Article View: sci.logic
Article #418Re: "Solvability" in Chess
From: CUFFELL TIMOTHY MICH
Date: Tue, 29 Sep 1992 09:04
Date: Tue, 29 Sep 1992 09:04
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3633 bytes
In article <xeno.717575523@pv34ad.vincent.iastate.edu> xeno@iastate.edu (Gary L Snethen) writes: >In <1992Sep26.132508.24956@cbnewsl.cb.att.com> ed@cbnewsl.cb.att.com (edward.m.hummel) writes: > >>In article <xeno.717471510@pv34ad.vincent.iastate.edu> xeno@iastate.edu (Gary L Snethen) writes: >>>It is not possible for both players to have better than a draw and >>>less than a win.... What one player has, the other does not. One's >>>loss is the other's win... zero sum game. >>> >>>How do I prove this? The rules of chess state it quite plainly... >>>If white wins, black loses. If black loses, white wins. A draw is >>>considered a perfect 50%/50% game for each (a half-loss, half-win situation). > >>There is a loop hole: the rules do not give a value to games that do >>not end. > >I beg to differ, but they most certainly do! This is called a 'draw'. If >it were NOT considered a 'draw' then a king vs. king position would very >plainly fall under the category of such a loop hole. If you then say >'well, there is not enough of a material advantage for either side to win >so therefore it is obviously a draw since all paths lead to draws, but in >another example, this might not be the case' then my response is: > >You've added a synthetic rule to the game which states that lack of material >advantage is a draw. (Note that this is *not* really synthetic as the rules >of chess plainly state that such positions are draws, JUST as they state >that indefinite loops are draws... if you take one, you MUST take the other). > >If you are interested in 'rigor' then all you need do is add these two rules: > >(1) ANYTIME a position has been repeated three times, the game is a draw. > >and/OR (yes, OR... either rule suffices) > >(2) If 50 moves pass with no capture, the game is a draw. > > >You are accusing the rules of chess of having 'loop holes' whereby players >can claim a condition other than win/lose/draw... If you wish to contort >the rules of chess to create such synthetic loop holes to support your >argument, then at least explain it as such. If there ARE loopholes and I >am still confused on the issue, PLEASE try to create an example situation >where this question would arise. > >Even if so, I think I can easily gain a consensus amoung the players here >on the net that if a game lasts forever (ie., has infinite moves whether in a >loop or not), then that game is a draw since neither side has a hope to >win unless the other side makes a mistake. But luckily, the accepted rules >of play prohibit such situations from arising. > >Now, if you are interested in a variant of chess where these rules do not >apply, then your argument is completely founded. But then we are no longer >talking about a finite game, so the previous discussions do not apply. > > >---Xeno > The rules also describe a tournament director who can decide the outcome of games that take too long.
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Newsgroups: sci.logic,sci.math,rec.games.chess Path: arc1-ca.pugleaf.net!sparky!uunet!cis.ohio-state.edu!magnus.acs.ohio-state.edu!usenet.ins.cwru.edu!agate!boulder!ucsu!spot.Colorado.EDU!cuffell From: cuffell@spot.Colorado.EDU (CUFFELL TIMOTHY MICH) Subject: Re: "Solvability" in Chess Message-ID: <1992Sep29.090457.25696@ucsu.Colorado.EDU> Sender: news@ucsu.Colorado.EDU (USENET News System) Nntp-Posting-Host: spot.colorado.edu Organization: University of Colorado, Boulder References: <xeno.717471510@pv34ad.vincent.iastate.edu> <1992Sep26.132508.24956@cbnewsl.cb.att.com> <xeno.717575523@pv34ad.vincent.iastate.edu> Date: Tue, 29 Sep 1992 09:04:57 GMT Lines: 59