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Member since May-04-12 · Last seen Sep-22-17
I am only a butterfly dreaming of being Chuang Zhu, dreaming of being Tiggler.

Favorite WCs all time: Kasporov, Alekine, Botvinnik, Lasker, Capablanca. Best of the rest: Nimzovitch, Rubinstein, Korchnoi, Keres. Bring back the 24 game WC matches and 12+ game candidates matches so that we can have heroic champs and challengers again. Kasparov, Alekhine, Botvinnik, Lasker, Capablanca, Steinitz, Nimzovitch, Tal, Morphy, Anand, Karpov, Fischer, Rubinstein, Keres ....

Apart from actual chess, the two topics that keep me coming back to this site are the mysteries of the Elo and related ratings schemes, and the the even more strange oddities of chess search engines.

With respect to ratings, I don't mean the routine operation of the calculations, but the scale which these operations create, sui gerenis. What is the mathematical basis, and is it reduceable to a Haar measure? Is there any reality hiding behing the statistical artifact? Are there undiscovered truths about the distribution of ratings points, and do they regress to the mean?

Engines are a big mystery to us. Not so big a mystery to us as we to them, however. <DcGentle> has a zealous purpose to create an engine that understands positional chess. If he succeeds, he will also create an engine that might be mistaken for a human, and whose moves will be explicable. My interest is more prosaic: to understand the engines in their own terms. Why do they not seem to perform correct searches at the depth they advertise. Would a better search result in more "chessic truth"? They are designed to win at short(ish) time controls, and compromise their searches to do it. But CC players need the really best moves, not some practical compromise. They don't build engines for that, so how can we trick the engines that we do have into finding the best moves, and not just winning because their blunders are not awful?

These questions lack answers, so if you have the answers, please be so kind as to post them in my chessforum.

Since I first wrote my profile I have revised my all-time favorites hall-of-fame. As before, Fischer is struggling to keep a place in the top ten. The main change, of course, is to include Carlsen, who has now not only won the world title, but also defended it. I now rank him ~even with Anand, whom he has beaten twice, though Anand remains his strongest challenger (written 4/28/2015) after a very enduring career with two defenses of the uncontested title.

Here is my current list:

1. Garry Kasparov
2. Mikhael Botvinnik
3. Alexander Alekhine
4. Raoul Capablanca
5. Emmanuel Lasker
6. Anatoly Karpov
7. Wilhelm Steinitz
8/9. Vishwanath Anand/Magnus Carlsen
10-13. Robert Fischer/ Mikhail Tal/ Paul Keres/ Vasily Smyslov 14. Tigran Petrosian
15-18. Aron Nimzovitsch/ Akiba Rubinstein/ Viktor Korchnoi/ Boris Spassky 19/20. Vladimir Kramnik/ Max Euwe

The above list includes all the recognized World Champions, plus the four best who never achieved that honor. Notably absent are Morphy and Philidor, who are the claimants most difficult to classify. If I were to include Morphy, I think he might bump Fischer et al. from the top ten, and Fischer from the no 1 spot among US players.

Comments on the above are welcome, of course. Full Member

   Tiggler has kibitzed 5633 times to chessgames   [more...]
   Sep-21-17 Big Pawn chessforum (replies)
Tiggler: <Big Pawn> Did you read it? Plenty of opinion on Darwin from people who never read him. And it is quite easy to read, compared, say, to Newton's Principia.
   Sep-20-17 World Cup (2017) (replies)
Tiggler: < And, with the white pieces, he decided not to look for struggle, putting his hopes in tiebreaks. He is considered the slight favorite at a faster time control.> <cro777> Yes, very good insight. MVL is favorite against Aronian in fast time controls.
   Sep-18-17 Louis Stumpers (replies)
Tiggler: <jb> OK, I get that. If you ever teach math anywhere, your students will add: any math topic taught by a blowhard. Isn't Stumpers a recreational page, or do you have a professional mission to enlighten and impress, even here?
   Sep-11-17 Yu Yangyi vs Svidler, 2014 (replies)
Tiggler: <malt: 33.Rh5+ gh5 34.Qg8+ Kh6 35.Qg6# or 35.Rg6#> Yu Yangyi vs Svidler, 2014
   Sep-04-17 O Balogun vs Carlsen, 2017 (replies)
Tiggler: Lenderman may be the lowest ranked player to get to the next round. If so I guess he will play Carlsen.
   Aug-26-17 Kramnik vs A Giri, 2016 (replies)
Tiggler: <Jimfromprovidence: 42...e4!? might be a saving move for black.> Yes, I think that draws. But white's 40.Ba3 was a mistake: [DIAGRAM] 40.Qd3 was correct.
   Aug-14-17 N Zwirs vs P V Nandhidhaa, 2016 (replies)
Tiggler: According to Houdini, White has 49 legal moves and at least 16 of them are mate in 7 or less.
   Aug-11-17 Sinquefield Cup (2017) (replies)
Tiggler: MVL is a very worthy winner. Strangely weak performance by all the Americans.
   Aug-08-17 Carlsen vs Nakamura, 2017 (replies)
Tiggler: <AylerKupp> As you well know, the advantage of those sites is that one does not need to even look at the position to know what is going on, because the evaluation tells the story.
   Aug-05-17 Carlsen vs M Vachier-Lagrave, 2017 (replies)
Tiggler: Gutsy play by MVL. He kept playing the sharpest moves until Magnus derailed. Now MC is looking at the wreckage.
(replies) indicates a reply to the comment.

Never kid a kidder

Kibitzer's Corner
< Earlier Kibitzing  · PAGE 16 OF 16 ·  Later Kibitzing>
Premium Chessgames Member
  Tiggler: <I see no reason why the St. Louis Chess Club would not be able to appoint Rich as Chief Arbiter next year>

Of course they could: it just would not be very smart. Just as Rich's choice was not, though of course he could.

Premium Chessgames Member
  morfishine: Good Evening <Tiggler>

I hope you don't mind me dropping by your forum here for the first time.

For sure, Fischer cannot be out of your top-10

This cannot be possible

Best, morf


Premium Chessgames Member
  Tiggler: <morf> Welcome, of course. Fischer has no shortage of admirers, but I am not one of them.
Premium Chessgames Member
  morfishine: <Tiggler> FWIW: I am no big admirer of Fischer myself, but from an objective point of view, IMHO, he has to be placed in the top 5

It all depends on what metrics one subscribes to and how objective one can be, all things considered


Premium Chessgames Member
  Tiggler: <It all depends on what metrics one subscribes to>. I don't think anyone succeeds in defining these <from an objective point of view>, and I don't try. I do place great weight on cumulative accomplishments over a career and on contributions to the development and history of chess. That might explain the reason for some of my selections. Botvinnik, for example.
Premium Chessgames Member
  morfishine: <Tiggler> Its a great testament to Botvinnik's character and fighting spirit that he could lose then regain the title not once, but twice

The reason I include Fischer is his 20 consecutive wins vs Masters. I don't think this feat will ever be matched

Premium Chessgames Member
  Tiggler: Topalov has to be considered as one of the best players never to win the uncontested WC. I'd like to see him in a match v Carlsen.
Sep-15-15  DanLanglois: Fischer's winning streak as a world champion candidate seems incredible to me, to the extent of being unique. I'm not insisting that he's the greatest ever, but there is that..
Premium Chessgames Member
  Tiggler: Well Hi, Dan! I never see you post anywhere except the correspondence match pages, but you are a welcome visitor here.

You are right about the Fischer streak. My problem with him is that his dominance was so brief. Dereliction of duty as WC, IMO.

Premium Chessgames Member
  thegoodanarchist: <Tiggler: <offramp: Listen fellas. When I hear the word haiku I reach for a gun...>

That one gets my vote for best haiku so far.>

Needs 1 more syllable:

Listen fellas. When
I hear the word haiku I
reach for a pistol.

Premium Chessgames Member
  thegoodanarchist: Even better (IMO) is

Listen up fellas.
When I hear the word haiku
I reach for a gun.

Premium Chessgames Member
  Tiggler: I think I found the origin of the mysterious differences between the FIDE tables for ratings based expected scores and the cumulative normal distribution with sd = 400.

The wiki article on the ELO system states:

" FIDE continues to use the rating difference table as proposed by Elo. The table is calculated with expectation 0, and standard deviation 2000 / 7."

If so, then it appears that Elo used the approximation 1/sqrt(2) = 0.7 .

For a difference in scores the corresponding distribution has sd multiplied by sqrt(2), so instead of getting sd = 400, as I had previously assumed, we get 404.061 .

So now the expected score (per game) is given by

=ERF(ratings difference/404.061)*0.5+0.5

This formula does match the tables in section 8.1 of the FIDE handbook.

Premium Chessgames Member
  Tiggler: In an interesting post on the WC Candidates forum, <AylerKupp> mentioned that Arpad Elo suggested the use of a t-distribution:

World Championship Candidates (2016)

The t-distribution (Student's t) is used to find the distribution of the differences between pairs of values drawn INDEPENDENTLY from the same normal distribution (my emphasis).

Elo's underlying assumption is that the performance of a player in a single game is distributed normally about his expected value, and that the standard deviation of the distribution is the same for all players.

So when two players come to the board the difference in their performance is based on their two independent random samples from their individual distributions. Hence the t-distribution.

This seems to me to be extremely contrived, though of course Dr. Elo can make whatever ad hoc assumptions he choses in his system.

I prefer the following argument, however. When two players come to the board, the distribution of the differences in their performance is the fundamental one, and the most parsimonious (in the Occam sense) description of this is the normal distribution.

We cannot say that in a single game the deviation of player A's performance from his expectation is independent of the deviation of player B's performance from his expectation. On the face of it that is absurd.

Premium Chessgames Member
  Tiggler: Chess could be made a lot more interesting, and more difficult for computers if it were an incomplete information game. Suppose that each player's move was kept secret until after their next move was played? Clocks would only start after white's second move, at which point the first would be revealed. Illegal moves would have to be announced by the arbiter and taken back with no penalty, other than the obligation to make another move with the same piece if possible.
Premium Chessgames Member
  Tiggler: Instead of minimax, the engines would have to use counterfactual regret.
Premium Chessgames Member
  Tiggler: Counterfactual regret - that's my latest pet phrase. Applicable to incomplete information game theory, or to posts from <Abdel Irada>.
Premium Chessgames Member
  AylerKupp: <Tiggler> I think that I've found another possibility for the "mysterious" use of SD = 2000/7 when calculating the values in Table 8.1b in the FIDE Rating Regulations. I re-read Dr. Elo's description of what he calls "the normal probability function, or standard sigmoid" (i.e. the CDF) in his book "The Rating of Chessplayers, Past and Present" where he says he used a "normal distribution function" (what I think is now consistently called the Normal Probability Density Function or PDF) with SD = 200 when determining the distribution of a player's individual performance. I thought that meant that he also used SD = 200 when calculating the CDF.

But no. As should have been obvious to anyone but me the random variable that this CDF refers to is NOT the distribution of a player's individual performance but the distribution of the <difference> between <two> player's performances in their individual games. Duh. Then if each player's individual performances are normally distributed with SDs = SD1 and SD2, the differences between the players' performance, d, in their individual games will also be normally distributed with SD = SQRT(SD1^2 + SD2^2), assuming that they play a sufficiently large number of games against each other (which is typical of today's top players). Then, if SD1 ~ SD2 ~ 200, SD = 200*SQRT(2) ~ 282.8. And that's another simplifying assumption that he uses, that the differences in SDs between the results of two players in the same pool are sufficiently close so as to not make a significant difference in the calculations.

Now, 282.8 is fairly close to 2000/7 ~ 285.7, and maybe he found it simpler to use 2000/7 rather than SD = 200*SQRT(2) when calculating P(Win/Draw) in Table 8.1b based on the player's rating difference, particularly since P(Win/Draw) is only being calculated to 2 significant digits. And indeed, if the midpoint of the ranges in FIDE's Table 8.1b is used (2 if the range is 0-3, 29 if the range is 26 32, etc.), then using either the definition of a Normal CDF = 1/2[ 1 + ERF[ (x Mean)/(SD*SQRT(2)) ] or Excel's NORMDIST function with either SD = 2000/7 or 200*SQRT(2) yields the same results as FIDE's Table 8.1b when rounded to two significant digits.

It was Dr. Elo's use of the term "normal probability function" for what is now consistently called the Cumulative Distribution Function that made me think that he was using SD = 200 for both of them. But of course that's no excuse, I should have read his description more carefully.

Premium Chessgames Member
  AylerKupp: <Tiggler> I think that you and I still have a different interpretation of the t-Distribution. I am under the impression that the t-Distribution is applicable when the sample size is small (e.g. when two players have not played a large number of games against each other) and therefore the use of the Normal distribution is not appropriate.

Since the t-Distribution approaches the Normal Distribution as the number of samples increases, then it would seem to me to make sense to use the t-Distribution with the appropriate degrees of freedom (number of games played 1) instead of the Normal Distribution when calculating the P(Win/Draw) between two players. But since FIDE uses the P(Win/Draw) to only two significant digits to calculate a player's rating change and then rounds this rating change to the nearest integer before specifying the player's new rating, I doubt that using either the t-Distribution or the Normal Distribution (or for that matter, many other distributions such as the Logistic Distribution) makes any difference.

Premium Chessgames Member
  AylerKupp: <<Tiggler> Chess could be made a lot more interesting, and more difficult for computers if it were an incomplete information game.>

It seems like you're talking about Kriegspiel or a variant of it. See if you're not familiar with it, as well as possible variations.

Jul-28-17  sea otter: How about an incomplete information game where the pawns formations are controlled by a computer? This would allow more pieces on the board and a new approach for human strategists, since they could better concentrate on maneuvering their many rooks and other pieces. Part of the skill would be in the interaction between pawns and pieces on the same team.
Premium Chessgames Member
  Tiggler: <AylerKupp> Yes, I suppose you could see the game I proposed as a variant of Kriegspiel, though not one of those mentioned in the wiki article. I think it is quite a lot different, though, because each player sees all the opponent's pieces in their correct spots, except for the piece they moved last.
Premium Chessgames Member
  Tiggler: <sea otter> "pawns are the soul of chess" (who said that?), so the game you propose seems a bit soulless to me.

And why is that an incomplete information game? An incomplete control game, maybe: partly a game of chance.

Premium Chessgames Member
  Tiggler: <AylerKupp> Yes, I am quite sure that Elo knew the sd should be 200*sgrt(2), but he just used 10/7 as an approximation for sqrt(2).

10/7 = 1.42857...
sqrt(2) = 1.414213562 etc

Almost exactly 1% off.

Premium Chessgames Member
  Tiggler: The "cumulative distribution" could mean the integral over any distribution, unless you specify the "cumulative normal distribution".
Jul-29-17  sea otter: <Tiggler> For example if the human and pawn-pusher both moved at the same time, 2-moves per turn - a pawn move by the cpu and a piece move by the human. Keeping the moves secret from the computer by requiring it to plan out a possible sequence of pawn moves, or maybe a small group of possible moves a few turns before it actually occurs and assigning the few possible chosen plans to each possible real move by the human might lead to interesting interplay between the programs and humans.

I've started playing the Bb4 winawer today, and it's interesting how the formations seem to limit scope and increase depth of calculation. There may be some implementation of the game I outlined with good aspects of the soulful pawn play in chess. For example in the winawer in one game I considered pushing my black g and h pawns, with a weak f7 pawn and f6 square, or in the sveshnikov-pelikan the empty d5 square. With fourteen pawns per side these types of concessions could easily be offset by other considerations.

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