Author: Don Dailey
Date: 11:51:05 09/06/98
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On September 06, 1998 at 13:49:07, Robert Hyatt wrote: >On September 06, 1998 at 13:15:47, 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. >> >> > > >I'd hope there is no debate here. A combination is a sequence of moves >that ends up either winning material, or winning some positional compen- >sation that is worthwhile, such as an unstoppable passed pawn, or some >such thing. I generally apply it only to material, such as the occasional >"queen sacs" that happen on ICC. Only they aren't sacrifices when Crafty >plays Qxg7 with a score of +9 or Mate. They are winning combinations. >I include positional compensation because sometimes a sequence of captures >ends with a positional killer rather than a direct win of material... > Bob, I think most of us do agree in general about what a combination is. We all have an intuitive sense of this. But I'm talking about a strict definition, mathematically strict if you will. Your definition is certainly acceptable and is fairly typical of ones I see in the books. But can you write a program that will tell me if a sequence of moves fit your definition? Where EXACTLY does a combination start and where does it end? Most definitions include the phrase "a forced sequence of moves." Forced by who? Forced in what sense and exactly how is "forced" measured? The implied answer is that a response is the only "reasonable" reply. But what is reasonable may vary from person to person. Do you get my point? We don't have a mathmatically strict definition for what a combination is (and I'm not really complaining about this, I don't really care so much but I just think this is an intersting point.) To me "forced" in the most technical sense means that there is only one legal reply. But this is pretty strict and would break most peoples sense of which situations are combinations. So another reasonable definition of forced is that there is only a single "BEST" response. Best in the game theoretical sense, one move draws the rest lose, or one move wins, the rest draw or lose. But even this is not compatible with our intuitive notion of what a combination is. "Forced" probably simply means there are a limtited number of "reasonable" responses. BUT WAIT, we did not strictly define "limited" or "reasonable"! Maybe there is no such thing as a combination! I do not know how to define a combination in a provable sort of way. I do not think I could write a program that will go through a game and define (in a completely ambiguous sort of way) every single combination, the exact move where it started and where it actually ended. I actually have a definition, but to make it completely strict it does not resemble our intuitive notion of a combination very well. - Don
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