Author: Don Dailey
Date: 12:26:39 09/06/98
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On September 06, 1998 at 14:55:16, Robert Henry Durrett wrote: >On September 06, 1998 at 14:27:08, Don Dailey wrote: > >>>>Shall we try it on the group? What is a combination? Give an answer >>>>that has no ambiguity whatsoever. I have never seen one in any book, >>>>but I've seen many attempts. You may be able to come up with a strict >>>>definition of what a combination is, but I'll be many will disagree >>>>about what this definition should be. Your definition will probably >>>>not match peoples perception of what they think a combination is. >>> >>>>- Don >>> >>> >>> An interesting game. I tried to give an objective definition of a >>>combination. at first sight it seemed easier than it was in reality! Here is my >>>attempt : >>> >>> >>>Combination : A series of 2 or more consecutive moves involving the sacrifice or >>>investment of material, and by which the player that initiated it gains some >>>sensible benefits whatever his/her opponent play to counter it. The benefits >>>could be a greater material win in the end or in another form (e.g. a huge space >>>advantage, a strong passed pawn etc.). >>> >>> >>> >>> Having said that, I will now give (I did not look at it before writing mine) >>>the one of IM Nicolas Giffard in his book "Le guide des echecs" (that could be >>>translated as "The Guide of Chess". The translation is from me : >>> >>> >>>Combination: A series of moves from one side provoking forced or almost forced >>>replies, allowing to achieve a concrete goal. A combination correctly realized, >>>this way, could bring a small advantage or as well the checkmate of the >>>opponent. >>> >>>Serge Desmarais >> >> >>Nice try, but not good enough! Not to worry, I don't think I can do >>much better. >> >>The Serge Desmariais definition is more ambiguous than yours! He >>did not even define what a concrete goal is. I suppose it does >>not matter, it's only important that your combination achieves >>whatever you define to be your own personal concrete goal. >> >>Your definition does not tell me anything about when the huge win >>or advantage was achieved. Do you determine this by doing a >>quies search and trusting the results? You have to use a lot >>of human judgement to determine if your move sequence fits the >>definition. In other words it will be possible in principle to >>contruct borderline cases where experts will disagree. >> >>The definition must be completely free of any ambiguious terminology. >>100/100 people should be able to apply your defintion to any >>sequence of moves and determine exactly where a combination starts >>and stops. >> >>- Don > >If you want to be completely rigorous about this you must treat this the same >way a mathematician develops a theory, such as boolian algegra. In every case, >the theory is founded on unproven axioms. Then there is a bunch of definitions >and theorems, connected by proofs. The steps in the proofs must be generally >accepted as being valid, but the validity of the steps in logic cannot be proven >and are like the unproven axioms which form the foundation of any mathematical >theory. > >Note that definitions are never proven! They are selected by those who are >developing the theory. If the theory is being developed by a group of people, >as the case here, then everybody must agree on the ACCEPTABILITY of the >definitions, but not on the "truth or falseness" of the definitions. There is >no such thing as a "true" definition or a "false" definition. But there sure >can be "ambiguous" definitions. These ambiguities become apparent whenever a >proof is attempted in which the assertion to be proven uses the defined term as >part of the definition. > >I suggest that some "reasonable-sounding" definitions be selected and see where >they lead. If a term later proves to be poorly defined, there is always the >opportunity to change the definition. > >But this is the BIG question: Do you guys really want to go through all of >this? Perhaps it is worth it, perhaps not. I can define a combination in a very sterile way. Construct a chess program with no evaluation other than 1 3 3 5 9 material scores for pieces. Full width search, no extensions, classic quies search with infinite cpatures, no checks in quies, mate is 9999 and draw is zero. A combination is defined as the PV (or any possible PV) returned from a 2 ply or greater search, where the score returned is greater than the score returned by the 1 ply search! The combination ends at the shallowest depth where this material win is seen and is defined by the principal variation. It's ugly but I believe it is strict and would un-ambiguously define a combination and approximately matches the book definition. Of course it makes goals other than winning material invalid and also will return move sequences that might not really work in a real game. For instance you may win a queen but get mated later! Another problem is that the first or "key" move may be completely unremarkable. We could add that the first move must be a capture or check but this will still fail in some cases to be remarkable (since the move might be a simple and necessary recapture) Trying to nail down a sense of where the combination started is difficult. My definition is artificial and sterile. - Don
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