Author: Michael Neish
Date: 03:15:50 01/30/00
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On January 29, 2000 at 14:11:01, Enrique Irazoqui wrote: >Come on, come on. Where did I say I don't believe in statistics? I have >questions about yours. Namely 2: the effect of non-transitivity and Matthias' >point about a game of chess being not necessarily one and only one probabilistic >event. Christophe: I don't have your statistics clear, that's all. I haven't read Matthias's post (perhaps I should). What argument does he use to support his assertion that a game of Chess is not a single probabilistic event? I'm curious. Let's say we look at all the games of the Cadaques tournament, once it is over. Let's say, for example, that 30% of the total 420 games are draws, and the rest wins either for White or Black. It doesn't matter what the exact figures are for the sake of this argument. So, then, in a 20-game match between computers of equal strength, we can expect on average that six games will be drawn and the rest will be wins or losses. Again it doesn't matter that the computers are not really of equal strength for this argument. Now, a game of Chess is not a single probabilistic event, I agree, because a series of errors can occur from one or the other player, which might compensate for each other in the course of a game. But this is totally *irrelevant* because the outcome of all these little errors one way and the other is *still* the fact that 30% of games will be drawn and 70% not. What you model by statistical analysis is the sequence of the results. In what order do the draws, wins and losses occur? Do you win the first seven games, draw the next six and lose the next seven? Do you win, lose, win, lose and then draw the last six? There are millions of possible combinations. By chance you might win nine games insted of the expected seven, and score more over the 20-game match than you should. You might win more games in one match and fewer in another. Sorry, this is an obvious fact I think -- but maybe not so obvious to those who support Matthias's opinion. This is the whole point of statistics -- you model large numbers of events because studying the inner workings of one single event is too difficult. The outcome of one game might depend on errors, the wind direction, what Player A had for breakfast, the colour of his shirt -- all this is irrelevant!! You can still say that there is a 30% chance of a draw, 40% chance of White winning and 40% chance of Black winning (or whatever the real figures are), and take it from there. It's mildly disturbing when you attempt to model some complicated interaction, such as a game of Chess, as a single event. It rebels against our intuition. Collect all the exam results from your university for the last thirty years, put them all together and plot them, and you'll get a nice Bell curve. Each component of the collection is an individual human being leading her or his own life, with her own problems, motivations, ability, circumstances, etc. One candidate might get Question 30 right, but 45 wrong; another might get both right. It all doesn't matter. You combine everyone together and you get a nice-looking curve. You don't need to know the details of everyone's life -- you know what the probability of someone passing the exam is, based on the curve; you can predict how many will pass this year (though this number is also subject to statistical fluctuations). But you can't tell who will or won't pass. Likewise you cannot tell in advance what the outcome of a single game will be. So it's easy for those who think that modelling Chess results as single event is a gross oversimplification, but I contend that it works, and if someone disagrees, please try to prove me wrong. Cheers, Mike.
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