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| Tags: chess, initial, mutual, position, zugswang |
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#31
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On Feb 21, 9:25 pm, "Jason 911" wrote:
I'm actually higher rated than Innes and much stronger. Nonsense; the nearly-an-IM claims a rating of 2450, which is much higher than anything claimed by the creature. (Of course, it could be that all such claims are vacuous.) There's a reason he hasn't played rated chess in ten years. Fear of meeting up with, say, Taylor Kingston OTB? As usual help bitch, your ability to "analyze" is tantamount to a turtle stuck on it's back You're so helpless it's pathetic! A turtle stuck on its back requires a turning over -- a helping hand. But somehow I strongly suspect you are the type who would, with great pleasure, to be sure, run over it instead. :( You're another loser that can't play serious chess so you've become a mouthpiece usenet troll. Too bad the creature is not intelligent enough to have read about my many brilliancies, both at GetClub (where I have been named a "star") and at RedHotPawn, where I have (so far) amassed a perfect record against all comers. If only the lowly creatures could learn to read, and to *think*! Alas, it pains me to imagine all that they are missing of the art of chess, so clearly exhibited in my games. Yet precious few have the discerning understanding to comprehend the depth thereof, the subtlety of my moves. So sad. So pitiful. BTW, the creature *could* in fact get its wish, by simply joining the tournaments hosted by Rob Mitchell (a poor patzer, not unlike the creature); for these tourneys have included IM Innes, among others. Oh, probably it will now run away, for the prospect of facing a dyed-in-the-wool nearly-an-IM must prove terrifying! Oh, well. -- help bot |
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#32
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"help bot" wrote in message ups.com... On Feb 21, 9:25 pm, "Jason 911" wrote: I'm actually higher rated than Innes and much stronger. Nonsense; the nearly-an-IM claims a rating of 2450, which is much higher than anything claimed by the creature. (Of course, it could be that all such claims are vacuous.) There's a reason he hasn't played rated chess in ten years. Fear of meeting up with, say, Taylor Kingston OTB? As usual help bitch, your ability to "analyze" is tantamount to a turtle stuck on it's back You're so helpless it's pathetic! A turtle stuck on its back requires a turning over -- a helping hand. But somehow I strongly suspect you are the type who would, with great pleasure, to be sure, run over it instead. :( You're another loser that can't play serious chess so you've become a mouthpiece usenet troll. Too bad the creature is not intelligent enough to have read about my many brilliancies, both at GetClub (where I have been named a "star") and at RedHotPawn, where I have (so far) amassed a perfect record against all comers. I'm alot more intelligent than you could dream about being help bitch. Your comments and inability to comprehend simple concepts are proof enough of that. So your computer is good at beating people. Big deal. How do you do when you have to make your own moves. You're a trolling idiot that posts drivel in usenet groups while your fritz 10 is playing your corr. games for you. FYI, your boyfriend Innes is nowhere near being an IM, or even an FM for that matter. The burned out old geezer doesn't even have a FIDE rating at all. And his last uscf rating, which is more than ten years old, is only 2042 JMR |
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#33
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On 21 Feb 2007 12:43:08 +0000 (GMT), David Richerby
wrote: Ray Johnstone wrote: David Richerby wrote: Ray Johnstone wrote: wrote: Is the initial position in chess a mutual Zugswang? We will probably never know. See: http://members.iinet.net.au/~ray/Chessgames.htm Just because chess is likely impossible to brute-force doesn't mean we can never know the outcome of theoretical best play. [...] I agree, which is why I said "probably". OK. Your web page seems a little more certain than that, though. I can't imagine any method other than brute force but I couldn't have imagined calculus, Newton's laws... :-) Strategy-stealing (as used in chomp) is the usual way to produce a proof that one player can force a win without knowing how to do it. But that doesn't apply to chess because there's no first move that white can make that is equivalent to passing. One possibility would be to come up with a proof along the following lines. Somehow, classify positions as `good' or `bad' and produce a score for each position that is a positive integer, such that every position where White has given checkmate is scored 1 and all other positions have scores greater than one. If you could then show that the initial position is `good' and that, furthermore, whenever White is in a `good' position, he has at least one move such that every one of Black's replies leaves the game in another `good' position with a strictly lower score, you would have shown that, with best play, chess is a forced win for White. I don't see how this helps. You would still need to examine a vast number of positions. Even an enormous sample would not be adequate. (The point of the `good' positions is that the scoring function can behave arbitrarily on bad positions without affecting the argument.) Also, there is an error in your web page. You write, ``Suppose White wins a particular game [with perfect play] which began with say a3. Consider Black's last unforced move. All other moves at that branch point must also lead to mate in as many moves or fewer or Black would have chosen one of them in preference. This argument applies at every branch point so all games starting with a3 must then be wins for White. Games starting with the other 19 possible moves are of little consequence. They could all be wins for the unfortunate Black, who would never get to play them. ``Black's prospects are therefore rather gloomier: to win any game it is necessary that every game be a win for Black.'' -- http://members.iinet.net.au/~ray/Chessgames.htm First, there's the unimportant point that, in perfect play, the concept of a move being forced or not doesn't really exist: the whole point of saying that all perfect games are won for White is that it really doesn't matter what Black plays. Since he has no hope of winning, it doesn't really make much sense to assert that avoiding a mate in one to allow a mate in ten is `forced'. But that doesn't really matter. "Forced" is generally used in chess to describe a move which must be played to avoid a disastrous loss of material or position but I use it here to describe a move which is the only legal move. Perhaps I shoould have made this clearer. There are two copies of the same problem in these two paragraphs. You say that ``... all games starting with a3 must then be wins for White''. This is not true. All you can conclude is that all games in which White plays a3 and then continues to play perfectly are wins for White. There are plenty of games starting with 1.a3 that are losses for White. For example, 1.a3 a6 2.f3 e5 3.g4?? Qh4#. I think the context makes it clear that "game" as used here refers to "perfect games". The same problem occurs in the second paragraph. Black only has to win the games in which he plays perfectly: the other games are, as you have observed, of no relevance. This means that he must have a winning reply to each of White's 20 possible first moves but that's not really so much worse than White's situation because, if chess is a win for White, he must have a winning reply to each of Black's 20 possible first moves, too! "Black’s prospects are therefore rather gloomier" is my weakly humorous attempt to describe Black's situation. In the hypothetical case I describe only games beginning 1 a3 are perfect games. Apologies if this all sounds rather pedantic -- I'm reading rec.games.chess.* while I'm supposed to be writing an academic paper on game theory. ;-) Dave. |
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#34
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Chess One wrote:
"David Richerby" wrote in message ... Ray Johnstone wrote: wrote: Is the initial position in chess a mutual Zugswang? We will probably never know. See: http://members.iinet.net.au/~ray/Chessgames.htm Just because chess is likely impossible to brute-force doesn't mean we can never know the outcome of theoretical best play. For example, it is known that the game of `chomp' is a theoretical win for the first player but nobody knows how to force the win except in very simple cases. http://en.wikipedia.org/wiki/Chomp Yeah, this is always an interesting debate, but its not even known if /theoretically/ if it is white or black who wins, or the game is a draw. To make such a claim the basis of it needs to be discussed, and strangely, must deal with this factor:- [psychology] No, Phil, psychology is completely irrelevant to the question of whether chess is a theoretical win for one of the players or a draw. The question is entirely mathematical. I don't know if any mathematician has ever seriously proposed which of these two states, potential :: action, is superior from any theoretical model. Again, what's this double-colon you're using? What does it mean? Mathematical game theory doesn't deal with `potential' `::' or `action'. It deals with sequences of moves leading to wins or losses. Chess is not even conveniently describable /as a process/ as a Finite or Infinite Game. Chess is trivially describable as an infinite game by omitting the three drawing rules (dead position, three-fold repetition, 50-move rule). It is then easy to prove that it suffices to consider only finite games because of the drawing rules. Although chess is ostensibly finite, if you take the way it is played /the modus/ as the rules applicable to that part of the game, then the rules do change as the game progresses [there are no pawn promotions in the opening, eg] That's not a change in the rules!!! The rules are fixed throughout the game; it's just that some of them can't apply. You can tell that they're fixed by checking FIDE's website after each move you make. but there is no /fixed/ prescription for when pawn promotions become a consideration to actual play - and 'continuing the play' is what happens in balanced or even dynamically unbalanced positions - You've misunderstood the phrase `continuing the play' and are trying to apply it outside its context. That context is a particular class of infinite games. Infinite games are often defined as follows. The two players alternate moves and, if some condition is reached, the game is over and player 1 has won; player 2 wins only if the game continues forever. (Not all infinite games work like this. Consider the following game, the name of which I'm afraid I don't recall. The game is defined by a set S of real numbers between, but not including, 0 and 1. We start with `0.' written on a piece of paper and take turns to add one digit to the end of the number written so far. I win if the infinitely long decimal we produce is in S; you win if it isn't.) and there are no fixed number of moves to any game of chess, except as metaphysically decided by others. What on earth is the word `metaphysically' doing in the middle of that sentence? This has nothing to do with metaphysics. Can any mathematician or logician suggest even an objective basis for determining the result of chess as Finite/Infinite [?] game. Yes. It's a finite game so, as far as a mathematician or logician (raises hand) is concerned, the objective basis is `analyze each of the possible cases in turn.' If you want to know whether there's a practical way of doing it, you're straying into the realms of computer science. Can the statement, "black always wins" be refuted Yes. Consider the game 1.e4 e5 2.Bc4 Bc5 3.Qh5 a6 4.Qxf7#. The statement `Black always wins with perfect play' can be refuted, in principle, by case analysis. or can it be shown to be unprovable? No because it is not unprovable. Dave. -- David Richerby Edible Cyber-Umbrella (TM): it's like www.chiark.greenend.org.uk/~davidr/ an umbrella that exists only in your computer but you can eat it! |
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#35
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On Feb 21, 11:58 pm, "Jason 911" wrote:
Too bad the creature is not intelligent enough to have read about my many brilliancies, both at GetClub (where I have been named a "star") and at RedHotPawn, where I have (so far) amassed a perfect record against all comers. I'm alot more intelligent than you could dream about The creature apparently imagines itself to be very intelligent, however... Lesson #1: There is no such word as "alot". This error may have first come into play indirectly, from the fact that there is a word which sounds similar: allot. Allot is a verb, meaning to apportion or grant. The creature may try to remember not to make this *telling* error again by thinking of "alittle", which of course is also a non-word, but which is not so commonly mucked up by the ignorant, the uneducated, the stupid. So your computer is good at beating people. Big deal. FYI: I welcome and even invite any and all attempts to demonstrate that I have been using a chess program to select my moves. Clearly, although my moves are very often brilliant, there nonetheless remain signs of human weakness, here and there. Not to mention the issue of my frequently selecting less than optimal moves, as we humans so often do. It is understandable that the low creature known as Jason Repa is unfamiliar with such things, being of an entirely different species. How do you do when you have to make your own moves. At present, I have *finally* achieved a position requiring a deep think. Two pawns ahead, I need to select the right follow-up or my attack will falter. This is in fact, the very first time I have seen fit to set up a chessboard and men. All my games at GetClub and all my games at RedHotPawn have been played rather offhandedly, up 'till now. (Even so, I am considered a "star" at GetClub.) Perhaps you could recruit IM Innes in this endeavor? He has the latest, greatest chess program ever: Rybka, which undoubtedly can improve on my actual moves about 90% of the time. Against forms of artificial intelligence I do not try to compete, nor against the lower animals such as yourself. You're a trolling idiot that posts drivel in usenet groups while your fritz 10 is playing your corr. games for you. I don't have Fritz 10, nor was I even aware they had progressed so far. At one time I had Fritz 5.32, but it won't install on this machine. If I were to buy a chess program, I would feel pressed to buy the very best one (Rybka, I believe). FYI, your boyfriend Innes is nowhere near being an IM, or even an FM for that matter. The burned out old geezer doesn't even have a FIDE rating at all. That is disturbing. Living so near to NY city, I should have expected him to at least have *some* FIDE rating, even if only, say, 1850. Perhaps he cannot afford the entry? And his last uscf rating, which is more than ten years old, is only 2042 In my (admittedly limited) experience, many of the large metropolitan centers tend to induce a sort of local ratings inflation, as compared to the back woods areas like, say, Kentucky. For instance, even playing in a mid-sized city such as Indianapolis is quite a different experience from playing in a tournament in Louisville, where only the locals show up to compete. I seem to recall having great difficulties against more than one "lower-rated" opponent there, quite unlike my experiences among the Indy dwellers. Yet I recall that of all the places I played, Chicago was by far the most over-rated, and in fact I returned home carrying with me over a hundred "captured" rating points, despite an ordinary performance on my part. I expect a "raid" on NYC or Houston or Las Angeles might well have resulted in a similar experience, from what I have seen. Yet IM Innes' apparent inactivity is quite a handicap, for who can keep his chess skills honed and sharpened without some practice, now and then? Lucky for me, I am immune to this problem, being a genuine, natural- born chess genius and all. ;D -- help bot |
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#36
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On Feb 20, 7:26 pm, "Chess One" wrote:
"David Richerby" wrote in message ... Ray Johnstone wrote: wrote: Is the initial position in chess a mutual Zugswang? We will probably never know. See: http://members.iinet.net.au/~ray/Chessgames.htm Just because chess is likely impossible to brute-force doesn't mean we can never know the outcome of theoretical best play. For example, it is known that the game of `chomp' is a theoretical win for the first player but nobody knows how to force the win except in very simple cases. http://en.wikipedia.org/wiki/Chomp Yeah, this is always an interesting debate, but its not even known if /theoretically/ if it is white or black who wins, or the game is a draw. To make such a claim the basis of it needs to be discussed, and strangely, must deal with this factor:- Usually people think white has all the chances, since white is the first player with initiative and wins chess games at about twice the rate as black, but immediately at the first move white is vulnerable to having transmuted that initiative [potential] into action. Black then has a momentary initiative, but different than at the previous ply, since white has committed himself, and turned that mutable potential into relatively fixed position. I don't know if any mathematician has ever seriously proposed which of these two states, potential :: action, is superior from any theoretical model. Adorjan's books analyse white/black wins as much from a psychological basis, as anything else - that we have an expectation [or even obligation] to do better with white and different expectation with black [getting a draw is good!]. But there is no objective basis in chess for either attitude! -------- Chess is not even conveniently describable /as a process/ as a Finite or Infinite Game. James Carse makes a few ad hoc or generalising descriptions of finite/infinite, he says;- a) a finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play. and b) the rules of a finite game may not change; the rules of an infinite game must change. Although chess is ostensibly finite, if you take the way it is played /the modus/ as the rules applicable to that part of the game, then the rules do change as the game progresses [there are no pawn promotions in the opening, eg] but there is no /fixed/ prescription for when pawn promotions become a consideration to actual play - and 'continuing the play' is what happens in balanced or even dynamically unbalanced positions - and there are no fixed number of moves to any game of chess, except as metaphysically decided by others. --- Adorjan even says that we are conditioned to always prosecute our chess from white's point of view - and that all chess diagrams are presented as if you were sitting behind the white pieces, eg. and this reinforces the conscious perception of 'white to move and win.' Players overconcentrate their study with what to do with the white pieces, and this imbalanced study coupled with received expectations of what to do with white or black, creates a self-fulfilling result. But after 1.e4, which side actually choses the opening? If the Sicilian is played, which side choses the sub-variation, to play the Taimanov or Pelikan vars? Can any mathematician or logician suggest even an objective basis for determining the result of chess as Finite/Infinite [?] game. Can the statement, "black always wins" be refuted, or can it be shown to be unprovable? Phil Innes Dave. -- David Richerby Beefy Smokes (TM): it's like a pack www.chiark.greenend.org.uk/~davidr/ of cigarettes that's made from a cow!- Hide quoted text - - Show quoted text - A revisit to Black is Ok by Adorjan will not be a bad idea. http://www.gmsquare.com/BlackisOKAdorjan.html |
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#37
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wrote:
A revisit to Black is Ok by Adorjan will not be a bad idea. http://www.gmsquare.com/BlackisOKAdorjan.html Thanks for the URL! By the way, could you cut down the quoted text, please? It makes the post much easier to read if one doesn't have to scroll through huge amounts of irrelevant quoted material to find the new stuff. :-) Cheers, Dave. -- David Richerby Surprise Spoon (TM): it's like a piece www.chiark.greenend.org.uk/~davidr/ of cutlery but not like you'd expect! |
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#38
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Ray Johnstone wrote:
David Richerby wrote: Ray Johnstone wrote: I can't imagine any method other than brute force but I couldn't have imagined calculus, Newton's laws... One possibility would be to come up with a proof along the following lines. Somehow, classify positions as `good' or `bad' and produce a score for each position that is a positive integer, such that every position where White has given checkmate is scored 1 and all other positions have scores greater than one. [...] I don't see how this helps. You would still need to examine a vast number of positions. Even an enormous sample would not be adequate. The advantage would come if you could find some sort of structural property that allowed you to identify the `good' and `bad' positions without having to list them all. By a `structural property', I mean something like `White has a knight that isn't on the edge of the board'. Of course, that doesn't guarantee that White will win since there are many (drawn) KNvK positions that satisfy it. But you get the idea, I hope. At the very least, the property would have to include the requirement that White have enough material to checkmate a naked king. (By the way, we know that a scoring function of the required type exists: just let the score of the position be the length of the shortest forced checkmate! In fact, we can do mo define `good' to be `White has a forced checkmate'. By definition of `forced checkmate', from any `good' position, White can get back to a `good' position after any Black move. So now, you just have to prove that the initial position is `good' and we're done. :-D ) First, there's the unimportant point that, in perfect play, the concept of a move being forced or not doesn't really exist "Forced" is generally used in chess to describe a move which must be played to avoid a disastrous loss of material or position but I use it here to describe a move which is the only legal move. Perhaps I shoould have made this clearer. Aaaah. I see. That makes perfect sense so I think you should make it clearer on the page. There are two copies of the same problem in these two paragraphs. You say that ``... all games starting with a3 must then be wins for White''. This is not true. I think the context makes it clear that "game" as used here refers to "perfect games". I don't think that's so clear -- it wouldn't hurt to add the word `perfect' in a few more places. :-) Dave. -- David Richerby Poetic Tree (TM): it's like a tree www.chiark.greenend.org.uk/~davidr/ but it's in verse! |
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#39
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"David Richerby" wrote in message ... Yeah, this is always an interesting debate, but its not even known if /theoretically/ if it is white or black who wins, or the game is a draw. To make such a claim the basis of it needs to be discussed, and strangely, must deal with this factor:- [psychology] No, Phil, psychology is completely irrelevant to the question of whether chess is a theoretical win for one of the players or a draw. The question is entirely mathematical. I agree David, psychology is irrelevant to theoretical win, draw, loss- though as another poster pointed out by implication, for most players it is the way most games are decided. But your sort of answer is what I looked for in my two interogatories. I don't know if any mathematician has ever seriously proposed which of these two states, potential :: action, is superior from any theoretical model. Again, what's this double-colon you're using? Its an advanced colon, as used by ... well, no jokes occur to me. It is very like a single colon, though more signalled. What does it mean? Mathematical game theory doesn't deal with `potential' `::' or `action'. It deals with sequences of moves leading to wins or losses. Chess is not even conveniently describable /as a process/ as a Finite or Infinite Game. Chess is trivially describable as an infinite game by omitting the three drawing rules (dead position, three-fold repetition, 50-move rule). It is then easy to prove that it suffices to consider only finite games because of the drawing rules. But finite is itself an arguable determination. Is it used synonymnously for 'theoretical', even though there are more moves than atoms in the universe, or time for /whom?/ to determine right play? Chess challenges finite/infinite resolution, since if the damned universe decays before any means of resolution is achieved, what does finite mean? It means if something we don't know could go faster within the available time, right? But this rests finite upon a supposition on an unknown, much as we normally determine use of 'infinite'. Although chess is ostensibly finite, if you take the way it is played /the modus/ as the rules applicable to that part of the game, then the rules do change as the game progresses [there are no pawn promotions in the opening, eg] That's not a change in the rules!!! The rules are fixed throughout the game; it's just that some of them can't apply. You can tell that they're fixed by checking FIDE's website after each move you make. No look-ups! But these are asides, for colour only.but there is no /fixed/ prescription for when pawn promotions become a consideration to actual play - and 'continuing the play' is what happens in balanced or even dynamically unbalanced positions - You've misunderstood the phrase `continuing the play' and are trying to apply it outside its context. That context is a particular class of infinite games. It is, yes. Infinite games are often defined as follows. The two players Or two or more, but yes... alternate moves The tricky part of inifinite games is that the rules themselves evolve, so that some moves may condition new rules. This may except alternating moves. This is a quibble, but still... and, if some condition is reached, the game is over and player 1 has won; player 2 wins only if the game continues forever. (Not all infinite games work like this. Consider the following game, the name of which I'm afraid I don't recall. The game is defined by a set S of real numbers between, but not including, 0 and 1. We start with `0.' written on a piece of paper and take turns to add one digit to the end of the number written so far. I win if the infinitely long decimal we produce is in S; you win if it isn't.) This again is an aside, but is this infinite, or simply an undetermined linear extension of a theme? Now - since you bite on my own asides, here is the scientific conundrum, Sheldrake, among others, has positied that the universe evolves, pace Darwin, but also in physics. The question is if the rules of manifestation also evolve? How come a certain crystall with varieties of manifestion into 3 possibilities achieves any singular one, and is this one a trend? In other words, as the universe evolves, do the causitive factors of manifestation also evolve? At the time of the big bang, did the rules governing manifestion of elements preceed the manifestations? Did these include mutations or optional forms? have they since changed? This is serious physics and philosophy - but still on the 'infinite game' plan of an evolution of the rules governing the activity itself. it is of course highly controversial, yet attracts and engages the best philosophic minds. and there are no fixed number of moves to any game of chess, except as metaphysically decided by others. What on earth is the word `metaphysically' doing in the middle of that sentence? This has nothing to do with metaphysics. I use the word in its technical sense - 'without person' which is sometimes also a transcendent, thus; through person, but in this instance not through the player but an arbiter. It is not an unusual or normative intellectual phrase to describe how decisions are made. In this sense the game of chess is decided not by the players [the persons] but by non-players implementing their determination of rules. Can any mathematician or logician suggest even an objective basis for determining the result of chess as Finite/Infinite [?] game. Yes. It's a finite game so, as far as a mathematician or logician (raises hand) is concerned, the objective basis is `analyze each of the possible cases in turn.' If you want to know whether there's a practical way of doing it, you're straying into the realms of computer science. Which is to say, of logical method extrapolated to the Nth by brute force projection. Yet what is the answer to even hypothesised projections? Can the statement, "black always wins" be refuted Yes. Consider the game 1.e4 e5 2.Bc4 Bc5 3.Qh5 a6 4.Qxf7#. The statement `Black always wins with perfect play' can be refuted, in principle, by case analysis. Though its also true that black can mate quicker than white - so perhaps the explicit statement 'with best play' needs to be added, and if so, is there any answer? or can it be shown to be unprovable? No because it is not unprovable. shrug So can you prove with best play - instead of one-sided manipulation to invoke worst play - that your assertion is true? Phil Dave. -- David Richerby Edible Cyber-Umbrella (TM): it's like www.chiark.greenend.org.uk/~davidr/ an umbrella that exists only in your computer but you can eat it! |
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#40
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"help bot" wrote in message ups.com... At present, I have *finally* achieved a position requiring a deep think. Two pawns ahead, I need to select the right follow-up or my attack will falter. This is in fact, the very first time I have seen fit to set up a chessboard and men. All my games at GetClub and all my games at RedHotPawn have been played rather offhandedly, up 'till now. (Even so, I am considered a "star" at GetClub.) Perhaps you could recruit IM Innes in this endeavor? He has the latest, greatest chess program ever: Rybka, which undoubtedly can improve on my actual moves about 90% of the time. Even a master such as myself can improve upon a 1300-beater such as Kennedy, who is deeply puzzled by his position, and uncertain of the theme which can conclude the game. That, though, is not the problem, since the question is about Jason, the on-line 16xx player, and would not necessarily understand what I say. More importantly, doesn't care to hear it. It's common enough, people write in and ask how to be super-stars at chess and boost their rating and I rarely agree with 1700 players giving advice to 1350 players. This does not shake them in the least! If they like open positions or taking the initiative at all costs they will recommend that, thought this is less usual than a more defensive strategm of maintaining parity and gradual increment with the least risk. Neither has an objective basis in respect of any chess position! You have to get beyond what you like or don't like in any position to make that sort of assessment - something chess training courses and how-to books rarely point out. Jason has not the slightest interest in improving his chess, since he writes like an immortal teenager, full of **** and vinegar. That's okay! Normal, no? Perhaps in 20 years? But he already killed his mature self, [a self-defeating paradigm] but that is psychological inhibition emerging from his own personal circumstances, and no public matter. Phil Innes |
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