AUTUMN 2009

The Journal of Chess  is not only about chess. Its scope is wider. It is about chess and learning and about how chess can be linked to education. To read all the articles and texts' lines that link chess and learning, just click edit then search or find and type learning in the search box.


October 23, 2009

Does Chess follow Game Theory? What is Game Theory? An answer to a chessmate

Last month I had a discussion with a chessmate at the Chess and Checkers' House about my manuscript Chess and the Bayesian Statistics in which the chessmate, Hawk, tried to refute my concept that Chess obeys to Bayesian Statistics and argued that Chess obeys to Game Theory which he says is a "theory of luck".
    Game theory is a mathematical field that analyses the optimal choices or events that, under given conditions, will lead to a desired outcome. It is more related to statistics and probability than to any other field of mathematics since it gives the "chance" or the possibilities of winning for any game whatever it is sport or saloon game. It gives the pro and con. "Single-person games", like Solitaire," although they may be complex and interesting from a probabilistic view, are not rewarding from a game-theory perspective, for no adversary is making independent strategic choices with which another must contend" (Game Theory," Microsoft(R) Encarta(R) 98 Encyclopedia. (c) 1993-1997 Microsoft Corporation). In Wikibooks Game theory is described as it follows: "Game Theory might be better described as Strategy Theory, or Theory of Interactive Decision Making. A strategic situation involves two or more interacting players who make decisions while trying to anticipate the actions and reactions by others." (Introduction to Game Theory, Wikibooks Wikimedia, Wikipedia Encyclopedia). And in Wikipedia Encyclopedia it is said "Game theory uses math to study strategy. Game theory studies more than just board games, sports, and games of luck. It also studies things like business and military decisions. In game theory, people call all of these situations "games." In other words, you can use game theory to study any situation where more than one person makes choices." (Game Theory, Wikipedia Encyclopedia). Luck is described as a very small possibility of wining. In a lottery game this possibility is always the same for any player while in Chess it is rarely if never the same.
    "Game theory can be traced back to Babylonian times, in the so called Marriage Contract Problem, although this was only recognised as such in 1985. Game Theory really began to emerge as a" scientific "subject in the 1900s. Firstly by Ernst Zermelo in his paper Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels ("On the Application of Set Theory to the Theory of Chess") of 1913, in which the first 'theorem' of game theory was published." This theory (known as Zermelo's Theorem) states that in the game of chess" either side - black or white - can force a win, or both sides can force at least a draw. (Introduction to Game Theory/Short history, Wikibooks Wikimedia, Wikipedia Encyclopedia).
    Chess may obey to Game Theory but Chess does not obey to luck and both players (Blacks or Whites) do no not have an equal chance of wining unless they are of equal strenght, a very rare event. An example to understand what is Game Theory and how it differs from luck is the Prisoners' Dilemma. It's an imaginary situation ...: the police catch two criminals after they committed a crime. The police do not know which person committed the crime and which person just helped. They question the two in separate cells. Each prisoner can either stay silent or betray (hurt) the other by blaming the crime on them. If both stay silent, they only go to jail for 6 months. If one betrays and the other stays silent, the one that stays silent goes to jail for 10 years and the other one does not go to jail at all. If they both betray each other, they each go to jail for 2 years. No matter what happens, the prisoners will never see each other again."
    But what is Bayesian Statistics? In the first chapter of the manuscript I have extensively explained that Chess obeys to mathematical laws and that Bayesian statistics deals with the intrication of probabilities that is encountered in a Chess game. Thus, Bayesian statistics like Game theory Game theory is "a branch of applied mathematics" that can be used in any science - "social sciences, most notably in economics, as well as in biology, engineering, political science, international relations, computer science, and philosophy" - in any situation where one may attempt "to mathematically capture behavior ... in which an individual's success in making choices depends on the choices of others", thus on probabilty. In fact, Bayesian statistics are only part of Game theory which, like the theory of Relativity, for example, explains Nature in general and eliminates Chance or its contrary, the Hands of God (reserve a l'auteur).
    Finally, While Mr. Hawk knows a good deal about science and knows that Chess obeys to Game theory, it does not know what is Bayesian statistics and it is there where its error of judgement came from. While Game theory includes chance which can be identified as a very minute probability and its contrary, certitude, which is a probabilty of 100% or things that are linked (seemingly) with no probability* like for the evolutionary forces. Bayesian statistics cannot take into account the former since it is Statistical inference that deals with conditional probability, the one that depends on the anterior moves which all begin with the Opening.
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* Unlike economics, the payoffs for games in biology are often interpreted as corresponding to fitness. In addition, the focus has been less on equilibria that correspond to a notion of rationality, but rather on ones that would be maintained by evolutionary forces. (Game Theory/, Wikipedia Encyclopedia; last modified on 19 September 2009).

** l'évolution est comme une grande stratégie de jeu ayant plusieurs matrices profitables comportant plusieurs entrées variables (tirées de l'hérédité et de l'environnement); l'extinction , l'espéciation et l'exclusion ou la domination par la compétition peuvent être envisagées comme des sorties après un "pari", un jeu sur telle ou telle entrée . Cependant, même cette définition paraît un peu trop simple, car l'évolution a une directionalité et ne fait pas marche arrière. (Dr Qualo R; Les Grandes Notions Contemporaines de Biologie: Évolution: Ce Que C’Est et Historique; New York, 1999, 2003

September 11, 2009

A Giuco Piano analyzed and commented

September 10, 2009

What is new with my opening? Ordinary I make a cautious opening: Whites: 1.d3 d5 2.e3 e5 3.h3 Nf6 4.Be2 Bd6 5.Nf3 O-O 6.Nbd2 c5 7.O-O. However because I wanted to improve my game and because i am often lost at he beginning of the midlle game, I begun to learn other openings. I knew fast results with beginners when I played the Giuco Piano and overalll it is fun, interesting and learn you new tactics. However, I begun to fell too often against intermediate players, some of them I was even to win against before. I decided to analyse the causes of those losses. I saw that the openings learned, already at the number of seven - Queen's Gambit, Ruy Lopez, Giuco Piano, Sicilian Defense, Dutch Defense, Reti System and Caro-Kann Defense - exposed too much my game and the non beginners knew often what I am going to do and found easy solutions. Other blows I have noticed in my game are: I have been exposing my pieces unnecessarily without a good plan of attack and have been losing often a knight at the begiining of the game; it was also harder for me to defend my king while at the same time doing an assault. I decided then to return to my old opening with which I can be more cautious at the beginningand will be able to lead an assault while defending my king. They often think that the knights are valuable at the beginning; I discovered that they are more valuable at the middle-game* while the pawns shall have the priority for the assault at the beginning of the game. Nevertheless, the other pieces shall be moved and placed in such a way and in such a position to be able to assist the attacking pawns, to build a good defense by protecting each other and to plan a good attack. I try my opening against the classic Giuco Piano and I got those answers with the computer playing itself then after: at the end of the opening "You have a minimal advantage", at the middle-game , "The game is level", at the end of the middle-game, "You have a minimal advantage", at the end-game "You have a sizable advantage". The impression I got is that my opening has confered me an advantage but this was not evident till the end-game. What is more important is that this opening can be played with either set black or white, as defense or as attack (1.e4 d6 2.Nf3 e63.Bc4 a6 4.Ng5 Nf6 5.Qf3 Nbd7 6.d4 Nb6 7.Nd2 h6 8.Nh3 Nxe4 9.Qxe4 Nxc4 10.Nxc4 d5 11.Qd3 dxc4 12.Qxc4 Bd7 13.Bf4 Bb5 14.Qc3 Qd5
15.f3 c5 16.Be3 cxd4 17.Bxd4 Rd8 18.Bb6 Rd7 19.Qc8+ Ke7 20.Be3 Qe5 21.Qc5+ Qxc5 22.Bxc5+ Kf6 23.Nf2 Bxc5 24.Ne4+ Ke5 25.Nxc5 Rc7 26.b4 b6 27.Nd3+ Bxd3 28.cxd3 Kd4 29.Kd2 Rhc8 30.Rac1 *)

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* The knights are more valuable at the middle-game where they can assist the queen, a better combinaison than the Queen and the bishop in Capablanca words; in this game, the black knight and the black queen pawn have made a coordinated attack that has led first to and advantage for the blacks then to victory (9.Qxe4 Nxc4 10.Nxc4 d5 11.Qd3 dxc4).

September 9, 2009

A Game Played with Infractions to the Rules: Yesterday I was playing my old chessmate. At a point of the game, he moved his queen to capture my rook and even touched the rook. I precipitate myself to take his queen while he was still holding it. When he saw his mistake he changed his mind and wanted to do another move. Discussions and disagreeements follow. The rules have not been observed and we were both guilty. What are the rules then? And what should have been done? The artticles of the FIDE LAWS OF CHESS about that are:

  • "article 4.3: you must capture the piece touched and if you touch more than one piece you must capture the first touched "
  • "article 4.6: if none of the pieces touched can be captured the player can make any other legal move" but it was definitely not the case
  • "4.6 When, as a legal move or part of a legal move, a piece has been released on a square, it cannot then be moved to another square. The move is considered to have been made when all the relevant requirements of Article 3 have been fulfilled.
    1. in the case of a capture, when the captured piece has been removed from the chessboard and the player, having placed his own piece on its new square, has released this capturing piece from his hand"

However, the capture was not yet completed when I try to capture the queen of my chessmate. In such a situation wha would have done a referee to solve our disagreement? I have different opinions.

  1. The first one is that my mate should have been forced to redo move and capture my rook. Then I will have have captured his queen after he ha completed the move.
  2. The second one is that my mate should have been allowed to do another move but should have been obliged to move his queen
  3. A third one is the annulation of the game

Those infractions to the rules are common at the Chess & Checkers' House where the game is played between friends who often ignore the rules. Last week a player suffering probably of bipolar disorder misbehave himself and put the place in disrepute, while I was learning a kid the Giuco Piano opening. Article 12 about the conduct of the player is as follows

  • " 12.1: The player shall take no action that will bring the chessgame into disrepute"
  • "12.6: It i forbidden to distract or annoy any of the other player "

September 8, 2009

In honour of cousin Mario and Capablanca. A young cousin, Mario Aguiar whose father was of Cuban origin like the great Chess master Jose Raul Capablanca has teached me how to play chess . Chessmetrics ranks Capablanca among the toppest of all times having been a master in both Speed and Regular Chess games (reserve a l'auteur: p1 et p.2)

September 7, 2009

Chess and Temperance: Does Chess foster temperance? My answer is Yes. In playing Chess you have to use moderation and self-restraint, as in behavior or expression and that is what temperance is about. Article 12 of the Fide Laws of Chess sets the rules for the behavior of the player. A player, for example, is forbidden to distract or annoy his opponent in any manner whatsoever - using cell phone, playing music, etc., including even unreasonable claims or unreasonable offers of a draw.
    Can Chess correct dysfunctional behaviors? My answer is No. Any person suffering of a dysfonctional behavior shall have his behavior problems either healed or controled by medicine or pschology. Bipolar disorders, for example, may not disturb the mind enough to prevent a person of playing Chess but whenever such behavior problems manifest themselves while somebody is playing Chess the body shall refrain himself or be refrained of playing Chess till his behavior is under control. Last week a player suffering of bipolar disorders has a misbehavior that brought the game of chess into disrepute at The Chess & Checkers' House in Central Park, fghting, assaulting other players and having come at the Chess terrace under substance and alcohol influence. (Reserve a l'auteur)

erve a l'auteur)