< Earlier Kibitzing · PAGE 51 OF 51 ·
|May-12-15|| ||AylerKupp: <cro777> With regards to "The influence of technological tools over the game of chess is controversial", that is certainly true. And I think that a lot of it has to do with players' and authors' ignorance of how computers work in general and how chess engines work in particular, as well as a failure to understand certain basic mathematical and engineering principles.|
Take for example "A Chess Engine is NOT Your Friend!" (http://www.chess.com/article/view/c...) by IM Jeremy Silman. The second and third paragraphs say:
"A zillion people were using a zillion chess engines and they were all raving about how the grandmaster was in trouble."
"I found this funny, since the computer only had White a tiny bit ahead. (Why is the grandmaster in trouble if the number shows only a small plus?)" (The engine apparently evaluated the position at [+0.21])
I'm clearly biased but I think that whenever an author uses the world "zillion" he is automatically exaggerating to make a point, and his impartiality becomes immediately questionable. And to consider an evaluation of [+0.21] to be significant just shows that the people being referred to don't understand that such an evaluation is in the noise and effectively means that the position is even. They also don't understand the concept of significant digits, and it might be better if engines reported evaluations with a resolution of 0.5. Should computers in general and chess engines in particular be blamed because they don't know the lack of significance of an evaluation like [+0.21]? That's like saying that ¾ of the world's population should be considered illiterate because they might not be able to read and write English.
Mr. Silman later goes on to say that " CHESS ENGINES ARE OFTEN DETRIMENTAL TO THE CHESS HEALTH OF NON-MASTERS", further saying that "once the engine’s alarm bells go off, the innocent reader often views the concept as false, and all that he might have learned gets thrown out the window." Is that the fault of the engine or the fault of the "innocent reader".
Later on he discusses Fischer vs Reshevsky, 1966 which Fischer won partly (or perhaps largely) because Reshevsky didn't find 39...Rh8!! (found by Houdini). He does not consider the game any less beautiful and artistic in spite of Reshevsky not finding the drawing line, and I agree with him. But then he goes on to say that "When amateurs look at master games, the point is NOT to find errors, but to learn enough to appreciate the game’s beauty, and learn the lessons that eventually will allow you to create that same beauty in your games." I guess that I don't consider those two objectives to be mutually exclusive; one can learn enough to BOTH appreciate a game's beauty and learn the lessons that will eventually allow you to create the same beauty. But how can you do the latter if you don't find that your "beautiful" concept was in error?
His opinion and bias can be summarized in his last sentence: " As for Mr. Weski, please do yourself a favor and turn off the engine. You’ll be a better player if you do." Needless to say, I disagree with ALL his recommendations. He just doesn't know how to use chess engines to improve your chess and has a built-in bias against them because of his ignorance.
|May-12-15|| ||AylerKupp: <kwid> Thanks for thinking of me but, while interested, I probably wouldn't be able to make good use of them. I also have a significant chess book collection (but I suspect that it is nowhere as good as yours) and I don't have the time or ability to make much use of them. It reminds me at a restaurant I visited recently when, after a big multi-course dinner, the server asked me if I was interested in dessert. My answer: Interested, yes; capable, no."|
|May-12-15|| ||cro777: Argumentum ad ignorantiam.
<I think that a lot of it has to do with players' and authors' ignorance of how computers work in general and how chess engines work in particular, as well as a failure to understand certain basic mathematical and engineering principles.>
The other component is the kowledge of the characteristics and processes of creativity in general, and creativity in chess in particular.
The widening of one's horizon is a necessary step to "understand why work with computers adds a new creative layer to the game."
|May-13-15|| ||AylerKupp: <<cro777> The widening of one's horizon is a necessary step to "understand why work with computers adds a new creative layer to the game.">|
I agree, but unfortunately as far as this step is concerned we are all Luddites to a certain degree. Many apparently see computers as dehumanizing and tend to downplay any accomplishments made with their help, as though getting inferior results with computer assistance is somehow more "noble". I suppose that whenever a radical new technology that impacts our lives is introduced there is a time where that attitude prevails in many people, particularly those that do not fully understand it or, as Heinlein would say, "grok" it.
If these people would only realize that using computers in different and more effective ways is the same as exhibiting creativity in that particular domain and does not demean the final result, we will have moved forward a step or two.
|May-13-15|| ||morfishine: <AylerKupp> I wanted to clear something up. I always enjoy
non-engine 'Brain Games'. I think those are the most
rewarding. As for engine-assisted White vs Black games,
those are fine too since these are fairly balanced.
The point I was trying to make is that WT games vs ANY individual do not interest me anymore since there is nothing to prove. IMO, there just isn't any challenge when hundreds of engines are lined up against any single GM.
So, I look forward to the next Brain Game and hope we end up on the same team!
|May-14-15|| ||AylerKupp: <morfishine> I like both engine and non-engine games since they are very different in many ways and yet similar in so many others. They exercise different brain cells, at least for me.|
One aspect of these team games that is not mentioned as much as I think it should be are the interactions with the various players and the efforts necessary to support your move preferences, particularly if you feel strongly about a particular move. The latter is both funny and sad; to see the emotional state that some players work themselves into in support for or antagonism against a particular move. But, after all, it's only a game, and I don't think that anyone's livelihood is dependent on whether their team wins, so the emphasis should be on having fun and enjoying yourself. Unfortunately some players seem to get carried away and spoil the game to some extent for many of us.
I agree with you that there isn't much to prove anymore when playing against a single GM. In the original Chessgames Challenge the question was: "Can a group of chess amateurs team up to beat a grandmaster?" The answer is clearly YES, at least with engine assistance. Any grandmaster regardless of their talent and experience, with their busy schedule and limited computer resources is going to have a hard time against a group of amateurs with lots of time and dedication and supported by an array of computers and the latest chess engines. So I've occasionally mentioned that the question should be reversed into something like "Can a grandmaster beat a group of dedicated amateurs armed with the latest chess technology?" Still, it would be great fun to play against, say, Carlsen or Nakamura, regardless of computer assistance don’t you think?
And, yes, I'm also looking forward to the next Battle of the Brains game. As far as being on the same team, be careful what you ask for. You might need to read all my verbose posts just in the rare case that I say something useful. :-)
|Jun-07-15|| ||AylerKupp: <Investigation of search tree pruning improvements in the last several years> (part 1 of 2)|
In Kasparov vs Deep Blue, 1997 (kibitz #123), in response to a question by <Alan Vera> as to which computer system would win in a match, Komodo 9 or Deep Blue, I stated my opinioin that Komodo 9 would win easily because of its ability to prune its search tree much more effectively, thus compensating for its relatively much slower position evaluation time due to Deep Blue's special hardware assistance. I therefore ran an analysis of this critical position from The World vs Naiditsch, 2014 after 13...d5, when the World Team needed to decide between 14.e5 and 14.exd5:
click for larger view
The World Team narrowly chose 14.e5, 135 votes vs. 127 votes for 14.exd5, and the character of the game would have been very different if 14.exd5 had been chosen.
At any rate, I decided to see how quickly earlier versions of Komodo, Houdini, and Stockfish reached the various search depths compared to the latest versions of Komodo, Houdini, and Stockfish on the same computer, and thus see how search tree pruning efficiently had improved in the last few years. Of course, this wouldn't be the entire reason since evaluation function efficiency might also have been improved as well as the overall code.
The earliest versions of these engines I have are Komodo 1.3 (Jan-2011), Houdini 1.03 (Oct-2010), and Stockfish 1.91 (Nov-2010). The latest versions of these engines I have (which I believe are close to the latest versions available) are Komodo 9.01 (May-2015), Houdini 4 (June 2014), and Stockfish 6 (Jan-2015). Komodo was a little bit more complicated since up to version 5 it was a single-processor (SP) engine and only starting with version 5.1 did it become a multi-procesor (MP) engine, and I didn't think that it would prove much comparing the time to search depth between SP and MP engines. So I ran and compared analyses between Komodo 1.3 and Komodo 5, and between Komodo 5.1 and Komodo 9.01.
And, since I had some time on my hands, I also ran analyses of intermediate versions of Komodo and Stockfish; Komodo 3 (SP, Aug-2011), Komodo 7 (MP, Jun-2014), and Stockfish 3 (May-2013). I chose these intermediate versions so that their release dates would be roughly half-way between the earliest and latest engine versions, just to see the expected improvement. Unfortuantely, I was too cheap to buy any intermediate Houdini versions (Houdini went commercial starting with version 2.0), but at least Houdini 1.03 was also MP.
|Jun-07-15|| ||AylerKupp: <Investigation of search tree pruning improvements in the last several years> (part 2 of 2)|
Summary of Results:
Engine <Nodes/Sec> Max Depth
Komodo 1.03 (SP) <750,800> 26
Komodo 3 (SP) <449,064> 26
Komodo 5 (SP) <428,054> 26
Komodo 5.1 (MP) <1,638,104> 32
Komodo 7 (MP) <1,917,337> 27
Komodo 9.01 (MP) <1,768,387> 24
Houdini 1.03: <4,229,000> 30
Houdini 4: <4,885,000> 33
Stockfish 1.91 <3,202,904> 31
Stockfish 3 <2,816,137> 36
Stockfish 6 <2,928,442> 38
1. As expected, the more recent the version of Houdini, Stockfish, and Komodo MP, the quicker it reached a specific search depth. But this did not apply to Komodo SP; the latest SP version (Komodo 5), took longer to reach a specific depth than either of the 2 earlier SP versions, Komodo 1.03 and Komodo 3.
2. Komodo 9.01 seems to be a substantial improvement over Komodo 7 in terms of reaching deeper depths more quickly. So Komodo's claim seems accurate, although its improvement over Komodo 8 (which I didn't run) is probably less than its improvement over Komodo. Still, no challenge to Stockfish.
3. The fastest Nodes/sec rate does not necessarily correspond to the latest engine version. The reduction in Nodes/sec might indicate the additional time spent per node in pruning the search tree (time well spent).
4. As expected the Nodes/sec figure improved dramatically between the Komodo SP and the Komodo MP versions, almost 4X between the latest SP version and the first MP version. However, the changes in the Nodes/sec between all engines' versions was not strictly monotonic.
5. The evaluation trends for all the engines seem consistent except for Stockfish 3 which had substantially different evaluations from d=25 to d=33 for its top line.
6. All engines evaluated the two moves, 14.exd5 and 14.e5 quite closely, with not much to chose between either move. Later versions of Komodo seemed to evaluate 14.e5 somewhat higher than 14.exd5, but not enough to be significant.
Those interested in seeing the ply-by-ply changes and charts of the time-to-depth and evaluation change trends can download an Excel spreadsheet from
|Jun-07-15|| ||morfishine: <AylerKupp> Thanks for the reply. On some of your comments: <One aspect of these team games that is not mentioned as much as I think it should be are the interactions with the various players and the efforts necessary to support your move preferences, particularly if you feel strongly about a particular move. The latter is both funny and sad; to see the emotional state that some players work themselves into in support for or antagonism against a particular move. > I'm not sure where you are going with this. I really don't know if interactions with other members needs to be mentioned. However, the social aspect is powerful. I've made many friends here at <CG> through such interactions. One learns who is and who isn't their friend(s) pretty quickly. Also, one must proceed with caution since there's a separation through digital communication. For example, what may sound sarcastic was actually not intended, or vice versa.
<I agree with you that there isn't much to prove anymore when playing against a single GM...Still, it would be great fun to play against, say, Carlsen or Nakamura, regardless of computer assistance don’t you think?> Well, that depends on your definition of 'fun'. I don't think any single GM has any chance at all of winning...zero. So regardless of whether its Carlsen or Nakamura, where is the challenge? IMO, if there's no challenge, there's no fun. And the other thing that bugs me is no GM has expressed the slightest interest in any meaningful post-mortem. Its invariably “Thanks for the game” and thats it. There's no discussion with the GM, which I think most people desire.
<And, yes, I'm also looking forward to the next Battle of the Brains game> Me too. These are not identical to regular OTB conditions of any time control. We have access to opening and ending books and can setup the pieces or use a PGN viewer to work out lines. Still, the lines are purely our own creation without any engine input|
|Jun-08-15|| ||AylerKupp: <morfishine> I wasn't consciously going anywhere with my statement about needing to support your move preferences if you feel strongly about a particular move. Just mentioning what I think is a fact, some players feel strongly about particular moves and, if they do, they sometimes go to what I think are extremes to either campaign in favor of a particular move or campaign against other moves. That's just human nature, I guess. I think that <RandomVisitor>'s approach is best; provide the data and let others do with it what they wish.|
As far as my definition of "fun", I think that having bragging rights is "fun". If we were able to beat Carlsen or Kasparov in a team game with engine assistance then being able to brag about it would be "fun", even if the outcome might have been predictable. But I don't think that the outcome of playing against a <motivated> current or former OTB world chess champion, with the <resources> to have a staff performing engine analyses, and one who is willing to devote <adequate time> to the game is necessarily predictable. As a team we would probably still have the advantage of numbers (unless out opponent was <really> serious about defeating us and was willing and able to hire a staff of 100 players to perform engine analyses) and our opponent would have the advantage of superior chess knowledge, experience, and judgment.
I share your disappointment about not having our GM opponents participate in our post-mortems. I think that Arno Nickel both in his rematch game and to a lesser extent in the first game was the only one who participated extensively in post mortem discussions. Unfortunately, that was before I began to participate in these games.
But in a way I can't blame them for not participating. They are typically very busy people and if they lost the game that was probably one of the reasons, their inability to devote a sufficient amount of time and effort to the game. Besides, it's probably not much fun losing to a bunch of amateurs, whether supported by immense computer power or not, and then having to relive the experience.
Hopefully I'll see you during the next Battle of the Brains.
|Aug-18-15|| ||juan31: < AylerKupp> you're are invited to the <♔ Game Prediction Contest for Sinquefield Cup 2015 ♔> Golden Executive forum.
Carlsen, Caruana, Nakamura, Anand, Topalov, So, Grischuk, Giri, Aronian, Vachier-Lagrave.
< We hope your attendance>
|Sep-02-15|| ||Golden Executive: Hi <AylerKupp>. I am so glad you visited my forum to participate in the prediction contest. I feel honored. Thanks.|
I want to share with you my 'secret weapon' to make the predictions when I have no idea what to do. I bought it about 30 years ago in Radio Shack: https://www.youtube.com/watch?v=YVX...
|Sep-22-15|| ||NeverAgain: Hey, AK!
Seeing how often you refer to your setup as "antiquated" and you being one of the handful of regulars whose posts are always worth reading, I thought I'd share the results of the upgrade I undertook last week.
My main box is even older than your laptop, as you no doubt saw in my posts in the Stockfish thread. Even after overclocking that Core 2 Duo to 3.6 GHz I don't get more than about 2,000 kN/s with the official SF6 32-bit release.
Last week, after several hours of research I decided to break down for a dual Xeon X5670, which I reckoned to be the best deal for chess analysis. In your earlier post you mentioned reaching d=29 in under 3 minutes on your setup. Well, how 'bout 9 *seconds* with the Sep 18 x64 POPCNT (aka "modern"/"sse4") build?
Lenovo ThinkStation D20 Workstation:
benchmark in Arena (The World vs Naiditsch, 2014 position above):
The moves/lines have been edited out for better readability. In short, you reach d=35 (our mutually agreed minimum trustworthiness level) in 3:05 and d=40 in 26:28, with the speed maxing out at just over 13.3 mN/s.
That's quite a complex position to analyze from scratch, you can expect faster speed when you go through the whole game move by move with automatic analysis. That's why I advocate this particular workstation model, for its generous 48 GB memory bank. A 32 GB hash really helps for up to 9,000 mN (about d=36 here), then things slow down somewhat. Also note that I leave one core out of 12 for the system, so you can do other stuff on it at the same time and keep the CPU temps down a bit.
With 5-pcs Syzygy TBs you can reach pretty ridiculous depths in endgames, I've seen d=60+ reached literally within a couple of minutes, with kN/s going over 20,000.
All in all, it's a great deal, IMO.
For comparison to other top systems benchmarking an August build of SF6, see Sedat's site:
As you can see, my box is in the 6th place, above a lineup of more recent i7s, each costing a couple of grand (and most of which are overclocked to boot, which you can't do with this system). Which is pretty damn amazing for an under-$800 box, shipped.
Of the top five entries, four are from the much more recent Xeon E5 crop. Those babies retail for $4000-6000 - a *chip*. I haven't had a good look at the complete workstation prices, they were too scary. ;) So if 1/2 the speed for 1/20th the price is your idea of a good deal, the D20 should be right up your alley.
A note about Sedat's benchmarks: the position and the engine setup he uses allows for some pretty inflated numbers, don't expect to see them in your everyday deep analyses. However, as long as everyone uses the same benchmark, I see no big problem: the numbers should reflect the ratios between various systems.
If that particular model sells out before you get there, or if you opt for a different config, here's a handy Amazon search link for "Dual Xeon X5670":
Note that most of these come with an OS (typically Win7 Pro x64), but some may come without, so read the small print in the descriptions carefully. And of course, they are all refurbished (the MSRP on this particular box was close to 10 grand) but as the seller has a nearly 100% feedback rating, I think it's a safe choice.
Please post *your* benches if you decide to go for it. ;)
|Sep-27-15|| ||AylerKupp: <NeverAgain> Thanks for the information and links. I have been thinking about upgrading my system for the last 2 years but, just like my analog Sony TV that I was happy with for so many years, my current "oldish" system has been running reasonably well for almost everything I use it for and it just grates me to replace something that is still working reasonably well. But I finally gave up on my TV and I replaced it, and the other analog TVs I had in the house, with recent LCD TVs.|
In my experience in order to get a noticeable increase in performance you need to double your system's speed. In my case that would be a minimum of 8 processors. But that's not that much anymore, so I have set my sights on what I refer to as my "sweet 16" system; 16 cores, 16 GB RAM, 16 TB disk. But 16 GB of RAM is not that much anymore, and 16 TB disk is probably overkill and unnecessary unless I wanted to install 7-piece Lomonosov tablebases, and then it wouldn't be enough.
Christmas is coming up and so is my birthday (January). So maybe those will be the excuse and push I need to do it. And you can count on my posting benchmarks; that will probably be one of the first things I do when I get a new system to see how much faster the new system is compared to my old one.
One question, though. Why are you only running 5-piece Syzygy tablebases when 6-piece are relatively compact (about 160 GB)? You can get SSDs that will hold them easily and provide you fast access. But even that is probably not necessary.
|Oct-13-15|| ||NeverAgain: SSDs are a must for the 6-men Syzygy, as these tables feature a dozen files larger than 1 GB and two over 2 GB. Reading those repeatedly from a regular HDD will kill the NPS *and* the drive quickly, heh.|
At the time of your post I already had the 6-men Syzygy downloaded, two torrents a little under 150 GB combined - thanks to the 64 Mbit cable, I shudder to think how long it would have taken to leech them with my old DSL, never mind dial-up! - but had trouble making them work on my main box, the 32-bit XP Core 2 Duo one. Both Komodo and SF kept throwing up an exception and dying as soon as TB were accessed. Seems like a 64-bit OS is another requirement, as they work fine on the Win 7 Pro x64 with the new 240 GB Samsung SSD (from Amazon as well).
You are right - it was all worth the hassle in the end, though. With Komodo 9.2 I get usually around 14-15 mN/s. With the 3+4+5 Syzygy it went up to 20+ in endgames. With the 6-men TB I have seen over 30!
BTW, Komodo has been going the SF way pruning-wise. Remember those earlier versions, v5 and v6 (now both freeware) - they were like Rybka and Houdini, starting in low-to-mid teens and slowly working their way over the 20-ply hump. Then v9.02 started reaching mid-20s pretty quickly, and now v9.2 will typically get you to d=30 in seconds!
I agree with you on HDD space, those terabytes are completely redundant for chess. What engines support the Lomonosov TB anyway? And is there even consumer-grade hardware capable of handling them? I think for now it's strictly super-comp stuff for scientists and enthusiasts with more disposable income than common sense (wish I were one of the latter ;).
As for memory, I urge you not to consider anything below 24 GB. This way you'll be able to have a 16 GB hash table, at least. Remember, that its size is limited to powers of two (for the mainstream engines, at least). Additionally, Komodo will use some 10% less of the hash table allocated. So if you go for a 16 GB box now your max hash will be 8 GB. That's good for about 4,000 mN, give or take a couple hundred, not an exceedingly impressive number for someone who habitually does overnight analyses.
I did some hash tests with SF, and it seems to perform progressively slower (500-1,000 kN/s) as you go over 1 gig. That's on individual positions. If you do the whole game at once - either automatically, or by sliding back or forth a ply at a time - the benefits of a large hash really come to the fore. In some middle-game positions it can take over 5 minutes to get to d=35, about 10 min to d=38. Then you slide a ply and - boom - you get d=33 almost instantly!
Go for at least 24, I say and if you can find (and afford) 48 or 96 you won't regret it in the long run.
|Oct-13-15|| ||NeverAgain: <With the 3+4+5 Syzygy it went up to 20+ in endgames. With the 6-men TB I have seen over 30!>|
Heh. The question is, if you put the Lomonosov TB on a today's Cray equivalent, will it be *over 9,000!* ?
|Oct-19-15|| ||AylerKupp: <NeverAgain> I had found out some time ago that 6-piece Syzygy tablebases don't work on 32-bit machines. I suspect that there are some 64-bit data structures that don't map well or were improperly mapped to 32-bit machines and that were not properly tested. After all, who bothers with 32-bit machines these days? But, as you have also properly found out, if you restrict the tablebases to contain only 5-pieces then they work just fine. So I run with 5-piece Syzygy databases on my 32-bit machines and with 6-piece databases in my slow 64-bit laptop, and neither has an SSD.|
Yes, I know about Komodo entering the search tree pruning wars with Stockfish. This started with Komodo 9.01 and its Selectivity (minimum 10; maximum 200; default 80 for Komodo 9.01 and 9.02, 68 for Komodo 9.1, and 74 for Komodo 9.2; I guess they must still be calibrating it for best overall performance) and Reduction (minimum -1500, maximum 150, default 0) parameters. I have been curious for a while but haven't had the time (and keep forgetting) to try a race between Stockfish and Komodo with its Selectivity and Reduction parameters set at the maximum and see what happens. At least Komodo gives you the option to change them.
I don't think that any engine yet that supports 7-piece Lomonosov tablebases nor do I know whether the tablebase probing code has been released (a quick search did not show anything) because their size, approximately 140 TB, is pretty much out of reach for mere mortals like us. So, without a ready market capable of having the tablebases, there wouldn't likely be any motivation for the engine developers to include their usage in their engines, particularly if, in the absence of freely distributed tablebase probing code, they would have to invest their resources to develop it.
And, yes, I will definitely get as much memory as I can afford when the time comes. I remember quite a few years ago when a friend told me that he had a spare memory board (yes, they were boards in those days) and whether I needed more memory in my computer. I of course told him that one always needs more memory that one has.
|Oct-20-15|| ||juan31: ♔ ANNOUNCEMENT ♔
<Game Prediction Contest> for the <Bilbao Masters 2015> tournament. In <Golden Executive Forum>
Round 1 will be played next Monday October 26 16:00 CET(UTC+1:00). The posting pairings (probably sometime Sunday). At that point, the game prediction contest will be open.
Viswanathan Anand, Anish Giri, Liren Ding, Wesley So.
Rounds: 6 (double round robin).
Sofia and Bilbao rules apply.
<ALL ARE WELCOME >
|Oct-25-15|| ||juan31: ♔ ANNOUNCEMENT ♔ <Game Prediction Contest> for the <Bilbao Masters 2015> tournament. In <Golden Executive Forum>. < IS OPEN > < TODAY> Line-up:
Viswanathan Anand, Anish Giri, Liren Ding, Wesley So.|
Rounds: 6 (double round robin).
Sofia and Bilbao rules apply.
<ALL ARE WELCOME >
|Nov-18-15|| ||NeverAgain: AK: time to gather the stones ;)
Y Gusev vs E Auerbach, 1946
|Nov-28-15|| ||juan31: To < AylerKupp>
♔ ANNOUNCEMENT ♔
In < Golden Executive forum > <Game Prediction Contest> for the <London Chess Classic 2015> tournament. Round 1 will be played next Friday December 4 16:00 GMT(UTC +0:00).
Carlsen, Caruana, Nakamura, Anand, Topalov, Grischuk, Giri, Aronian, Vachier-Lagrave, Adams.
The full pairings are released; the game prediction contest is open right now.
Just post your predictions before each round begins.
|Dec-24-15|| ||Golden Executive: Merry Christmas and a Happy New Year 2016 to you and yours <AylerKupp>!|
|Dec-25-15|| ||WinKing: Merry Christmas & Happy Holidays to you <AylerKupp>!|
|Dec-25-15|| ||wordfunph: <AylerKupp> Merry Christmas!|
|Jan-02-16|| ||Dionyseus: <AylerKupp> My computer analysis shows that Fischer could have drawn the first game in his 1972 match against Spassky with 31...Ke7. I posted my analysis at Spassky vs Fischer, 1972|
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