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Aug1915
  Tiggler: <morf> Welcome, of course. Fischer has no shortage of admirers, but I am not one of them. 

Aug1915
  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 ***** 

Aug2015
  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. 

Aug2115
  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 

Aug2515
  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. 

Sep1515   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.. 

Sep1515
  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. 

Dec1215
  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. 

Dec1215
  thegoodanarchist: Even better (IMO) is
Listen up fellas.
When I hear the word haiku
I reach for a gun. 

Mar2316
  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. 

Mar2316
  Tiggler: In an interesting post on the WC Candidates forum, <AylerKupp> mentioned that Arpad Elo suggested the use of a tdistribution: World Championship Candidates (2016) The tdistribution (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 tdistribution. 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. 

May2117
  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. 

May2117
  Tiggler: Instead of minimax, the engines would have to use counterfactual regret. 

Jun0617
  Tiggler: Counterfactual regret  that's my latest pet phrase. Applicable to incomplete information game theory, or to posts from <Abdel Irada>. 

Jul2817
  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 reread 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 03, 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. 

Jul2817
  AylerKupp: <Tiggler> I think that you and I still have a different interpretation of the tDistribution. I am under the impression that the tDistribution 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 tDistribution approaches the Normal Distribution as the number of samples increases, then it would seem to me to make sense to use the tDistribution 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 tDistribution or the Normal Distribution (or for that matter, many other distributions such as the Logistic Distribution) makes any difference. 

Jul2817
  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 https://en.wikipedia.org/wiki/Krieg... if you're not familiar with it, as well as possible variations. 

Jul2817   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. 

Jul2917
  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. 

Jul2917
  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. 

Jul2917
  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. 

Jul2917
  Tiggler: The "cumulative distribution" could mean the integral over any distribution, unless you specify the "cumulative normal distribution".
https://en.wikipedia.org/wiki/Cumul... 

Jul2917   sea otter: <Tiggler> For example if the human and pawnpusher both moved at the same time, 2moves 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 sveshnikovpelikan the empty d5 square. With fourteen pawns per side these types of concessions could easily be offset by other considerations. 

Nov2717
  OhioChessFan: I think engines have had the happy, unintended consquence of getting people to think about such things. 

Dec2517
  Penguincw: Happy Holidays <Tiggler>. 



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