ugfailau@sunybcs.UUCP (Fai Lau) (03/09/86)
I have the following question, I am interested in what people in the net think about it. It seems that if any strategic game (i.e. chess) is played flawlessly by all participants making the best possible moves (assuming the entire game tree is available for reference), there is only one possible outcome for each type of game; either one player wins or a tie if the game is so allowed. Since in reality it is impossible to built an entire game tree for all but the most elementary strategic games such as tic tac toe, it is impossible to know who is 'supposed' to win in any given type of game. Therefore, it seems that the one who wins is the one who makes the fewer mistakes during the couse of the game. Now let's consider a game tree is available for SCORING ONLY for the game of chess. Every arc of the tree is assigned a point value denoting the quality of the move comparing to other moves branching from a common node. That is, the best move following every node carries the point value of one, second best two, third best three, etc.. The tree is traversed by a pointer. Whenever a player makes a move, the pointer traverses to the corresponding node through the corresponding arc. The player than picks up the point value of the arc and adds it to his score. So at any given moment of the game, the player who has the lower score is making less deviation from a perfect play. The question is: IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME??
ark@alice.UucP (Andrew Koenig) (03/11/86)
> IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE > ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE > MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME?? Sure. For instance: there might be more than one winning move from a position; the second-best move is second only in the sense that it wins less quickly than optimum play.
dpb@philabs.UUCP (Paul Benjamin) (03/11/86)
> > I have the following question, I am interested in what people > in the net think about it. > > It seems that if any strategic game (i.e. chess) is played flawlessly > by all participants making the best possible moves (assuming the entire game > tree is available for reference), there is only one possible outcome for > each type of game; either one player wins or a tie if the game is > so allowed. Since in reality it is impossible to built an entire game tree > for all but the most elementary strategic games such as tic tac toe, it is > impossible to know who is 'supposed' to win in any given type of game. > Therefore, it seems that the one who wins is the one who makes the fewer > mistakes during the couse of the game. > Now let's consider a game tree is available for SCORING ONLY for > the game of chess. Every arc of the tree is assigned a point value denoting > the quality of the move comparing to other moves branching from a common > node. That is, the best move following every node carries the point value > of one, second best two, third best three, etc.. The tree is traversed > by a pointer. Whenever a player makes a move, the pointer traverses to the > corresponding node through the corresponding arc. The player than picks > up the point value of the arc and adds it to his score. So at any given > moment of the game, the player who has the lower score is making less > deviation from a perfect play. > The question is: > > IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE > ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE > MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME?? Yes. Since you have scored the moves qualitatively, and not quantitatively, it is possible for a winner to choose second-best moves very often, but still have a very good game, and for the loser to choose the best move on every move but the last, when he chooses a second-best move. Unfortunately for him, any move but the best move lost instantly.
trb@haddock (03/11/86)
> Whenever a player makes a move, the pointer traverses to the > corresponding node through the corresponding arc. The player than picks > up the point value of the arc and adds it to his score. So at any given > moment of the game, the player who has the lower score is making less > deviation from a perfect play. > The question is: > > IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE > ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE > MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME?? Clearly, in most any position with substantial material on the board, either player can win, with the help of the other player. Let's say I (a mediocre player) am playing a grandmaster. After 25 moves, I may be busted, with the GM having racked up a big "score." Within a few helpful blunderous moves, he can help me mate him. Higher score, but still lost. This isn't a typical situation, but applies to a more subtle extent in actual play. (I regret that I know this from personal experience.) Herein lies your problem: > Therefore, it seems that the one who wins is the one who makes the fewer > mistakes during the couse of the game. This isn't true. What is essentially true is that the last player to get caught making a mistake loses. Also, it is practically impossible to come up with exact scores for positions early in the game. We make judgement calls, which is what gives chess its variety. Andrew Tannenbaum Interactive Boston, MA 617-247-1155
landy@inmet.UUCP (03/11/86)
Quite easily! (At least with your scoring system) Plenty of people have had the humiliating experience of having a superior position, lots of extra material, and walking into a mate in one move.
dim@whuxlm.UUCP (McCooey David I) (03/12/86)
> Now let's consider a game tree is available for SCORING ONLY for > the game of chess. Every arc of the tree is assigned a point value denoting > the quality of the move comparing to other moves branching from a common > node. That is, the best move following every node carries the point value > of one, second best two, third best three, etc.. The tree is traversed > by a pointer. Whenever a player makes a move, the pointer traverses to the > corresponding node through the corresponding arc. The player than picks > up the point value of the arc and adds it to his score. So at any given > moment of the game, the player who has the lower score is making less > deviation from a perfect play. > The question is: > > IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE > ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE > MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME?? Yes, it seems possible as follows: The loser may be in a position at some point where there are very few possible moves, so that a truly disasterous move may have a relatively small point value. Similarly, the winner could have made a slightly inferior move at some point in the game where there were many possible moves. The point value of the winner's slight mistake could therefore be larger than that of the loser's disasterous move. It seems that the definition of perfect play needs to be better defined than from a rank ordering of the moves in each position. Even scaling them so that the best move always has point value 1 and the worst move always has point value, say, 1000 will not work because there will always be positions where "almost anything will do" and others where "the slightest mistake is fatal." Dave McCooey AT&T Bell Labs, Whippany ihnp4!whuxlk!dim
kwh@bentley.UUCP (KW Heuer) (03/12/86)
In article <2916@sunybcs.UUCP> sunybcs!ugfailau (Fai Lau) writes: >Therefore, it seems that the one who wins is the one who makes the fewer >mistakes during the couse of the game. I've heard it said that the winner is the one who makes the second-to- last mistake. > Now let's consider a game tree is available for SCORING ONLY for >the game of chess. Every arc of the tree is assigned a point value denoting >the quality of the move comparing to other moves branching from a common >node. That is, the best move following every node carries the point value >of one, second best two, third best three, etc.. Who decides which move is "best", "second best", etc.? Let's take a specific example: suppose I have three ways (a,b,c) to mate on the move, one (d) which will throw away the mate threat but leave sufficient material advantage for a clear win, one (e) which will stalemate, and one (f) which is a losing blunder. How would you assign numerical values to these? I think the only fair system is to compare against perfect play; i.e. (a-d) are equally good, since they all win (although (a-c) are "faster" wins); I'd assign them a score of zero. (e) is a mistake, since it converts a won game into a draw; I'd assign it a score of one (along with any other move whose outcome is a draw after subsequent perfect play). (f) is a double-mistake, equivalent to a win->draw and a draw->lose at the same time; I'd assign it a two. These are the only possible values in my scheme. At the end of the game, your total score is the number of mistakes you've made. > IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE >ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE >MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME?? With my counting scheme, assuming the initial position is a draw under perfect play (which seems extremely likely), each mistake changes the game value by one, so if one player wins, he has made one less mistake than his opponent. The game ends in a draw iff both players have made the same number of mistakes. I realize that the "mistake-score" of a move cannot, in general, be computed. But how else are you going to assign a score? Karl W. Z. Heuer (ihnp4!bentley!kwh), The Walking Lint.
tim@ism780c.UUCP (Tim Smith) (03/13/86)
Consider an ending of K+P vs. K+P. White pawn on a7, black on h2, white king on a2, black on h7, white to move. If white has the higher score, then perfect play by both sides will lead to a win by white, with white still having a higher score. If white has a score 10 or more lower than black, he can make a king move, which gives black a winning position. Since white only has 9 possible moves, he can't make a move worse than 9, so his score will stay lower than blacks, and thus black will win with a higher score. If white has a score 9 or less lower than black, then let white play these moves: a8Q, Qh1, Qh2, and let black respond with three perfect moves. The situation is now K+Q vs. K, with whites score no lower than nine lower than blacks score. Now let white, while keeping his king at a2, play a series of checks by placing his unprotected queen next to the black king, making sure that the black king has a move available other than taking the queen. Since the white queen always has at least fourteen moves, and at most three moves can satisfy the above conditions, there are at least 11 moves better than the ones white plays above. Let black respond to these checks by not taking the queen. There are at most four moves available to black, so he can make no move worse than fourth best, thus the score of white goes up at least 7 for each check in this series. Let white include at least two checks in the above series. Then white will have a higher score than black, but still have a won game. Let both sides then switch to perfect play, and white will win with a higher score. -- Tim Smith sdcrdcf!ism780c!tim || ima!ism780!tim || ihnp4!cithep!tim
rh@paisley.ac.uk (Robert Hamilton) (03/14/86)
In article <5112@alice.uUCp> ark@alice.UUCP writes: >> IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE >> ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE >> MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME?? > The discussion makes little sense using the scoring method suggested A bad (not perfect) MUST be given the score of BEST POSSIBLE POSITION the player can now get through PERFECT play from this point. SO if the loser makes only ONE non-perfect move which loses by force hos score must be - infinity forthat move. IN fact this brings an interesting point... For the above scoring method to be valid the game tree MUST be FINITE (taken from the first move) Ie from an move 1 tere MUST be a forced win for white or a forced draw for black. The question : IS THERE ? If there is not I think that chess might be considered non-deterministic in the sense that the only analysis possible is heuristic. PS We are fairly new on the news network. Is anyone out there interested in some skittles by mail ? -- UUCP: ...!seismo!mcvax!ukc!paisley!rh DARPA: rh%cs.paisley.ac.uk | Post: Paisley College JANET: rh@uk.ac.paisley.cs | Department of Computing, Phone: +44 41 887 1241 Ext. 219 | High St. Paisley. | PA1 2BE
hemphill@cit-vax.Caltech.Edu (Thomas S. Hemphill) (03/16/86)
Organization : California Institute of Technology Keywords: In article <2916@sunybcs.UUCP> ugfailau@sunybcs.UUCP (Fai Lau) writes: > >Therefore, it seems that the one who wins is the one who makes the fewer >mistakes during the couse of the game. To get right to the heart of the matter, this assertion is not correct. The loser is the person who made the last mistake. The winner is his opponent. As others have pointed out, the loser can have a better (i.e. lower) total "point score" (one for best move, two for next best, etc.) than the winner. This should not be surprising, since one bad move, even the "second best" could lose for a player who had outplayed his opponent for the rest of the game. But there is another way of assigning point totals that *does* work. 0pts -- assigned to all moves that keep a won game won or a drawn game drawn. Also assigned to all moves in a lost position. 1pt -- assigned to a poor move that causes a won game to become theoretically drawn, or a drawn game to become lost. 2pts -- assigned to a blunder that causes a won game to become lost. One other detail--is chess a theoretical win for white? If so, then you need to give one point to black just for being black.
ugfailau@sunybcs.UUCP (Fai Lau) (03/18/86)
> > Since the white queen always has at least fourteen moves, and at most > three moves can satisfy the above conditions, there are at least 11 > moves better than the ones white plays above. > > Let black respond to these checks by not taking the queen. There are > at most four moves available to black, so he can make no move worse > than fourth best, thus the score of white goes up at least 7 for each > check in this series. > > Let white include at least two checks in the above series. Then white > will have a higher score than black, but still have a won game. Let both > sides then switch to perfect play, and white will win with a higher score. > > -- > Tim Smith sdcrdcf!ism780c!tim || ima!ism780!tim || ihnp4!cithep!tim This is a perfect case to illustrate what I mentioned in my follow up to the original article. In this example it is clear that Black manages to avoid cranking his points up by being in a totally defensive position where his best choice happens to be his only choice. It is interesting to note that no matter what kind of scoring scheme is used or how wide the score gap between White and Black, White will eventually 'catch up' with Black by using the second best (not necessary the worst) move strategy to force Black to make the best (which may often be the only legal) move in every response. Well, guess the truly great chess players are not necessary the ones who make perfect plays, but the ones who can AFFORD deviations. +-----------------------------------------------------------------------------+ | Fai Lau | | ECE / CS SUNYAB | | BI: ugfailau@sunybcs | +-----------------------------------------------------------------------------+
ugfailau@sunybcs.UUCP (Fai Lau) (03/18/86)
> > > > Since the white queen always has at least fourteen moves, and at most > > ........ >> > > Let white include at least two checks in the above series. Then white > > will have a higher score than black, but still have a won game. Let both > > sides then switch to perfect play, and white will win with a higher score. > > > > -- > > Tim Smith sdcrdcf!ism780c!tim || ima!ism780!tim || ihnp4!cithep!tim > > This is a perfect case to illustrate what I mentioned in my follow > up to the original article. In this example it is clear that Black > .......... > (not necessary the worst) move strategy to force Black to make the > best (which may often be the only legal) move in every response. > It seems that I posted the previous article in a hurry, without looking at the end game situation carefully. The basic philosophy is the same, however. The case was actually that Black was helping White to increase his score by not making his best move which would be to take the queen. With queen's many move options, White could pile up his points with ease. +-----------------------------------------------------------------------------+ | Fai Lau | | ECE / CS SUNYAB | | BI: ugfailau@sunybcs | +-----------------------------------------------------------------------------+
ags@pucc-h (Dave Seaman) (03/28/86)
In article <39@paisley.ac.uk> rh@cs.paisley.ac.uk (Robert Hamilton) writes: >Ie from an move 1 tere MUST be a forced win for white or a forced >draw for black. >The question : IS THERE ? >If there is not I think that chess might be considered non-deterministic >in the sense that the only analysis possible is heuristic. In tic-tac-toe there is no forced win for the first player or the second. Are you claiming that tic-tac-toe might be considered non-deterministic in the sense that the only analysis possible is heuristic? -- Dave Seaman pur-ee!pucc-h!ags