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In addition, you'll not be surprised if we express here all our enthusiasm for the very great talent of Larry Elmore, to which we owe the illustration of this page. We thank very much him for this!!... Don't be missing to vist both sites suggested here; his own website and another which is partially devoted to him.
The objective is here to analyze how the hazard gets into the heart of a chess game, although Chess isn't a game of chance; we precisely describe the four sources of the hazard in Chess.
*** THE HAZARD ***
1°) The hazard expresses the limit of our knowledge of the future, whether it is with short or or more or less long term. Thus, the hazard is a more or less significant component of any human activity. 2°) The French expression "par hasard", seems to be correctly translated by "perchance", "by (any) chance", "accidentally"; people may use correctly this expressions only in the sense of "coincidence", such as in the theory of parallel causal series of Carnot (typical example: the man who walks in the street and receives a tile on the head). 3°) The hazard (or chance if you want) is known as "objective" if it intervenes, in the evolution of the universe, independently of any observer. To accept its existence quite simply amounts denying the integral determinism, such as Laplace conceives it. This introduced a great philosophical debate which, also enthralling is it, does not have its place here. 4°) The hazard is known as "subjective" if it refers to an observer - individual or collective; example : you and me are observers, but very whole humanity, just as any group made up, is also an observer -. Then, the hazard, the chance (I mean luck or bad luck), relative to a given observer, precisely express all that this observer cannot provide; cannot predict.
5°) The hazard emerges as soon as there are uncertainty, doubt, risk, chance or bad luck. As much to say that the chance is present in any human activity. Therefore, in particular in any play. And consequently in the chess game. 6°) In much observable phenomena, it's easy to identify a deterministic component and a random component. For example: a TGV (French train, high-speed railway) goes from Paris to Lyon. Its course is a priori entirely foreseeable. However the hazard (or risk if you prefer) is involved on two levels: i) vibrations. ii) mishaps, which are of technical or human origin. 7°) Complexity and hazard: The more complex one deterministic situation is, the more one part of the information which explicitely describes it risk to escape to us; this way, the hazard is introduce by our incapacity to perceive the necessary information in its entirety.
*** CHESS AND HAZARD ***
Being in the course of a game, I launch into a more or less risky sacrifice. I devote 15 minutes of my time to analyze, as precisely as possible, the consequences of my choice. Finally, I retain the idea of this sacrifice, whereas it's impossible for me to examine entirely all its implications ... I thus run a risk ... The hazard intervenes.
Thus it is clear that the hazard is present in any circumstance of the life where there are uncertainty, risk, doubt, chance or bad luck, so that the hazard is one of the ingredients of every chess game. This being said, there are players who, after a game, will tend to say or think that if they winned it is because they played really well and that if they lost it is primarily by bad luck... It's then a beautiful example of intellectual dishonesty, as well it is true that, with the chess game, the quality of play produced imports more than the chance.
*** HAZARD AND PROBABILITY ***
Some observable phenomena lend themselves easily to a modeling. It is typically the case of games of chance (dice, 421, LOTO, playing cards etc...). For some other phenomena it's not easy at all to find an appropriate modelisation. Lastly, in many cases, it is impossible to find a suitable probabilistic model.
*** THE 4 SOURCES OF THE HAZARD IN CHESS ***
1°) The player himself. Indeed, each player doubts, more or less, of his faculties to produce, in the time which is assigned to him, a certain quality of play. Will I be able to keep me calm? Will I have, in any moment, a rather high level of concentration? Will I be able to rely upon my memory, in view to avoid traps of the opening? Will I find the suitable strategy? Will I be enough clear-sighted to preserve an acquired advantage? Will I keep myself enough under control to treat correctly the final and to conclude? In other words, how will I behave vis-a-vis the game? 2°) The adversary. He can be completely unknown, in wich case one doesn't have other elements, to forge an idea of his playing level that his ELO Rating and can come out from his physical appearance and his personality. In case that the opponent is known, either of reputation or personally, that adds other known data. But, at all events, the moves which will be chosen by him, just as its times of reflection, essentially, are ignored and prone to hazard (therefore to risk). 3°) The game. In a given position, the hazard expresses the share of information which it contains and which we do not menage to detect, have regard with its too great complexity. This concept is very subjective and depends obviously on the specific qualities of each one. Players of the most level, such Fischer, Kasparov or Alekhine, have a depth of analysis which transcendsof much ours. However, this one has limits all the same. In a very complex position, even the greatest genius cannot discover all that it conceals, so that even for him the hazard intervens. 4°) The external world. Even if people would tend to pass this aspect under silence, it should well be held account owing to the fact that the two players, just as the chessboard, form part of the universe in evolution and are thus subjected to the hazard (in fact all the risks) that it carries with him. One will smile if I speak here about an air attack, an earthquake, or an intrusion, into the club or the room tournament, of an armed commando: but, one can think also, more prosaically, of the referee's decisions, the behaviors of other present players, the unexpected interruptions of play etc...
*** CHESS AND MODELISATION (or MODELING) ***
The difficulty of probabilistic modeling (in fact I prefer the French word : "modelisation", because modeling seems to me rather not clearly defined if one considers its various usages!) arises then. Can people find good models adapted to the chess game? All depends, in this respect, of the objectives which one lays down. Either you wish to tackle the problem of hazard in his entirety, or you are satisfied to deal with specific problems.
1°) The hazard, intervening with Chess, is primarily not medelisable (modeling if you prefer). I quated the four sources of the hazard in Chess. However, each of them is too much complex to be the object of probabilistic modeling; what to say then of the four intermingled? 2°) One can extract from the chess game some elementary problems, being able to lead to elementary probabilistic models. Here are, on a purely illustrative basis, some examples:
i) A player learns the rules of chess, without being initiated with the least element of the theory. He plays the first move of his first game, with the White. Taking into account the fact that there are 16 moves of pawn and 4 possible move of a Knight, we are led to think that the probability so that player opens his game by a move of a Knight is: 20% (either: 0.2). ii) For an experienced player, for which we don't have any particular information, the probability (empirical) so that he begins with a Knight is 10% (either precisely : 0.100330617 (source: ChessBase)). iii) If one knows a player beginning always his games by: 1.Nf3, one can estimate at 1% the risk which he abruptly changes opinion and consider that the probability that this player begins by a Knight is about 99% (either: 0.99). iv) If a chess player starts his game by 1.e4, the empirical (i.e. experimental) probability of winning, excluding the draw ones, is for him of 53% (either: 0.53 (source: ChessBase)). If he plays 1.d4 or 1.Nf3, this empirical probability is of 55% (either: 0.55 (source: ChessBase)).
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