10 00:00:00 14kN, tb=5
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3
+- (2.27) Depth: 11 00:00:00 16kN, tb=12
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5
+- (2.27) Depth: 12 00:00:00 19kN, tb=26
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.29) Depth: 13 00:00:00 25kN, tb=56
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.29) Depth: 14 00:00:00 33kN, tb=110
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.29) Depth: 15 00:00:01 40kN, tb=186
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.33) Depth: 16 00:00:02 61kN, tb=394
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.33) Depth: 17 00:00:03 79kN, tb=714
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-f8
+- (2.33) Depth: 18 00:00:04 99kN, tb=1190
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 19 00:00:06 147kN, tb=2283
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 20 00:00:09 204kN, tb=3559
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 21 00:00:14 295kN, tb=5321
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 22 00:00:21 399kN, tb=7763
62...Bc6-d5 63.Rb2-b8 Bd5-c6 64.Rb8-c8 Bc6-d5 65.Rc8-e8+ Bd5-e6 66.Kg3-f3 f7-f6 67.Kf3-e3 Ke5-d5 68.Ke3-f4 Kd5-d6 69.Re8-b8
+- (2.36) Depth: 23 00:00:36 569kN, tb=11238
(, 24.08.2007)
Note that it is not the only case when I find more than +2 by rybka in drawn position in analysis.
Rybka is simply not reliable when there are not many pawns in the board and I think that her scores should be smaller in these situations.
This problem cannot be solved by installing the 6 piece tablebases because I am sure that you can find positions with one more pawn when her score is not reliable(and I have in analysis of a different game that is not finished score of more than +2 when the position is drawn and there are 8 pieces in the board but fortunately I do not have to go to that position so I can win).
Uri
You obliquely bring up an interesting observation I noted recently. The general tendency of evaluations at successive ply-depths is, in a large majority of cases, toward 0.00. In statistical terms, the mean evaluation of a collection of random opening positions at ply 10 and ply 20 will be 0.00, but the standard deviation will be measurably higher at ply 10, meaning greater convergence toward a draw the deeper you go.
If you think about it, if all positions are either drawn or mated, the deeper the search, the more the evaluation must trend toward mate or draw. And indeed, in most opening book positions if you search deep enough you can find forced or apparent draws. (It figures the Cato team would notice this.)
If you think about it, if all positions are either drawn or mated, the deeper the search, the more the evaluation must trend toward mate or draw. And indeed, in most opening book positions if you search deep enough you can find forced or apparent draws. (It figures the Cato team would notice this.)
That's all very true. Trust me, if you try the same with 1.f3, it will also converge towards 0.00. So, be brave, be unpredictable! I really look forward to spending 15 minutes on move 1 figuring out what to reply to 1.f3 against Anson in a coming freestyle tournament :-)
Yes, Dagh. But you see, we are trying to WIN, not draw. Much more likely we will play 1.e3 2.Ke2.
I´m sure, you believe that chess is drawn and smart guys can´t loose with white. I´m not convinced.
Because nobody has a quantum computer let alone 32-piece EGTBs white can still lose. Anybody can screw up the opening or fall prey to a killer novelty, even "smart guys". It just that they are less likely to make those kinds of mistakes and are more apt to uncork the novelties than fall victim to them.
Don't believe the banter between the top teams. They are all arrogant and scared at the same time. All except maybe Vas have nightmares and wake up screaming incoherent things like "goddamit, five blacks AGAIN!" or "hard drive crashed!"
Don't believe the banter between the top teams. They are all arrogant and scared at the same time. All except maybe Vas have nightmares and wake up screaming incoherent things like "goddamit, five blacks AGAIN!" or "hard drive crashed!"
![[hu]](/mwf/v12/flags/hu.png "Hungary")
Actually, there are two types of chess players. The absurdly over-optimistic, and the paranoid. Those in the second category tend to play better - it helps with prophylactic thinking, which is important in chess. I'm more in the first category, which is rather unfortunate :)
And yes, with infinite search, all drawn positions will end up at 0.00 and all won positions will end up at +mate. It's logical to think that the progression will be gradual.
Vas
And yes, with infinite search, all drawn positions will end up at 0.00 and all won positions will end up at +mate. It's logical to think that the progression will be gradual.
Vas
That is exactly the question we hope to address soon with a "draw and White" handicap match with a grandmaster.
FWIW, I would bet differently on #2. I'm ready to bet that every single 960 position is theoretically drawn.
Vas
Vas
I am not talking about displayed evals, or anything specific to any one chess program. My opinion is that in the opening stages of a game of chess, for one side to be theoretically winning he needs an advantage of around 2/3 of a pawn. In other words, a pawn up with no (or slight) compensation should win the game, but a half-pawn advantage like a free bishop pair is probably not enough to win against perfect defense. This is based on my experience as both an IM and as someone who has tested Rybka in huge numbers of games with various advantages, but of course I could be wrong, as Rybka is still far from a perfect player. It's just the best estimate I have about this. I would be interested in the opinion of top grandmasters on this question.
As for displaying scores that can be converted to accurate winning percentages, you are correct that no programs now do a good job of this. However I expect that some future version of Rybka will do this well; I think we could make this happen, but it's just not a priority right now.
As for displaying scores that can be converted to accurate winning percentages, you are correct that no programs now do a good job of this. However I expect that some future version of Rybka will do this well; I think we could make this happen, but it's just not a priority right now.
FWIW - I haven't really changed my mind since we last discussed this.
In general, if one side is up a pawn, but the other side has any sort of tangible compensation, my guess is that at least one more mistake will be needed to lose.
Of course, it's hard to be sure - it's just a guess. And yes, I'm in the minority on the Rybka team :)
Vas
In general, if one side is up a pawn, but the other side has any sort of tangible compensation, my guess is that at least one more mistake will be needed to lose.
Of course, it's hard to be sure - it's just a guess. And yes, I'm in the minority on the Rybka team :)
Vas
The main analysis is finished. There were no positions in which Hiarcs 10 evaluated above +0.50 after 1 minute, and of the top 40 positions, none were evaluated above +0.50 after 10 minutes. Interestingly, the average evaluation for all 960 positions is +0.1399. The reason this is interesting is that position 518, also known as "normal chess", has an evaluation of +0.14, exactly this average. It's not just symmetry, either--if you switch the rooks and knights, yielding an apparently similar position (position number 326), the +0.45 after one minute and +0.48 after 10 minutes, the highest of all--but it goes down to +0.30 after an hour and +0.27 after 6 hours.
The top 35 positions after one minute are as follows:
326 0.45
322 0.42
343 0.39
886 0.39
646 0.38
54 0.37
120 0.37
338 0.37
610 0.37
342 0.36
902 0.34
70 0.33
845 0.33
829 0.31
13 0.30
232 0.30
317 0.30
662 0.30
461 0.29
868 0.29
134 0.28
653 0.28
710 0.28
189 0.27
198 0.27
214 0.27
247 0.27
283 0.27
367 0.27
502 0.27
577 0.27
620 0.27
724 0.27
864 0.27
872 0.27
Of these, the top 12 after 10 minutes, with the 1-minute evaluations in the middle column and the 10-minute evaluations in the right column, are as follows:
326 0.45 0.48
70 0.33 0.42
214 0.27 0.41
886 0.39 0.36
13 0.30 0.35
120 0.37 0.34
283 0.27 0.34
348 0.26 0.34
317 0.30 0.33
322 0.42 0.32
610 0.37 0.32
374 0.26 0.32
Of these, only position number 70 remains above +0.4 after 6 hours, giving an evaluation of +0.44 after an hour and +0.41 after 6 hours, though I've only checked the top three in the list for that length of time.
I'll keep taking a look at some of these, and give another report if one seems necessary, though I doubt anything significant will happen.
The top 35 positions after one minute are as follows:
326 0.45
322 0.42
343 0.39
886 0.39
646 0.38
54 0.37
120 0.37
338 0.37
610 0.37
342 0.36
902 0.34
70 0.33
845 0.33
829 0.31
13 0.30
232 0.30
317 0.30
662 0.30
461 0.29
868 0.29
134 0.28
653 0.28
710 0.28
189 0.27
198 0.27
214 0.27
247 0.27
283 0.27
367 0.27
502 0.27
577 0.27
620 0.27
724 0.27
864 0.27
872 0.27
Of these, the top 12 after 10 minutes, with the 1-minute evaluations in the middle column and the 10-minute evaluations in the right column, are as follows:
326 0.45 0.48
70 0.33 0.42
214 0.27 0.41
886 0.39 0.36
13 0.30 0.35
120 0.37 0.34
283 0.27 0.34
348 0.26 0.34
317 0.30 0.33
322 0.42 0.32
610 0.37 0.32
374 0.26 0.32
Of these, only position number 70 remains above +0.4 after 6 hours, giving an evaluation of +0.44 after an hour and +0.41 after 6 hours, though I've only checked the top three in the list for that length of time.
I'll keep taking a look at some of these, and give another report if one seems necessary, though I doubt anything significant will happen.
I should also mention that positions 462, 892, and 921 each have the three lowest evaluations, given at +0.02 after one minute. In fact, I wonder if perhaps Chess960 should become Chess27, as there are 27 positions with evaluations of +0.05 or less. While I'm willing to bet that all Chess960 positions are, in fact, drawn, I would say that there are almost certainly many that are a bit more difficult for black to draw than others.
So to summarize your findings, subject to the limitations of your methodology (which I think was excellent), the best positions give White an advantage of about 1/3 of a pawn (a pawn being worth 1.32 on Hiarcs per your earlier report), which is just half of what I consider a decisive advantage. In view of this, I think it is most probably that none of the 960 positions is won for White, unless I am seriously overestimating what constitutes a "won" game. On the other hand, the best positions give White roughly triple his normal advantage, which as a practical matter is pretty serious, considering how hard it is for Black to hold the draw consistently in top level chess today. So for chess 960 to be played seriously at the highest level, either two game sets from each position must be played, or positions above some threshold should be culled. Now drawing the line at .05 or at anything less than 0.14 seems silly to me, since that would exclude normal chess, and anyway the number of positions must be several hundred if we are to avoid having memorized opening theory become a big practical problem. Can you tell us how many positions would remain if we draw the line at 0.15, or at 0.20 for example?
This seems like an accurate summary. There are only 101 positions with evaluations above +0.20, so 859 positions with evaluations of +0.20 or below. There are 653 positions with evaluations of +0.15 or below. In fact, there are even a full 274 positions with evaluations of +0.10 or below, thus lessoning white's advantage compared with normal chess.
We also have a practical factor I remember we discussed in another thread a couple of months ago.
If the opening position is theoretically drawn, you could expect that the one-move opening advantage dissipates the more moves made.
So while opening theory helps black to equalize in normal chess, the worst FRC-positions are, practically, even worse for black.
If the opening position is theoretically drawn, you could expect that the one-move opening advantage dissipates the more moves made.
So while opening theory helps black to equalize in normal chess, the worst FRC-positions are, practically, even worse for black.
If the worst FRC positions are bad but not lost, then deeper searching should reduce the White advantage, though not by very much. In fact my estimate of 2/3 of a pawn for a winning advantage is based partly on observing that this is around the point where the score tends to rise with depth in the opening. But you are correct that the difference between a bad FRC position and the normal one might grow with depth, if the normal position advantage shrinks with depth.
Yes, I agree with this. Opening theory probably does more to help black draw than to help white win.
In some of the games from Mainz, there was a total mess on the board after just a couple of moves. This can happen in real chess as well, but then both sides are playing extremely well from their books.
Vas
In some of the games from Mainz, there was a total mess on the board after just a couple of moves. This can happen in real chess as well, but then both sides are playing extremely well from their books.
Vas
There is a boinc project to build up an opening book for FRC. I am afraid it is not very active at present, but my guess is that they have already used
muuuch mooore teraflops than you have (although, probably, they algorithm is worse than hiarcs). Here is the link
http://www.chess960athome.org/alpha/
Unfortunately, there is no book to download. You should contact the guys there to see if they have any useful data available.
As for me, I think it would be nice to create a good book for knight odds games. Any suggestion or how-to? (Or even better, any volunteer to create such a book?)
muuuch mooore teraflops than you have (although, probably, they algorithm is worse than hiarcs). Here is the link
http://www.chess960athome.org/alpha/
Unfortunately, there is no book to download. You should contact the guys there to see if they have any useful data available.
As for me, I think it would be nice to create a good book for knight odds games. Any suggestion or how-to? (Or even better, any volunteer to create such a book?)
Is that what they're trying to do ? Build an opening book ? I could never figure out what that project was all about.
I hate the concept of an opening book for FRC. One of the main reasons for FRC's existence as I understand it is to do away with an opening book ! The day a comprehensive opening book comes out for FRC, will be the day it dies. As it is, it's only half-alive, because it never really took off. Which is a great pity.
I hate the concept of an opening book for FRC. One of the main reasons for FRC's existence as I understand it is to do away with an opening book ! The day a comprehensive opening book comes out for FRC, will be the day it dies. As it is, it's only half-alive, because it never really took off. Which is a great pity.
I wouldn't worry about this too much. Even if a huge opening book for FRC came out, no human could remember more than a couple moves deep repertoire from each of the starting positions, and this would give him only a tiny edge. It might mean a bit more in engine games.
Have to agree with Larry on this one.One of the big headaches for OTB chess players is deciding what to play against your opponent.And when you think you know you start burning the midnight oil reading all the latest lines and can't get to sleep.So when you get to play you are too tired and can't play any good.With Chess 960 I would have a beer and go to bed early and play better chess the next day.Any study of 960 openings would be a waste if the opening setup was decided just before the game starts.But if you knew the day before what the setup was going to be then I suppose an opening database could be of some help.
![[ca]](/mwf/v12/flags/ca.png "Canada")
I'm not sure, but I thought I heard that one of their objectives was not to create an opening book (though it would be a natural outcome of the project), but to gather information on general opening theory for Chess 960.
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