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Date: 29 Jan 2008 03:38:07
From:
Subject: with perfect play, should it be 10, 01, or a draw?

If White and Black both play perfectly, who wins? Or is it a draw? I'd be interested to know how chessplayers' opinions on this question are distributed. Personally I think White wins, because he starts with a clear advantage. I suspect most people might think the game is a draw. Michael



Date: 08 Feb 2008 16:33:43
From: help bot
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 8, 11:59 am, David Richerby <dav...@chiark.greenend.org.uk > wrote: > To continue this little conversation with myself, I note that > Wikipedia says that Nunn says that, er, I'll start again. > > KRNKNN is a rather exotic sort of an endgame, that is unlikely to > occur in real play. On the other hand, for an ending as natural as > KQPKQ, Wikipedia says, > > ``Tablebases have shown that this can be won in many more positions > than was thought, but the logic of the moves is presently beyond > human understanding'', Where many humans fail in understanding such things is in taking the wrong approach to them; for example, in assuming that a direct attack is the only way to attack. Take the Trojan Horse, for instance. The Greeks could not "directattack" their way in, but all the same, they did have another method, and were st enough to find it. In the famous example of KQ vs. KBB  which was pronounced a draw by the leading authorities of the day  they forgot to consider that, if Black (i.e. the weaker side) had an "ideal fortress" position, all one need do is transfer the move to him, and kerpow: the perfect fortress is not so perfect anymore! The same principle applies to other forms of fighting (i.e. Em. Lasker: "chess is a fight"). I saw a video once of one of the Ultimate Fighting Championships, and the guy who won was on his back, getting the sh*t pounded out of him, but his assailant was so busy "winning" he left himself open to a decisive choke hold!  help bot


Date: 08 Feb 2008 16:21:31
From: help bot
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 8, 8:43 am, David Richerby <dav...@chiark.greenend.org.uk > wrote: > > In KRNKNN, are the programs winning when grandmasters would draw, or > > drawing when they would lose, or both? > > KRNKNN is won (in most cases) for the side with the rook. However, > in many cases, the forced win takes over 200 moves, almost always, the > game would be drawn by the 50move rule. In practice, the ending > never occurs but, if it did, humans would agree a draw (assuming that > a piece wasn't immediately lost) and the computer would go on to win > (assuming that the opponent didn't claim his draw by the 50move > rule). In a situation where it is the endgame tablebase versus a human player, it seems very likely that a poor defense by the human could result in no 50move rule draw, but rather, a legitimate win for the program. As far as I can recall from my own games, this ending has never occurred; but then, that might be in part due to a deliberate avoidance of this kind of simplification, since I always must win, and because my opponents aren't st enough to trade off all the pawns!  help bot


Date: 08 Feb 2008 01:35:11
From: help bot
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 6, 1:50 pm, Larry Tapper <larry_tap...@yahoo.com > wrote: > > But isn't the leading edge of theory mostly variations on lines > > popular in current practice? It doesn't necessarily represent best > > play up to, e.g., move 35. > > Yes, I agree. The main purpose of deep preparation is not to make a > modest contribution toward the general solution of chess, but to > figure out what to play against Kropotkin. > > I think it's well understood that many playable and interesting lines > can remain stagnant theoretically for decades just because they are > unfashionable. John Watson gives several instructive examples of this > phenomenon in his book Modern Chess Strategy. > > The point I wish to make, however, is that when a line _is_ > fashionable and therefore analyzed deeply by leading GMs, the work > they do is most likely worth something objectively, in the sense that > a perfect computer would view most of their efforts with qualified > approval. In many cases, the GMs may do 90% correct analysis, but all it takes to debunk an opening line is *one* improvement. I see this all the time when analyzing games with a computer. Tonight I went over an old game between Bobby Fischer and Tigran Petrosian, and was surprised when the daggone machine refused to follow the main lines  long presumed to be forcing  of the um, Pelikan(?) Sicilian. A few more seconds, I kept thinking... then it will finally "see" that it must play the book move here... but no. The same thing happened in the exchange Ruy Lopez between BF and BS from 1992 the computer refused to "cooperate". But I will say this: in the first game mentioned above BF played very, very well in the middle game, frequently matching the computer when there were perhaps 30+ legal moves to choose from! A real tough cookie, that guy was. Still, when you see GMs losing to computers at pawn odds  after gaining a crushing edge due to some programmers' misguided efforts to interfere  it is hard to take seriously any claims to nearperfection in human analysis. Much of it is built upon the flawed framework of prior human analysis, just presumed to be correct. Even what passes for computerchecked work these days is often shallow stuff not even remotely close to oldschool correspondence chess analysis work. Jose Capablanca was right: [computers should] learn the game backwards, starting with the endgame [tablebases]. I am still working on increasing the number of atoms in the "known" universe, to satisfy the numbskulls who can't accept reality and who are in denial over the data storage end of solving chess. Look there's another atom! Right there, behind that distant black hole; that's my next hard drive!  help bot


Date: 06 Feb 2008 16:23:00
From:
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 6, 5:29=A0pm, Larry Tapper <larry_tap...@yahoo.com > wrote: > On Feb 6, 11:15=A0am, David Richerby <dav...@chiark.greenend.org.uk> > wrote: [...] > It is true that grandmasters could conceivably look like ignoramuses > from the point of view of an omniscientchesscomputer, but I'm > inclined to doubt that the gap is _that_ wide. Opening theory, for > example, is dismayingly =A0deep nowadays =A0 possibly Kramnik had his > Corus game with Aronian prepared up to move 35! And this theory > represents a sort of massive collective effort on the part of highly > skilled and motivated inquirers. This isn't conclusive but surely it > counts for something. A perfect player would not even need the concept of "opening theory", which is based on the misting up of the tree of possibilities. Ditto those humans who have mastered noughts and crosses (tictactoe) need no such concept. Michael


Date: 06 Feb 2008 16:17:46
From:
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 6, 4:15=A0pm, David Richerby <dav...@chiark.greenend.org.uk > wrote: > <hanrahan...@yahoo.co.uk> wrote: > > As for the argument that "grandmaster play has shown no evidence > > that White can, with best play, keep his advantage, therefore it > > seems unlikely that that would happen even withperfectplay"  I > > wouldn't ascribe any appreciable weight to this. This is because > >perfectplay wold be *way* stronger than the greatest play by > > grandmasters. > > This depends on how much you think that current grandmaster play is > resemblesperfectplay. =A0If you believe that grandmaster play is very > much likeperfectplay but with a few mistakes thrown in, then you can > try todrawconclusions aboutperfectplay from grandmaster play. [...] > On the other hand, it might be that grandmaster play is nothing likeperfec= tplay. > > Consider what we know about endgames. =A0Tablebases tell us that > grandmasters can play KRPKR endings prettymuch perfectly. =A0We > understand the tablebases and know why the right move is the right > move. =A0On the other hand, the tablebase for KRNKNN looks, in most > cases like completely random moves  nobody can understand it. =A0In > this case, grandmaster play looks nothing likeperfect. Sounds like we know how to spot the difference in this type of endgame, whereas maybe we wouldn't in the middlegame or opening. The difference, whether spottable or not, comes from the huge difference in the number of positions analysed. In KRNKNN, are the programs winning when grandmasters would draw, or drawing when they would lose, or both? Michael

 
Date: 08 Feb 2008 13:43:19
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

<hanrahan398@yahoo.co.uk > wrote: > David Richerby <dav...@chiark.greenend.org.uk> wrote: >> Consider what we know about endgames. Tablebases tell us that >> grandmasters can play KRPKR endings prettymuch perfectly. We >> understand the tablebases and know why the right move is the right >> move. On the other hand, the tablebase for KRNKNN looks, in most >> cases like completely random moves  nobody can understand it. In >> this case, grandmaster play looks nothing likeperfect. > > Sounds like we know how to spot the difference in this type of > endgame, whereas maybe we wouldn't in the middlegame or opening. The > difference, whether spottable or not, comes from the huge difference > in the number of positions analysed. > > In KRNKNN, are the programs winning when grandmasters would draw, or > drawing when they would lose, or both? KRNKNN is won (in most cases) for the side with the rook. However, in many cases, the forced win takes over 200 moves, almost always, the game would be drawn by the 50move rule. In practice, the ending never occurs but, if it did, humans would agree a draw (assuming that a piece wasn't immediately lost) and the computer would go on to win (assuming that the opponent didn't claim his draw by the 50move rule). But if you look at perfect play in this ending, it just seems to be completely random. Nobody can work out what's going on because, whatever the subgoals might be (for example, in KBNK, they'd be driving the king to the edge, then driving him to the right corner, then mating), they take twenty or thirty or forty moves to achieve. You can see the longest win at the following URL http://www.xs4all.nl/~timkr/chess2/diary_3.htm or play through it (a reflected version of the same thing) at http://www.gothicchess.com/endings/chess_krnknn/game.htm It makes no sense at all. The pieces just bounce around for move after move after move. Incidentally, I've seen elsewhere that there's a 290move mate in KRRNKRR (sevenman). See the following link for discussion and an example of the longest mate: http://www.stmintz.com/ccc/index.php?id=456178 Dave.  David Richerby Surprise Toy (TM): it's like a fun www.chiark.greenend.org.uk/~davidr/ child's toy but not like you'd expect!

  
Date: 08 Feb 2008 13:44:32
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

David Richerby <davidr@chiark.greenend.org.uk > wrote: > KRNKNN is won (in most cases) for the side with the rook. I forgot to say  about 78% of cases, according to Wikipedia. http://en.wikipedia.org/wiki/Endgame_tablebase Dave.  David Richerby Indelible Voodoo Cat (TM): it's like www.chiark.greenend.org.uk/~davidr/ a cuddly pet that has mystical powers but it can't be erased!

   
Date: 08 Feb 2008 16:59:39
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

David Richerby <davidr@chiark.greenend.org.uk > wrote: > David Richerby <davidr@chiark.greenend.org.uk> wrote: >> KRNKNN is won (in most cases) for the side with the rook. > > I forgot to say  about 78% of cases, according to Wikipedia. > > http://en.wikipedia.org/wiki/Endgame_tablebase To continue this little conversation with myself, I note that Wikipedia says that Nunn says that, er, I'll start again. KRNKNN is a rather exotic sort of an endgame, that is unlikely to occur in real play. On the other hand, for an ending as natural as KQPKQ, Wikipedia says, ``Tablebases have shown that this can be won in many more positions than was thought, but the logic of the moves is presently beyond human understanding'', citing Nunn's _Secrets of Minor Piece Endings_. http://en.wikipedia.org/wiki/Endgame#Effect_of_tablebases_on_endgame_theory Dave.  David Richerby Natural Poisonous Goldfish (TM): it's www.chiark.greenend.org.uk/~davidr/ like a fish but it'll kill you in seconds and it's completely natural!


Date: 06 Feb 2008 10:50:40
From: Larry Tapper
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 6, 1:21=A0pm, Mike Murray <mikemur...@despammed.com > wrote: > On Wed, 6 Feb 2008 09:29:48 0800 (PST), Larry Tapper > > <larry_tap...@yahoo.com> wrote: > > Opening theory, for > >example, is dismayingly =A0deep nowadays =A0 possibly Kramnik had his > >Corus game with Aronian prepared up to move 35! And this theory > >represents a sort of massive collective effort on the part of highly > >skilled and motivated inquirers. This isn't conclusive but surely it > >counts for something. > > But isn't the leading edge of theory mostly variations on lines > popular in current practice? =A0It doesn't necessarily represent best > play up to, e.g., move 35. > Yes, I agree. The main purpose of deep preparation is not to make a modest contribution toward the general solution of chess, but to figure out what to play against Kropotkin. I think it's well understood that many playable and interesting lines can remain stagnant theoretically for decades just because they are unfashionable. John Watson gives several instructive examples of this phenomenon in his book Modern Chess Strategy. The point I wish to make, however, is that when a line _is_ fashionable and therefore analyzed deeply by leading GMs, the work they do is most likely worth something objectively, in the sense that a perfect computer would view most of their efforts with qualified approval. LT > >Actually that's not the way I remember it myself. It seems to me that > >back in the 80s I heard many people say, as if it were an obvious > >fact, that a computer could never play chess better than its > >programmer. But generally speaking, these skeptics were not chess > >masters, they were just interested laypeople who had various axes to > >grind against the notion of strong AI. > > I used to snigger at books such as Dreyfus' "What Computers Can't Do: > The Limits of Artificial Intelligence".

 
Date: 08 Feb 2008 08:25:08
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Larry Tapper <larry_tapper@yahoo.com > wrote: > The point I wish to make, however, is that when a line _is_ > fashionable and therefore analyzed deeply by leading GMs, the work > they do is most likely worth something objectively, in the sense > that a perfect computer would view most of their efforts with > qualified approval. There's no such thing as `qualified approval' by a perfect computer. To the perfect computer, any line is either winning, losing or drawing. Dave.  David Richerby Accelerated Expensive Beer (TM): it's www.chiark.greenend.org.uk/~davidr/ like a refreshing lager but it'll break the bank and it's twice as fast!


Date: 06 Feb 2008 09:29:48
From: Larry Tapper
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 6, 11:15=A0am, David Richerby <dav...@chiark.greenend.org.uk > wrote: > <hanrahan...@yahoo.co.uk> wrote: > > As for the argument that "grandmaster play has shown no evidence > > that White can, with best play, keep his advantage, therefore it > > seems unlikely that that would happen even with perfect play"  I > > wouldn't ascribe any appreciable weight to this. This is because > > perfect play wold be *way* stronger than the greatest play by > > grandmasters. > > This depends on how much you think that current grandmaster play is > resembles perfect play. =A0If you believe that grandmaster play is very > much like perfect play but with a few mistakes thrown in, then you can > try to draw conclusions about perfect play from grandmaster play. > That said, you'd have to give an argument that differentiated between > `White's mistakes mean that he draws games he should win' and `Black's > mistakes mean that he loses games he should draw.' =A0(The latter seems > more likely, since defending often requires making only moves, while > attacking usually has more flexibility.) > > On the other hand, it might be that grandmaster play is nothing like > perfect play. A wellframed answer, I think. It is true that grandmasters could conceivably look like ignoramuses from the point of view of an omniscient chess computer, but I'm inclined to doubt that the gap is _that_ wide. Opening theory, for example, is dismayingly deep nowadays  possibly Kramnik had his Corus game with Aronian prepared up to move 35! And this theory represents a sort of massive collective effort on the part of highly skilled and motivated inquirers. This isn't conclusive but surely it counts for something. Help bot's comment on the grandmaster consensus was that he recalled grandmasters insisting that computers would never reach master level. So what do they know? Actually that's not the way I remember it myself. It seems to me that back in the 80s I heard many people say, as if it were an obvious fact, that a computer could never play chess better than its programmer. But generally speaking, these skeptics were not chess masters, they were just interested laypeople who had various axes to grind against the notion of strong AI. The strong players I knew during that transition period tended to agree that the eventual triumph of the silicon beasts was inevitable, though there was disagreement about how long it would take. Larry T. > > Consider what we know about endgames. =A0Tablebases tell us that > grandmasters can play KRPKR endings prettymuch perfectly. =A0We > understand the tablebases and know why the right move is the right > move. =A0On the other hand, the tablebase for KRNKNN looks, in most > cases like completely random moves  nobody can understand it. =A0In > this case, grandmaster play looks nothing like perfect. > > Dave. > >  > David Richerby =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0= =A0Devil Chainsaw (TM): it's likewww.chiark.greenend.org.uk/~davidr/=A0 =A0= =A0 =A0 =A0 a lethal weapon that's possessed > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 = =A0 =A0 =A0 =A0 =A0 by Satan!

 
Date: 08 Feb 2008 08:22:34
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Larry Tapper <larry_tapper@yahoo.com > wrote: > A wellframed answer, I think. Thank you. > It is true that grandmasters could conceivably look like ignoramuses > from the point of view of an omniscient chess computer, but I'm > inclined to doubt that the gap is _that_ wide. Opening theory, for > example, is dismayingly deep nowadays  possibly Kramnik had his > Corus game with Aronian prepared up to move 35! And this theory > represents a sort of massive collective effort on the part of highly > skilled and motivated inquirers. This isn't conclusive but surely it > counts for something. It's hard to say. Perhaps grandmasters are, so to speak, getting really, really good at making fire by rubbing two sticks together, discovering all kinds of advanced techniques for how to shape the sticks and what angle to rub them at. And somebody's going to come along and invent the match. > It seems to me that back in the 80s I heard many people say, as if > it were an obvious fact, that a computer could never play chess > better than its programmer. Well, they were, frankly, idiots. Not because they were subsequently proven to be very wrong but because they were committing a basic error of reasoning. This is like saying that a robot can never run faster than its designer or, as Turing put it, like saying that no animal could possibly eat something bigger than itself. Or maybe, since you say they weren't generally strong chess players, they didn't realise that a large part of playing good chess is checking that you're not going to lose material, which is a largely routine process. Dave.  David Richerby Surprise Pants (TM): it's like a www.chiark.greenend.org.uk/~davidr/ welltailored pair of trousers but not like you'd expect!

  
Date: 08 Feb 2008 15:38:11
From: David Kane
Subject: Re: with perfect play, should it be 10, 01, or a draw?

"David Richerby" <davidr@chiark.greenend.org.uk > wrote in message news:6Sp*srW6r@news.chiark.greenend.org.uk... > Larry Tapper <larry_tapper@yahoo.com> wrote: >> A wellframed answer, I think. > > Thank you. > >> It is true that grandmasters could conceivably look like ignoramuses >> from the point of view of an omniscient chess computer, but I'm >> inclined to doubt that the gap is _that_ wide. Opening theory, for >> example, is dismayingly deep nowadays  possibly Kramnik had his >> Corus game with Aronian prepared up to move 35! And this theory >> represents a sort of massive collective effort on the part of highly >> skilled and motivated inquirers. This isn't conclusive but surely it >> counts for something. > > It's hard to say. Perhaps grandmasters are, so to speak, getting > really, really good at making fire by rubbing two sticks together, > discovering all kinds of advanced techniques for how to shape the > sticks and what angle to rub them at. And somebody's going to come > along and invent the match. Perhaps Mercury is home to a thriving colony of orangutans, living underground. Perhaps the human lifespan can be doubled by properly aiming HeNe laser beams at the proper complex combination of taste buds on the human tongue. Perhaps Knights really are much stronger than Rooks, but you just have to know how to use them properly. Fanciful speculations lacking a basis in reality are never worth much. They key with chess is that we have a largely consistent story  computers and tablebases etc are *not* refuting theory except for some extremely rare positions, most of which there has never been any reason for humans to analyze.

 
Date: 06 Feb 2008 10:21:13
From: Mike Murray
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Wed, 6 Feb 2008 09:29:48 0800 (PST), Larry Tapper <larry_tapper@yahoo.com > wrote: > Opening theory, for >example, is dismayingly deep nowadays  possibly Kramnik had his >Corus game with Aronian prepared up to move 35! And this theory >represents a sort of massive collective effort on the part of highly >skilled and motivated inquirers. This isn't conclusive but surely it >counts for something. But isn't the leading edge of theory mostly variations on lines popular in current practice? It doesn't necessarily represent best play up to, e.g., move 35. >Actually that's not the way I remember it myself. It seems to me that >back in the 80s I heard many people say, as if it were an obvious >fact, that a computer could never play chess better than its >programmer. But generally speaking, these skeptics were not chess >masters, they were just interested laypeople who had various axes to >grind against the notion of strong AI. I used to snigger at books such as Dreyfus' "What Computers Can't Do: The Limits of Artificial Intelligence".


Date: 06 Feb 2008 06:04:43
From:
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 4, 6:42=A0pm, Larry Tapper <larry_tap...@yahoo.com > wrote: > On Feb 1, 6:15=A0pm, hanrahan...@yahoo.co.uk wrote: > > > I still think it's a win. > > > What's your opinion, disregarding issues of proof and the feasibility > > thereof? > > > Michael > > For what it's worth, grandmasters who are asked this > question will typically tell you that chess is probably > a draw. There are some exceptions though, for example > the correspondence champion and computer pioneer Hans > Berliner, =A0who was famous for insisting that White has a > winning advantage. > > I think it's a draw myself. If you look in the rgcm > Google archives, you'll find several old threads with > sometimes astonishingly heated debates on the subject. I'm not sure that a grandmaster's opinion necessarily carries more weight than a nongrandmaster's on this topic. The argument that "White starts with an advantage, and therefore with best play ought to be able to keep it and convert it to a win" doesn't prove anything, but its weight is surely nonzero. As for the argument that "grandmaster play has shown no evidence that White can, with best play, keep his advantage, therefore it seems unlikely that that would happen even with perfect play"  I wouldn't ascribe any appreciable weight to this. This is because perfect play wold be *way* stronger than the greatest play by grandmasters. Michael

 
Date: 06 Feb 2008 16:15:31
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

<hanrahan398@yahoo.co.uk > wrote: > As for the argument that "grandmaster play has shown no evidence > that White can, with best play, keep his advantage, therefore it > seems unlikely that that would happen even with perfect play"  I > wouldn't ascribe any appreciable weight to this. This is because > perfect play wold be *way* stronger than the greatest play by > grandmasters. This depends on how much you think that current grandmaster play is resembles perfect play. If you believe that grandmaster play is very much like perfect play but with a few mistakes thrown in, then you can try to draw conclusions about perfect play from grandmaster play. That said, you'd have to give an argument that differentiated between `White's mistakes mean that he draws games he should win' and `Black's mistakes mean that he loses games he should draw.' (The latter seems more likely, since defending often requires making only moves, while attacking usually has more flexibility.) On the other hand, it might be that grandmaster play is nothing like perfect play. Consider what we know about endgames. Tablebases tell us that grandmasters can play KRPKR endings prettymuch perfectly. We understand the tablebases and know why the right move is the right move. On the other hand, the tablebase for KRNKNN looks, in most cases like completely random moves  nobody can understand it. In this case, grandmaster play looks nothing like perfect. Dave.  David Richerby Devil Chainsaw (TM): it's like www.chiark.greenend.org.uk/~davidr/ a lethal weapon that's possessed by Satan!

  
Date: 06 Feb 2008 09:55:33
From: David Kane
Subject: Re: with perfect play, should it be 10, 01, or a draw?

"David Richerby" <davidr@chiark.greenend.org.uk > wrote in message news:ZTC*iDN6r@news.chiark.greenend.org.uk... > <hanrahan398@yahoo.co.uk> wrote: >> As for the argument that "grandmaster play has shown no evidence >> that White can, with best play, keep his advantage, therefore it >> seems unlikely that that would happen even with perfect play"  I >> wouldn't ascribe any appreciable weight to this. This is because >> perfect play wold be *way* stronger than the greatest play by >> grandmasters. > > This depends on how much you think that current grandmaster play is > resembles perfect play. If you believe that grandmaster play is very > much like perfect play but with a few mistakes thrown in, then you can > try to draw conclusions about perfect play from grandmaster play. I don't think that play need be anything close to perfect in order to draw conclusions. Collectively, humanity/computers have explored chess' move tree and, from those explorations, we can draw conclusions. The only way that it would make sense to discount past explorations is to hypothesize that every time humans or computers have stumbled on the path to White's (or Black's) win, that they didn't *realize* that they had an advantage and hence didn't explore it further. This strikes me as extremely unlikely for a game like chess. > That said, you'd have to give an argument that differentiated between > `White's mistakes mean that he draws games he should win' and `Black's > mistakes mean that he loses games he should draw.' (The latter seems > more likely, since defending often requires making only moves, while > attacking usually has more flexibility.) > > On the other hand, it might be that grandmaster play is nothing like > perfect play. > > Consider what we know about endgames. Tablebases tell us that > grandmasters can play KRPKR endings prettymuch perfectly. We > understand the tablebases and know why the right move is the right > move. On the other hand, the tablebase for KRNKNN looks, in most > cases like completely random moves  nobody can understand it. In > this case, grandmaster play looks nothing like perfect. I don't think that is relevant. Those tablebases confirm that, in general, KRN is stronger than KNN, in conformity with the general chess principle that Rooks are worth more than Knights. GMs don't concern themselves with this simply because these types of positions are only rarely produced by chess' move tree. To make your case, you need to provide examples of *surprising* wins. > > > Dave. > >  > David Richerby Devil Chainsaw (TM): it's like > www.chiark.greenend.org.uk/~davidr/ a lethal weapon that's possessed > by Satan!


Date: 05 Feb 2008 20:11:39
From: help bot
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 4, 1:42 pm, Larry Tapper <larry_tap...@yahoo.com > wrote: > For what it's worth, grandmasters who are asked this question will > typically tell you that chess is probably a draw. Yeah, but the dismal record of grandmasters when making such guesses is not sufficient for us to conclude anything; after all, it's very possible for even the worst prognosticators to occasionally get something right. Long ago (or so it seems), these grandmasters were adamant in their denials regarding whether a chess computer or program would *ever* be able to defeat a master (later modified to GM). In essence, the answer was always "of course not, you fools, because "we" are so amazingly st!!". Food for thought... .  help bot


Date: 05 Feb 2008 09:11:25
From: Larry Tapper
Subject: Re: all the cheese in Canada

Phil Innes writes: PI > ...Secondly, if logic is these days divorced from mathematics, yet remains in play in philosophy, I am afraid that the mere enumeration of data is insufficient to resolve the issue by mathematics, since otherwise you might as well try to prove the existance of Canada by mathematics, or where cheese is located in Canada. Oh, sorry to hear that, nobody had told me about the divorce. You learn all sorts of things on the Internet. I wonder, was the divorce nasty or amicable? Who got custody of the field known as "mathematical logic"? Is mathematics now taking a walk on the wild side, dispensing with the notion of formal proof? LT

 
Date: 05 Feb 2008 15:20:28
From: Chess One
Subject: Re: all the cheese in Canada

"Larry Tapper" <larry_tapper@yahoo.com > wrote in message news:6198597369f7492787df4e65f637c527@l16g2000hsh.googlegroups.com... > > Phil Innes writes: > > PI> ...Secondly, if logic is these days divorced from mathematics, yet > remains in play in philosophy, I am afraid that the mere enumeration > of data is insufficient to resolve the issue by mathematics, since > otherwise you might as well try to prove the existance of Canada by > mathematics, or where cheese is located in Canada. > > Oh, sorry to hear that, nobody had told me about the divorce. You > learn all sorts of things on the Internet. > > I wonder, was the divorce nasty or amicable? Who got custody of the > field known as "mathematical logic"? Is mathematics now taking a walk > on the wild side, dispensing with the notion of formal proof? You talking with yourself Larry? Or about the issue of finite games, the role of math, any particular instance of anything you know enough about to write other than rhetorically. If you can't do, you know, sod off! There is enough shit on these newsgroups these days without cultmath showing up to suggest it has hairs on its chest. Maybe you just forgot some content to your message? Since you don't contest mine, but vagueout. Some people would think that indicates you couldn't answer, but protest anyway. Fair? PI > LT > >


Date: 04 Feb 2008 10:42:24
From: Larry Tapper
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 1, 6:15=A0pm, hanrahan...@yahoo.co.uk wrote: > I still think it's a win. > > What's your opinion, disregarding issues of proof and the feasibility > thereof? > > Michael For what it's worth, grandmasters who are asked this question will typically tell you that chess is probably a draw. There are some exceptions though, for example the correspondence champion and computer pioneer Hans Berliner, who was famous for insisting that White has a winning advantage. I think it's a draw myself. If you look in the rgcm Google archives, you'll find several old threads with sometimes astonishingly heated debates on the subject. LT


Date: 04 Feb 2008 03:00:16
From: Wlodzimierz Holsztynski (Wlod)
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 3, 9:47 am, David Richerby <dav...@chiark.greenend.org.uk > wrote: > > I think it was Turing who observed that a perfect game of chess > between Mr White and Mr Black would proceed in one of three ways: > > 1. Mr White announces, `I resign', > 2. Mr Black announces, `I resign' or > 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.' It is a corollary to the general Zermelo's theorem about finite games. It predates Turing. Wlod

 
Date: 05 Feb 2008 12:12:48
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Wlodzimierz Holsztynski (Wlod) <sennajawa@gmail.com > wrote: > David Richerby <dav...@chiark.greenend.org.uk> wrote: >> I think it was Turing who observed that a perfect game of chess >> between Mr White and Mr Black would proceed in one of three ways: >> >> 1. Mr White announces, `I resign', >> 2. Mr Black announces, `I resign' or >> 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.' > > It is a corollary to the general Zermelo's theorem about finite > games. It predates Turing. The general theory says that, with perfect play, the result of the game is either a win for white, a win for black or a draw. But I think it was Turing who phrased it in this way, with the two players not even bothering to make any moves. Dave.  David Richerby Frozen Evil Sword (TM): it's like a www.chiark.greenend.org.uk/~davidr/ razorsharp blade but it's genuinely evil and frozen in a block of ice!

 
Date: 04 Feb 2008 08:00:41
From: Chess One
Subject: Re: with perfect play, should it be 10, 01, or a draw?

"Wlodzimierz Holsztynski (Wlod)" <sennajawa@gmail.com > wrote in message news:e1fc788bc7bd46f99f227bdd6d4b263a@e23g2000prf.googlegroups.com... > On Feb 3, 9:47 am, David Richerby <dav...@chiark.greenend.org.uk> > wrote: > >> >> I think it was Turing who observed that a perfect game of chess >> between Mr White and Mr Black would proceed in one of three ways: >> >> 1. Mr White announces, `I resign', >> 2. Mr Black announces, `I resign' or >> 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.' > > It is a corollary to the general Zermelo's theorem > about finite games. It predates Turing. > > Wlod To interest you both, here is a 16th definition of Finite Games  which differentiates predictive theory, from the play itself: "One obeys the rules in a finite game in order to play, but playing does not consist of only obeying the rules. The rules of a finite game do not constitute a script. A script is composed according to the rules but is not identical to the rules. The script is the record of the actual exchanges between players  whether acts or words  and therefore cannot be written down beforehand. In all true finite play the scripts are composed in the course of the play. This means that //during the game// all finite play is dramatic, since the outcome is yet unknown. That the outcome is not known is what makes it a true game. The theatricality of finite play has to do with the fact that there is an outcome. Finite play is dramatic, but only provisionally dramatic. As soon as it is concluded we are able to look backward and see how the sequence of moves, though made freely by the competitors, could have resulted only in this outcome. We can see how every move fit into a sequence that made it inevitable that this player should win. The fact that a finite game is provisionally dramatic means that it is the intention of each player to eliminate its drama by making a preferred end inevitable. It is the desire of all finite players to be //Master Players//, to be so perfectly skilled in their play that nothing can surprise them, so perfectly trained that every move in the game is foreseen at the beginning. A true Master Player plays as though the game is already in the past, according to a script whose every detail is known prior to the play itself." //James P. Carse. Phil Innes

  
Date: 05 Feb 2008 12:16:03
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Chess One <OneChess@comcast.net > wrote: > "One obeys the rules in a finite game in order to play, but playing > does not consist of only obeying the rules..."  James P. Carse. Thank you but we were discussing games as an exercise in mathematics, not philosophy. But I now see where your confusion about the nature of finite and infinite games comes from. Dave.  David Richerby Broken Beer (TM): it's like a www.chiark.greenend.org.uk/~davidr/ refreshing lager but it doesn't work!

   
Date: 05 Feb 2008 11:26:53
From: Chess One
Subject: Re: with perfect play, should it be 10, 01, or a draw?

"David Richerby" <davidr@chiark.greenend.org.uk > wrote in message news:dxD*GtH6r@news.chiark.greenend.org.uk... > Chess One <OneChess@comcast.net> wrote: >> "One obeys the rules in a finite game in order to play, but playing >> does not consist of only obeying the rules..."  James P. Carse. > > Thank you but we were discussing games as an exercise in mathematics, > not philosophy. But I now see where your confusion about the nature > of finite and infinite games comes from. You do not understand what Carse proposes, that if the nature of a true finite game is, a priori, unpredictable, wherefore the imperative in the title of this thread  ie, 'should'? Secondly, if logic is these days divorced from mathematics, yet remains in play in philosophy, I am afraid that the mere enumeration of data is insufficient to resolve the issue by mathematics, since otherwise you might as well try to prove the existance of Canada by mathematics, or where cheese is located in Canada. As to cheese :: so to chess. Mathematics does not assess all, ony the quantifiable aspects of any system. Mathematics can even not theoretically assess all, since it is impossible to create a 1 :: 1 map. These are functions of logic, semantically phrased. The implication is that the resolution of chess may not have to do with mathematics any more than the location of the Canadian cheese. Phil Innes > > Dave. > >  > David Richerby Broken Beer (TM): it's like a > www.chiark.greenend.org.uk/~davidr/ refreshing lager but it doesn't > work!

    
Date: 06 Feb 2008 13:43:47
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Chess One <OneChess@comcast.net > wrote: > "David Richerby" <davidr@chiark.greenend.org.uk> wrote: >> Chess One <OneChess@comcast.net> wrote: >>> "One obeys the rules in a finite game in order to play, but playing >>> does not consist of only obeying the rules..."  James P. Carse. >> >> Thank you but we were discussing games as an exercise in mathematics, >> not philosophy. But I now see where your confusion about the nature >> of finite and infinite games comes from. > > You do not understand what Carse proposes I do not claim a full understanding of what Carse has written. But I understand it well enough to know that it is not relevant to the current discussion. However, if you believe that Carse's proposal of game as a metaphor and analytical tool for life is relevant to the solution of chess, you do not understand what he was written, either. > Secondly, if logic is these days divorced from mathematics, yet > remains in play in philosophy Logic is not divorced from mathematics. > Mathematics does not assess all, ony the quantifiable aspects of any > system. Mathematics can even not theoretically assess all, since it > is impossible to create a 1 :: 1 map. Huh? > These are functions of logic, semantically phrased. As far as I can see, that sentence is devoid of semantic content. > The implication is that the resolution of chess may not have to do > with mathematics any more than the location of the Canadian cheese. The solution of chess is precisely a quantifiable aspect of a mathematical system. It is absolutely a question of mathematics. Other aspects of chess, such as whether it will make any difference if we know the gametheoretic outcome of the game, are not questions of mathematics. Dave.  David Richerby Miniature OldFashioned Smokes (TM): www.chiark.greenend.org.uk/~davidr/ it's like a pack of cigarettes but it's perfect for your grandparents and you can hold in it your hand!

     
Date: 06 Feb 2008 09:33:42
From: Chess One
Subject: Re: with perfect play, should it be 10, 01, or a draw?

"David Richerby" <davidr@chiark.greenend.org.uk > wrote in message news:35d*K5M6r@news.chiark.greenend.org.uk... > Chess One <OneChess@comcast.net> wrote: >> "David Richerby" <davidr@chiark.greenend.org.uk> wrote: >>> Chess One <OneChess@comcast.net> wrote: >>>> "One obeys the rules in a finite game in order to play, but playing >>>> does not consist of only obeying the rules..."  James P. Carse. >>> >>> Thank you but we were discussing games as an exercise in mathematics, >>> not philosophy. But I now see where your confusion about the nature >>> of finite and infinite games comes from. >> >> You do not understand what Carse proposes > > I do not claim a full understanding of what Carse has written. But I > understand it well enough to know that it is not relevant to the > current discussion. Perhaps then, you cannot contest Carse to the extent that you say it is not relevant  especially since he says that prior determination by any means, including mathematics removes chess from being a finite game. You see, I simply represent his point that mathematics need to relate to something in the real world, which you have called 'philosophy' and I have called logic. Secondly, it may not be relevant /to you/. And as I wrote before, if you think you can prove the existance and whereabout of cheese in Canada by mathematics, then, you are right, logic and philosophy are not'relevant' for you. Below you cannot understand what you address, seemingly never before having encountered the 1:1 model paradigm. Therefore, someone like yourself who will not admit a logical proposition to your deliberations, will try to prove one could construct a 1:1 map. The other half of the sentence to which you reply, "Huh?" states that your own field of interest, mathematics, is concerned with quantification, by which we mean, to make numbers thereof. It is a statement of limits in philosophy, since by only making the numbers thereof, you have no idea if you represent 99% of the topic or just 1% of it  in fact, the quantification can be forgotten for what it is, a reduction, but believed to decribe the whole thing, 1:1. Which is why mathematicians should get out more, and look at some cool pictures. There is one titled: "This is not a hat." > However, if you believe that Carse's proposal of > game as a metaphor and analytical tool for life is relevant to the > solution of chess, you do not understand what he was written, either. > >> Secondly, if logic is these days divorced from mathematics, yet >> remains in play in philosophy > > Logic is not divorced from mathematics. > >> Mathematics does not assess all, ony the quantifiable aspects of any >> system. Mathematics can even not theoretically assess all, since it >> is impossible to create a 1 :: 1 map. > > Huh? > >> These are functions of logic, semantically phrased. > > As far as I can see, that sentence is devoid of semantic content. Maybe consult what semantics means? It means 'meaning'. >> The implication is that the resolution of chess may not have to do >> with mathematics any more than the location of the Canadian cheese. > > The solution of chess is precisely a quantifiable aspect of a > mathematical system. It is absolutely a question of mathematics. Those are metaphysical assertions, either true or untrue. They are not logical propositions. > Other aspects of chess, such as whether it will make any difference if > we know the gametheoretic outcome of the game, are not questions of > mathematics. Another suppositional statement with a'whether...if' formation followed by a metaphyscial 'we' and continuing to an assertion that "gametheoretic outcome" is even knowlable. By assertion all you say may or may not be true, and the simple substitution reveals the way you describe it, is apart from any logical content: The solution of where cheese is in Canada is precisely a quantifiable aspect of a mathematical system. It is absolutely a question of mathematics. Phil Innes > Dave. > >  > David Richerby Miniature OldFashioned Smokes > (TM): > www.chiark.greenend.org.uk/~davidr/ it's like a pack of cigarettes > but > it's perfect for your > grandparents > and you can hold in it your hand!

  
Date: 04 Feb 2008 08:39:27
From: Mike Murray
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Mon, 4 Feb 2008 08:00:41 0500, "Chess One" <OneChess@comcast.net > wrote: > Finite play is dramatic, but only provisionally dramatic. As soon as it >is concluded we are able to look backward and see how the sequence of moves, >though made freely by the competitors, could have resulted only in this >outcome. We can see how every move fit into a sequence that made it >inevitable that this player should win. > > The fact that a finite game is provisionally dramatic means that it is >the intention of each player to eliminate its drama by making a preferred >end inevitable. It is the desire of all finite players to be //Master >Players//, to be so perfectly skilled in their play that nothing can >surprise them, so perfectly trained that every move in the game is foreseen >at the beginning. A true Master Player plays as though the game is already >in the past, according to a script whose every detail is known prior to the >play itself." > > //James P. Carse. > >Phil Innes Almost seems Carse is speaking of Master Annotators rather than Players.


Date: 01 Feb 2008 15:15:30
From:
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Feb 1, 11:05 am, David Richerby <dav...@chiark.greenend.org.uk > wrote: > Chess One <OneCh...@comcast.net> wrote: > > I think we do not know if chess can be classified as a > > finite game, since it is so complex that even > > the /classification/ eludes us. Can any mathematico > > here affirm or contradict the previous sentence? > > We've already been through this a hundred times. You > evidently don't understand the answer but that doesn't > mean that the question is still open. > > Chess is, strictly speaking, an infinite game. Although > there are a finite number of possible positions, there > are plays that go on forever, for example by the players > moving their knights in and out. ...with neither player claiming a draw. It becomes finite if the 50move rule is changed so that a draw is automatic after 50 moves by both players without a capture or pawn move. > So, if chess is a forced win for either side, the winning > strategy will never involve repeating a position or > making more than fifty consecutive moves between pawn > moves and captures [...] [T]here can only be a finite > number of moves in a perfectly played game. This is true. Checkmate would occur before move X, where X is an integer for which an upper bound should not be too difficult to find. If chess is a draw with perfect play, the drawing strategy *will* involve repeating a position, claiming a draw after 50 moves without a capture or pawn move, or causing there to be insufficient material  and whichever of these it does involve, will occur within a finite number of moves. Otherwise it's just pushing wood... Although it might also be said that if chess is a draw with perfect play, a game between two perfect players might as well end in a draw before a move is played! :) I still think it's a win. What's your opinion, disregarding issues of proof and the feasibility thereof? Michael

 
Date: 03 Feb 2008 17:47:07
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

<hanrahan398@yahoo.co.uk > wrote: > David Richerby <dav...@chiark.greenend.org.uk> wrote: >> Chess is, strictly speaking, an infinite game. Although there are >> a finite number of possible positions, there are plays that go on >> forever, for example by the players moving their knights in and >> out. > > ...with neither player claiming a draw. > > It becomes finite if the 50move rule is changed so that a draw is > automatic after 50 moves by both players without a capture or pawn > move. Well, yes but, technically, that's a different game. The rest of my post argued that it's analytically equivalent because perfect play will result in immediately claiming a draw whenever one has the option because the opponent would never let you claim a draw if he had a way of winning. Thus, we may as well assume that the draws are automatic (though I didn't explicitly say that). > If chess is a draw with perfect play, the drawing strategy *will* > involve repeating a position, claiming a draw after 50 moves without > a capture or pawn move, or causing there to be insufficient material Not necessarily. It could end in stalemate from some positions. :P > Although it might also be said that if chess is a draw with perfect > play, a game between two perfect players might as well end in a draw > before a move is played! :) I think it was Turing who observed that a perfect game of chess between Mr White and Mr Black would proceed in one of three ways: 1. Mr White announces, `I resign', 2. Mr Black announces, `I resign' or 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.' (Technically, one should only offer a draw on one's own move so we can disregard the case where Mr Black offers the draw.) > I still think it's a win. > > What's your opinion, disregarding issues of proof and the feasibility > thereof? As I think I've already said in this thread, I think it's most likely that it's a draw and, if not, it's most likely that White has the win. Dave.  David Richerby Pickled Cheese TShirt (TM): it's like www.chiark.greenend.org.uk/~davidr/ a fashion statement that's made of cheese but it's preserved in vinegar!


Date: 30 Jan 2008 11:21:44
From:
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Jan 29, 4:22 pm, Sanny <softta...@hotmail.com > wrote: > On Jan 29, 4:38 pm, hanrahan...@yahoo.co.uk wrote: > > > If White and Black both play perfectly, who wins? Or is it a > > draw? > > > I'd be interested to know how chessplayers' opinions on this > > question are distributed. > > > Personally I think White wins, because he starts with a clear > > advantage. > > > I suspect most people might think the game is a draw. > > > Michael > > If Both are a perfect player of Equal Match. Say Master/Advance > Level at GetClub Chess then I think > > 90% chance it will be Draw. > 8% White Wins > 2% Black Wins. > It will depend on Opening the White/Black Chooses. There are 100s > of Openings and Each are perfect. So for Each opening we will have > different results. No, I am talking about two hypothetical perfect players, not two players at "master" or "advanced" level. Maybe only one first move by White is "perfect", necessarily leading, against perfect play by Black, to the best available result for White. Maybe several do. Noone knows! Noone even knows what that result is. It may be a win by White; it may be a draw. We can only speculate. It may conceivably be a win by Black. In that case, of course, ANY first move by a perfect player with the White pieces will lead to a loss against a perfect player with the Black pieces  so the idea of a "perfect" first move by White stops making sense! White would start with a losing position. I think you were answering a question different from the one I asked! To put the question in other words: take the starting position  is it a) a win for White, b) drawn with best play, or c) a win for Black? There are no other possibilities. Michael

 
Date: 31 Jan 2008 11:14:15
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

<hanrahan398@yahoo.co.uk > wrote: > Maybe only one first move by White is "perfect", necessarily > leading, against perfect play by Black, to the best available result > for White. Note that, if chess is a forced win for one player or the other, the concept of `perfect play' for the loser is moot. My personal opinion is that chess is most likely a draw. If it's not a draw, it's most likely a win for white but I don't totally discount the possibility that it's a win for black. Dave.  David Richerby Nuclear Lotion (TM): it's like a www.chiark.greenend.org.uk/~davidr/ soothing hand lotion that's made of atoms!

  
Date: 31 Jan 2008 11:37:10
From: Chess One
Subject: Re: with perfect play, should it be 10, 01, or a draw?

"David Richerby" <davidr@chiark.greenend.org.uk > wrote in message news:RNf*HTg6r@news.chiark.greenend.org.uk... > <hanrahan398@yahoo.co.uk> wrote: >> Maybe only one first move by White is "perfect", necessarily >> leading, against perfect play by Black, to the best available result >> for White. > > Note that, if chess is a forced win for one player or the other, the > concept of `perfect play' for the loser is moot. > > My personal opinion is that chess is most likely a draw. If it's not > a draw, it's most likely a win for white but I don't totally discount > the possibility that it's a win for black. In Finite and Infinite Games, Carse explains finite games as though which can usually be determined to be win draw or loss, and some which absolutely provide the first player with that result. I think we do not know if chess can be classified as a finite game, since it is so complex that even the /classification/ eludes us. Can any mathematico here affirm or contradict the previous sentence? Secondly, in previous conversations some people thought that chess was finite, but requiring thousands of years of human attention in order to prove any win  and therefore, in terms of human life spans, it seemed afinite. Noone thought it was an infinite game, since those typically evolve themselves in the play! Example, new rules are introuduced or mutated as the game progresses. Phil Innes > > Dave. > >  > David Richerby Nuclear Lotion (TM): it's > like a > www.chiark.greenend.org.uk/~davidr/ soothing hand lotion that's > made > of atoms!

   
Date: 01 Feb 2008 11:05:53
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Chess One <OneChess@comcast.net > wrote: > I think we do not know if chess can be classified as a finite game, > since it is so complex that even the /classification/ eludes us. Can > any mathematico here affirm or contradict the previous sentence? We've already been through this a hundred times. You evidently don't understand the answer but that doesn't mean that the question is still open. Chess is, strictly speaking, an infinite game. Although there are a finite number of possible positions, there are plays that go on forever, for example by the players moving their knights in and out. We should agree, although it's not stated in the rules for obvious practical reasons, that any infinite play is a draw. However, chess is analytically equivalent to a finite game. The fiftymove rule and the threefold repetition rule mean that ``I claim a draw'' is, in effect, a move in the game. When analyzing chess, we're interested in bestpossible play. Thus, neither player will give the possibility of a draw when they have a forced win because the opponent would immediately claim that draw because ``I claim a draw'' is better than playing a move that leads to a loss. So, if chess is a forced win for either side, the winning strategy will never involve repeating a position or making more than fifty consecutive moves between pawn moves and captures. Since any game can contain only a finite number of pawn moves (they only move forwards and will, eventually, hit the other end of the board) and only a finite number of captures (there are only thirty pieces on the board, apart from the kings, and each can only be captured once), there can only be a finite number of moves in a perfectly played game. Thus, for the purpose of deciding whether chess is a forced win for either side, chess is a finite game. This is good news, since it is wellknown that every finite twoplayer game of perfect information is determined: either one player has a forced win or the game is a forced draw. > Secondly, in previous conversations some people thought that chess > was finite, but requiring thousands of years of human attention in > order to prove any win  and therefore, in terms of human life > spans, it seemed afinite. Dude, afinite isn't a word. Something that isn't finite is, by definition, infinite. There's no room for an alternative notion between ``finite'' and ``infinite''. But, yes. While chess is effectively finite, it does seem that it would take an unfeasibly large amount of time to determine which player has a winning strategy and what that strategy is. This is nothing unusual. There are clearly a finite number of grains of sand in the Sahara but it would take an infeasible length of time to count them, even if you could somehow stop them blowing away. > Noone thought it was an infinite game since those typically evolve > themselves in the play! There is absolutely no requirement that an infinite game evolve in play! I can't think of a single infinite game that has been analyzed in mathematics that ``evolves'' in this way. Indeed, mathematically, a game (finite or infinite) is defined by: i) a set of possible positions; ii) a list of pairs of positions (X,Y) such that there is a move transforming position X to position Y; and iii) a list of positions that are won for each player. The rules are fixed at the start and never change. Dave.  David Richerby Frozen Toy (TM): it's like a fun www.chiark.greenend.org.uk/~davidr/ child's toy but it's frozen in a block of ice!

   
Date: 31 Jan 2008 23:32:50
From: Kenneth Sloan
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Chess One wrote: > > I think we do not know if chess can be classified as a finite game, Chess is finite. This comforts the theoretician. Chess is very, very, very, very, big. This concerns the practitioner.  Kenneth Sloan KennethRSloan@gmail.com Computer and Information Sciences +12059322213 University of Alabama at Birmingham FAX +12059345473 Birmingham, AL 352941170 http://KennethRSloan.com/

    
Date: 01 Feb 2008 11:07:41
From: David Richerby
Subject: Re: with perfect play, should it be 10, 01, or a draw?

Kenneth Sloan <KennethRSloan@gmail.com > wrote: > Chess One wrote: >> I think we do not know if chess can be classified as a finite game, > > Chess is finite. > > This comforts the theoretician. > > Chess is very, very, very, very, big. > > This concerns the practitioner. Au contraire. It comforts the practitioner a great deal, since it means that people can expect to play interesting games of chess for a long time to come. Dave.  David Richerby SolarPowered Chicken (TM): it's like www.chiark.greenend.org.uk/~davidr/ a farm animal but it doesn't work in the dark!


Date: 29 Jan 2008 08:22:23
From: Sanny
Subject: Re: with perfect play, should it be 10, 01, or a draw?

On Jan 29, 4:38=A0pm, hanrahan...@yahoo.co.uk wrote: > If White and Black both play perfectly, who wins? Or is it a draw? > > I'd be interested to know how chessplayers' opinions on this question > are distributed. > > Personally I think White wins, because he starts with a clear > advantage. > > I suspect most people might think the game is a draw. > > Michael If Both are a perfect player of Equal Match. Say Master/Advance Level at GetClub Chess then I think 90% chance it will be Draw. 8% White Wins 2% Black Wins. Play Chess at: http://www.GetClub.com/Chess.html It will depend on Opening the White/Black Chooses. There are 100s of Openings and Each are perfect So for Each opening we will have different results. Bye Sanny Play Chess at: http://www.GetClub.com/Chess.html

