|
< Earlier Kibitzing · PAGE 3 OF 4 ·
Later Kibitzing> |
| Feb-13-06 | | Fan of Leko: <A corollary of Zermelo's Theorem states: For chess, one of the following three possibilities holds: (i) White has a strategy which always wins.
(ii) White has a strategy which always at least draws, but no strategy as in (i). (iii) Black has a strategy which always wins.> Well, now we know that either white wins, black wins, or the game is a draw. The chess world is forever indebted to Professor Zermelo for that startling revelation. |
|
| Feb-14-06 | | whatthefat: <Fan of Leko>
The point is that one could create a game where none of those hold, i.e. the problem can't be solved. Because chess is finite, a solution exists, and regardless of how hard it is to find, that fact must be acknowledged. Unfortunately, no matter how many times this point is raised, someone will still insist that chess can't be solved, and so there's no such thing as a best move(s) in a given position. This is just complete rot. Whether we know what they are or not, doesn't deny their existence. |
|
| Feb-14-06 | | Fan of Leko: <whatthefat> To call that a theorem is just a pretentious way of stating the obvious. There are other factors in the game besides the position on the board (opponent's strengths and weaknesses, previous games, clock, tournament standing, etc.) so the "best" move in one situation may not be best in another, even if the piece placement is identical. |
|
| Feb-14-06 | | euripides: Game theory does not usually provide an 'optimal' strategy independent of the opponent's play. Typically, game theorists seek pairs of strategies that are optimal against each other - known as Nash equilibria. This is the sort of strategy <whatthefat> and <ARTIN> consider. But there are other concepts of equilibrium sometimes used in game theory, such as 'trembling hand perfection', where it is assumed that the opponent may make a mistake - and there are some models of play under bounded rationality. Given that the whole point of chess is that people do usually make mistkes, such concepts may be more relevant to the understanding of chess than Nash equilibrium. |
|
Feb-14-06
 | | LIFE Master AJ: I have actually taken some college courses in game theory. While interesting, their actual application to chess is vertually nil. |
|
| Feb-14-06 | | whatthefat: <LIFE Master AJ>
Not in the case where you have reasonable knowledge of your opponent beforehand. The thing is, most "chess psychology" is simply an intuitive application of game theory. So learning the actual mathematics of game theory may not be particularly helpful in a chess game, but the principles behind it certainly are. |
|
| Feb-14-06 | | Jim Bartle: "My web page pretty much speaks for itself."
I guess that's clear and correct, but it sure sounds strange. |
|
| Feb-14-06 | | euripides: You could certainly apply game theory to things like tournament strategy e.g. what effect a change in tournament structure might have on players' willingness to take risks. Under some circumstances you might get multiple equilibria that could be quite interesting e.g. if all the good players play conservatively, none of them has an incentive to play very riskily; but if one of them plays riskily, there is an incentive for others to follow suit (Topalov and Anand at Wijk an Zee might be an example). |
|
| Feb-14-06 | | Jim Bartle: Kotov in "Think" had a section on "To Analyze or Not to Analyze," advice on whether to accept or sacrifice, enter into complications or (metaphor alert!) sail toward calm waters, etc. depending on your tournament position. He used as an example a game where Smyslov was black against Keres at Zurich 1953. :White offered a rook on the h-file, and Smyslov, leading the tourney by a point or two (after 23 rounds!), had to decide whether to take it and go for a win, or refuse it. So Smyslov declined the whole rook, and ended up winning as Keres pressed for a needed win. |
|
| Feb-22-06 | | ARTIN: Fan of Leko,
it is not so obvious. In fact, if you remove the condition that if for 50 moves no pawns are moved or exchanges are made the game is a draw, the theorem ceases to be true. |
|
| Feb-22-06 | | Boomie: Every time I play over this game and watch that majestic march of the white king, I cannot help but laugh. <LMAJ's> analysis of this game at http://www.lifemasteraj.com/great_c... is a fine piece of work which I recommend to everyone. Concerning the discussion of black's alternatives after 9. cxd5, my first glance preference was for 9...Nxd5. If white takes the knight, black takes with the e-pawn and has solved most of his developmental problems. However white will not be so accomodating. 9...Nxd5 10. Bg3 Qa5
(10...Nb4 11. Qd2 h5 12. h4 Nf6  0.35/13)
11. Rc1 0.27/14
So the immediate exd5 does make sense. However white need not allow the piece trade after Nh5. After the simple 10. h3, black's best idea seems to be neutralising the potent bishop on f4. A big plus to exd5 is black's woeful q-bishop is unleashed. 9...exd5 10. h3 Ne8 11. Bd3 Bd6 12. Bxd6 Nxd6 0.30/13 Naturally the computer evaluations are in no way definitive and I include them only because they are available as raw data. |
|
| Oct-02-06 | | amuralid: <LMAJ> Nice work on the website. |
|
| Apr-07-07 | | Ulhumbrus: Max Euwe annotates this game in the book "The best in chess" one of whose authors is I A Horowitz. Euwe says something like "One of the best games was that won by Petrosian against Unzicker. In a style reminiscent of Capablanca, Petrosian acquires a small advantage and nurses it to victory. It looks very simple, but it is given only to a very few to perform so overwhelmingly in a contest with a first class master. Perhaps I can shed a little more light on this. After 12…b4 in reply to 11 a4 played in reply to 11…b5, Petrosian acquires not just one asset on the Queen side, but a number of them, which is to say that Unzicker contracts not just one weakness on the Queen side but a number of them. One consequence of this is that Petrosian acquires an additional asset on the Queen side, control of the c file, which is to say that Unzicker contracts an additional liability on the Queen side. All these make up collectively not a small advantage but a large advantage. In fact we can say that for the remainder of the game, Black's entire Queen side is crying in wounded agony, impairing completely Black's ability to contest the duel. Is it then any wonder then, that Petrosian should perform overwhelmingly, as Euwe says?
So the explanation is that Petrosian acquires not a small advantage but in fact a large advantage. |
|
| Apr-07-07 | | Ulhumbrus: Max Euwe annotates this game in the book "The best in chess" one of whose authors is I A Horowitz. Euwe says something like "One of the best games was that won by Petrosian against Unzicker. In a style reminiscent of Capablanca, Petrosian acquires a small advantage and nurses it to victory. It looks very simple, but it is given only to a very few to perform so overwhelmingly in a contest with a first class master." Perhaps I can shed a little more light on this. After 12…b4 in reply to 11 a4 played in reply to 11…b5, Petrosian acquires not just one asset on the Queen side, but a number of them, which is to say that Unzicker contracts not just one weakness on the Queen side but a number of them. One consequence of this is that Petrosian acquires an additional asset on the Queen side, control of the c file, which is to say that Unzicker contracts an additional liability on the Queen side. All these make up collectively not a small advantage but a great advantage. In fact we can say that for the remainder of the game, Black's entire Queen side is crying in wounded agony, impairing thoroughly Black's ability to contest the duel. Is it then any wonder then, that Petrosian should perform overwhelmingly, as Euwe says? So the explanation is that Petrosian acquires not a small advantage but a great advantage, a great advantage which Petrosian is able to make count, so as to perform overwhelmingly. |
|
| Jun-20-08 | | arsen387: WOW, what a use of the open file. Really a Capablanca style win as Euwe said. Starting from move 29 Petrosian carries out a great plan - brings his K to b1 where it is safe and starts to push pawns on the Kside to open lines around black K, while black hasn't that luxury and is doomed to unuseful moves. Notice that if 52..Ra7 to avoid material loss then 53.f5 Qxf5 54.Rxd8 Bxd8 55.Qb7! wins a piece. A true masterpiece by Petrosian, one of his best games I think. |
|
| Jul-29-08 | | norcist: 11...Nh5!?; 12.Be5! f6!? 13.Bc7!! Qxc7 14.Nxd5! Qxc2 15.Nxe7+ Kf7; 16.Bxc2 Kxe7; 17.Bg6 b6; 18.Bxh5 Bb7; 19.Nd2, '±' All thanks to <LMAJ> for this line |
|
| Jan-16-09 | | WhiteRook48: Petrosian was really a master... |
|
| Oct-18-10 | | timothee3331: <ARTIN> "Many chessplayers know the multiplication table of chess and even its logarithm table. That's why we should endeavour to prove that sometimes 2+2 = 5 " Mikhail Tal My opinion is that you're correct, they are three tpes of moves, but chess discoveries are made very often and i believe we don't fully understand the game. That's why i think this kind of approach is unuseful |
|
| Feb-06-11 | | GilesFarnaby: Regarding black´s 9th move I plugged it and found out that Houdini had only scope for ...Nxd5
click for larger viewAnalysis by Houdini 1.5a w32:
9...Nxd5 10.Bg3 c5 11.Be2 cxd4 12.Nxd4 Nxc3 13.bxc3 e5 14.Nf5 Bf6 15.Rd1 Qc7 16.Nd6 Nc5 17.Nxc8 Raxc8 18.0-0 Rfd8 19.Bf3 Ne6 20.Bd5 Qxc3 21.Qxc3 Rxc3 22.Bxb7 Rc2 23.Rxd8+ Nxd8 24.Bd5
= (0.17) Depth: 23/52 00:04:48 389mN
Other than that I couldn´t find a single game in my database (with over 4 million games) where a GM played that position with black, so I don´t think that helps too much. In any case most people will agree, I guess, that the 9th move by Unzicker was not the losing one, but rather the Q-side over expansion sequence. |
|
| Feb-07-11 | | masterzelman: Beautful to see how one advantage- the c-file- enables the creation of another- the attack on the king side once the king has wandered to the queen side. |
|
| Nov-12-11 | | Ulhumbrus: After 11... b5 Black's QB is bad, but after Black plays 12...b4 in order to exchange the bad QB, Black's KB becomes bad. |
|
| Aug-19-13 | | ForeverYoung: 11 ... b5 drew the censure by Clarke for weakening c6 and allowing white great positional play, but 9 ... cxd5 deserves to be knocked, playing into a symetrical position where white has all the chances. If black feared the minority attack he should not have played the black side of the queen's gambit declined. |
|
Mar-02-14
 | | Benzol: <AJ> It appears that you have left posts on this game page. |
|
| Mar-02-14 | | john barleycorn: < Benzol: <AJ> It appears that you have left posts on this game page.> Strange, isn't it. |
|
Mar-03-14
| | LIFE Master AJ: <Benzol> Yes indeedy. Apparently, I made a mistake ... using the drop-down menu. (I may have clicked on the wrong Petrosian, I had no idea that BOTH were <now> on the drop-down list.) |
|
 |
|
|
< Earlier Kibitzing · PAGE 3 OF 4 ·
Later Kibitzing> |
Kibitzing
Annotations by 