Author: Stephen A. Boak
Date: 20:39:57 07/15/00
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>Simplifying. I have a penny. >I toss it twice. >Heads, heads. >I toss it twice >Heads, heads. >I toss it twice >Tails, heads. >I toss it twice >Heads, tails. > >I count them up. > >Heads are stronger than tails. > >My conclusion is faulty. Why? Because I did not gather enough data. > >In the case of chess games, as the GM's learn from previous mistakes, the true >strength of the program will be revealed. The same would be true of a human >player. Given enough games, they will settle down to their true strength. > >With a computer, which is more deterministic than a human and if it learns, does >not learn nearly so well, the effect of more games will be far more devastating. > >At least according to the model I am imagining. But models can be wrong, or >imprecise. Ho hum. Here's some food for thought. Not all may be highly digestable! 1. If Junior6 plays 9 games against top grandmasters under tournament conditions, the results are (some) evidence of its strength. Period. Certainly the results are more evidence than existed before Junior6 played those grandmasters. The weight that should be given to those results is subject to debate and interpretation and will likely lead to differences of opinion, even opinion well-reasoned on different sides. But evidence it is. How much evidence is needed to draw a conclusion? a mathematical conclusion? When will a critic be convinced that a program is GM strength? Is there a mathematical confidence level that *all* critics will accept? Is that enough? See next point. 2. If enough trials are required to determine if, for example, a tossed coin is fair, how many trials is that? If 100 tosses is not enough, how many tosses would be enough? This is debatable also. If statistical uncertainty exists, no matter how many trials are conducted, does that mean certainty is never possible according to mathematics? I wouldn't continually pound sand to say there are not enough trials to draw a conclusion, if the math I relied on would never allow a certain conclusion to be drawn, strictly speaking in the language of mathematics. After all, with a fair coin the possibility of 1,000,000 tosses resulting in all heads is possible--even with the fair coin, right? 3. As to the belief that a GM would (likely) learn from a series of computer games, and the program would (likely) not learn the equivalent (about the GM's weaknesses): A. If, say, Kramnik studied carefully all the games of Akopian, and thereafter never lost a single game to Akopian but rather won 80% of the points, would that make Akopian *not* a GM? No. Would that mean that *all* GMs could accomplish the same feat as Kramnik? No. B. If modern GMs, having the advantage of many, many games of predecessors to study, would be able to study the games of a very strong player of the past, wouldn't it be likely that the modern GMs would be able to beat those historical figures--if a match could be arranged today between the same individuals--the modern figure and the historical one? After all, they have been able to study the historical player's games, but not vice versa. Would this make the older GMs not GMs after all? I don't think this is an automatic 'Yes' answer. The older players might have been able to learn and beat the modern players because they are also humans, and might adapt to modern play very quickly (learning also after some games). C. If a computer program is a 'learning' program, but the learning curve was slower (initially) than the GM opponents learning curves, would the fact that the humans quickly jumped on the computers weaknesses (choice of openings, etc) mean that the humans would *always* dominate the computers thereafter, or might the learning curve of the computer eventually surpass that of the humans, under some circumstances? D. If a GM ages and then fails to achieve the same results as when he was younger and played better (relative to his opponents, of course), was he not nevertheless a GM in his younger days, although his opponents continue to learn and eventually best him a lot more than previously? Maybe aging leads to a slowdown in learning ability or lessens the desire to study opponents's games. Maybe a GM fades sometimes not because his powers have become weaker, but because his opponents have (on the average) become smarter, better players, maybe due to use of learning tools the older GM does not rely on, such as computers, etc. E. If GMs learn about the weaknesses of a computer, and thereafter achieve better results against it, perhaps the computer was and is still a GM in strength, but the competition has improved itself (relative to the program). If the GM humans become better players (even if only relative to one program), then the computer should not have to win as great a percentage of the points to still be considered GM in strength. I hear arguments about the ability of the human GMs to learn and improve their play against the computers, but no corresponding credit is then given to the computers for playing against stronger (more learned) GM opponents. 4. Consider this--I compile a poly-program composed of all the program versions that have played at tournament time controls against human GMs. I run this poly-program on a poly-computer composed of all the hardware circuits and processesors that those programs have played on against human GMs in the past. Assume this poly-program randomly utilizes only some selected combination of program and processor that had been utilized in the past? Is my poly-program, running on a poly-computer, a GM (let's say, over 2500 ELO TPR), if its predecessor parts and predecessor programs in individual combinations achieved an average of 2500+ ELO TPR (calculated on the whole)? Is my program a GM in style, because it changes its style of play flexibly and often enough to make preparation by the opponent a very difficult matter? These are simply some things to ponder--I am not drawing any conclusions as yet. --Steve :)
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