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May0408   Terry McCracken: < MostlyAverageJoe: <Terry McCracken: ... Ba4! is by far the better move!>
If I may be excused for persistently voicing an opinion with a tiny hint of disagreement, I still see no evidence for a huge advantage of Ba4. Forward analysis at 21 or more pliespermove, followed by a backslide seem to indicate the following as the optimal line up to move 40:> Both appear to be winning, but I would give the nod to 31. Ba4 I don't have a quad computer and the time to devout a days worth of analysis. In my rough line White wins faster with 31. Ba4 and it's seems clearer than than 31. Bd3 unless Black is foolish enough to play NxB. 

May0508
  patzer2: For the difficult Saturday, May 3, 2008 puzzle, the decoy pseudo sacrifice 29. Rh8+! gives White a difficult winning attack. See <Terry McCracken> and <MostlyAverageJoe>'s posts for an interesting discussion of the merits of the alternative followup move
31. Ba4 versus the game move 31. Bd3 . 

May0608
  Richard Taylor: <znprdx: <Richard Taylor: ...As I have said before  "Chess is infinite!"> Well as much as one might agree with this sentiment...actually Chess is of course finite in strictly mathematical terms. > This is why John von Neumann who studied game theory and other mathematical matters  did not consider chess a a game but in reality  for us mortals chess is effectively an infinite puzzle... For myself  a bunny or a patzer par excellence, chess is infinitely baffling! I once looked up Infinity in the Britannica and there is big discussion of & by philosophers and mathematicians etc as to whether there is such a thing as infinity. There is no agreement on the concept... Of course I meant it in as a rhetorical or "poetical" kind of flourish... 

May0708   znprdx: <Richard Taylor: This is why John von Neumann who studied game theory and other mathematical matters  did not consider chess a a game –> By” this” are you implying the notion of “infinite” – because Chess “rules” lead to a clearly ‘zero sum’ outcome ( one win,one loser) but with the special possibility of equality due to unique drawing methods – in particular the unique concept of stalemate.... 

May1819   Pedro Fernandez: My great friend <Richard Taylor>, I hope your concept of infinity (or infinite) don't be an inference of Neumann words about chess, neither your namesake mathematician (you know, Wiles' pupil) knows about this, lol! Greetings! 

May1819
  Willber G: <Pedro Fernandez: My great friend <Richard Taylor>, I hope your concept of infinity (or infinite) don't be an inference of Neumann words about chess, neither your namesake mathematician (you know, Wiles' pupil) knows about this, lol! Greetings!> Erm, I know he's still around but Richard's last post on this game was eleven years ago... 

May1819   Hercdon: I suppose today’s theme is to create a lot of complications for an obviously weaker player to give him/her plenty of chances to go wrong 

May1819
  drollere: the B on c2 screams for a R sacrifice on h8, allowing Qh1+ and Qh7+ if it is captured; the e5 pawn and the stacked rooks provide a mating corner. but the R wasn't captured ... in the game, if 33. .. fxg6, black can't prevent mate following Qh1. 

May1819
  drollere: <actually Chess is of course finite in strictly mathematical terms.> this has a subtle application: i don't know of any algorithm that can countably exhaust the total domain of possible moves; that is, i don't know of any publication that states: "there are a total of N possible game histories (sequences of n permissible positions) in chess, N being less than infinity." it's likely that the number is not infinite but is "immeasurably large"  in the vague space between countable and infinite. but i don't know of any strictly mathematical *proof* that it is not infinite. instead, we have two "meta rules" that truncate a game sequence arbitrarily (repeated moves, insufficient material to mate), which are actually not rules for permutating positions but rules that let human players quit the toil. 

May1819
  thegoodanarchist: Puff Tuzzle 

May1819
  agb2002: Black threatens dxe3 and d3.
The open hfile suggests 29.Rh8+:
A) 29... Kxh8 30.Qh1+ Kg7(8) 31.Qh7+ Kf8 32.Qh8+ Ke7 33.Qf6+ Kf8 34.Rh1 Ne2+ 35.Kg2 Nf4+ 36.Kf1 Qb5+ 37.Kg1 Ne2+ 38.Kf2 dxe3+ 39.Ke1 Rd1+ 40.Bxd1 and mate next. B) 29... Kg7 30.Rh7+
B.1) 30... Kf8 31.Nf5 Bxf5 (31... Kg8 32.Rg7+ Kf8 33.Rxg5 looks very good for White) 32.gxf5 (32.Bxf5 Qd5 and the epawn looks lost) and the threat f6 seems to give White a considerable advantage. B.2) 30... Kg8 31.Bd3 (31.Qh1 Ne2+ 32.Kg2 Nf4+ 33.Kf1 Qb5+ frres d7 with tempo for the black king) B.2.a) 31... dxe3 32.Qh1 looks winning.
B.2.b) 31... Nxd3 32.Qh1 is similar. 

May1819   Cheapo by the Dozen: <drollere>,
There are only finitely many possible chess positions, and a triple repetition draw rule. So how could there possibly NOT be an upper bound on the possible number of moves in a game? 

May1819   Cheapo by the Dozen: Even after playing it through a few times, I'm having real trouble keeping straight why the Bd3 precaution is needed in the game line, but not in the line where Black accepts the h8 rook sacrfice. 

May1819   Patriot: There is a finite number of possible Chess positions, if we are talking about permutations of pieces on the board. But how many of those positions are reached by legal means and how many are impossible? Once you add rules to the problem, you have further limited the number of possibilities. Sure, I suppose if we had the mind of God then Chess would seem even less finite than TicTacToe. I'm only human so there is a method to my madness. I came up with the right solution, seeing that 29.Rh8+ Kxh8 30.Qh1+ Kg7 31.Qh7+ Kf8 32.Qh8+ Ke7 33.Qf6+ Kf8 34.Rh1 is a huge problem for black. And I noticed that 29.Rh8+ Kg7 30.Rh7+ needs to be played but after that I failed to come up with the right answer and here's why. I failed to see white's knight on e3 is en prise in the initial position. I'm not sure why but I had enough information to play the right move here. 

May1819
  Breunor: Since there has been endless speculation on this forum over whether 31 Bd3 or Ba4 is better, I ran the computer at 60 ply. This is Stockfish's answer at that ply: 1) +2.21 (35 ply) 31.Ba4 Kxh7 32.Bxd7 dxe3 33.Qc2+ Kg7 34.Bxe8 Rd2 35.Qxd2 exd2 36.Rd1 Nd3 37.Rxd2 Nxe5 38.b4 c6 39.f4 Nxg4 40.fxg5 Ne3 41.Rd8 Bxa2 42.Rb8 Nf5+ 43.Kf4 Nd6 44.Ke5 Nxe8 45.Rxe8 Bd5 46.Ra8 b5 47.Kf5 Be6+ 48.Kf4 f6 49.Rxa6 Bd5 50.Ra7+ Kg6 51.gxf6 Kxf6 52.Ke3 Ke6 53.Kd4 2) +2.12 (34 ply) 31.Rh8+ Kg7 32.Rh7+ Kg8 33.Ba4 Qe7 34.Qh1 Ng6 35.Qh6 Qf8 36.cxd4 Qxh6 37.Rxh6 Kg7 38.Rah1 Rh8 39.Nf5+ Kg8 40.Rxh8+ Nxh8 41.Bc2 Ng6 42.Rh5 Bxa2 43.Rxg5 Kf8 44.Rh5 Ke8 45.Rh2 Ne7 46.Be4 Nxf5+ 47.gxf5 c6 48.Rh8+ Kd7 49.Rxd8+ Kxd8 50.Kg4 Bd5 51.f6 Bxe4 52.fxe4 Kd7 3) +1.58 (34 ply) 31.Bd3 Nh5+ 32.Rxh5 dxe3 33.Qh1 Kf8 34.Rd1 e2 35.Bxe2 Qa4 36.Rxg5 Rxd1 37.Bxd1 Qxa2 38.Bc2 Ke7 39.Qc1 Kd7 40.Rh5 Kc8 41.Rh2 Rg8 42.g5 Qc4 43.Qe3 Qf1 44.Be4 Rd8 45.f4 a5 46.Rh1 Qb5 47.b4 c6 48.bxa5 Qxa5 49.Bf3 Kc7 So Ba4 is better (according to this source) by about .6 

May1819   BxChess: On the question of whether chess is infinite, I think a subtle but valuable feature is the irreversibility of the game. Pawns can't move backwards, and captured pieces can't return to the game. (A promotion is an irreversible pawn move.) This irreversiblity, combined with the 50 move rule, means that all games must move to an inevitable conclusion after a finite number of moves. Since the numbe rof possible moves is finite for each position, the numbe rof possible games must also be finite. There is a second more subtle form of irreversibility in chess. If a piece moves from a square, then that square can be attacked by a more minor piece, preventing the major piece from moving back. This type of irreversibility punishes retreats, and favors attacking play that seizes territory. I think this feature of chess is one of the reasons it is such a popular game. 

May1819   1stboard: What is wrong with white playing 31 ... Qh1 instead of the text move ( Bd3 ) ? 

May1819   Patriot: <BxChess><If a piece moves from a square, then that square can be attacked by a more minor piece, preventing the major piece from moving back.> It may not always be favorable but it could be in the realm of possibilities  it's called a sacrifice, just as 29.Rh8+ is a temporary sacrifice to achieve a positive end. 

May1819
  OhioChessFan: <1st> After 31. Qh1, then31...Ne2+ and I don't think White can escape the checks. 31...Kg2 32. Nf4+ etc
31...Kf2 dxe3+ and the e file collapses
31...Kh2 dxe3 and again the e file is a disaster. 

May1819   Patriot: <1stboard> It ends in a draw. I didn't realize that Ne3 is en prise which is key to the draw starting with 31...Ne2+. For example, 32.Kf2 dxe3+ opening the QR battery down the dfile. 

May2319
  Richard Taylor: <Pedro Fernandez: My great friend <Richard Taylor>, I hope your concept of infinity (or infinite) don't be an inference of Neumann words about chess, neither your namesake mathematician (you know, Wiles' pupil) knows about this, lol! Greetings!> This was from Jacob Bronowski I think in his book 'The Ascent of Man' based on his TV series. But the point is that chess is de facto a game as of course no one could ever remember all the moves etc so, well it remains and will remain a game. But in theory if it could be solved I believe (it that was one of the rules of it being a game), then it wasn't a game. But as Wittgenstein thought we have to abandon logic and realise we are always looking at language. Ultimately everything has to be in a language, or translated into one, to be read etc The only name sake I know was the Philosopher Richard Taylor. His area was metaphysics and possibly logic and he wrote something "proving" that there is no free will. This got David Foster Wallace to study logic and do a PhD thesis which was an attempt to disprove it using logic etc. He also did a PhD in literature in the same year, and went for lit. rather than philosophy. But I actually quoted Taylor (!) in an essay when I was doing a University degree in the 90s which included philosophy. I forget whether it was showing that Descartes' demon or alternative universe etc couldn't exist or it was the one about Plato's "proof" that as a slave boy could solve a geometry problem this meant certain mathematical ideas were inborn. And this leads to the idea which I thought dubious that numbers were like his Ideal Forms, something already existing in the universe. In any case, according to a tutor I had I failed to prove anything in either case. But neither did Plato I feel. Descartes was using his evil demon as a kind of point of departure to get to the Cogito. But I don't know that much about maths. I know von Neumann proved that something such as DNA could work and did some very complex mathematics. 

May2319
  Richard Taylor: <znprdx: <Richard Taylor: This is why John von Neumann who studied game theory and other mathematical matters  did not consider chess a a game –>
By” this” are you implying the notion of “infinite” – because Chess “rules” lead to a clearly ‘zero sum’ outcome ( one win,one loser) but with the special possibility of equality due to unique drawing methods – in particular the unique concept of stalemate....> I'm really saying that science and mathematics cannot simply remain objective things. The human is there. That is, they pertain to a social thing. Hard to put this. We cant get to an actual infinity. In any case we operate within certain human limits. We forget things. We don't want to be computers...I believe that theoretical mathematicians hate computers. In other words, they want to play a game. Keep playing a game. As a chess player (obviously an amateur club level player) I haven't got time even to properly study the openings I do play. Even Carlsen cant know a fraction of the games a computer could store....Something like that. And he refuses to play computers as he hates being beaten by something that is stupid, as he said in an interview... 

May2319
  Richard Taylor: <Pedro Fernandez: My great friend <Richard Taylor>, I hope your concept of infinity (or infinite) don't be an inference of Neumann words about chess, neither your namesake mathematician (you know, Wiles' pupil) knows about this, lol! Greetings!> I see what you mean. Mathematics was never my forte but I am interested in the ideas of maths. I remembered that I had picked up a book called 'Fermat's Last Theorem' by Singh as I see it now (I had googled the name Wiles) and indeed I see I am on page 292 of my Fourth Estate paper back edition (1998). I appear to be younger than I am!! It says somewhere nearby: "In January, Wiles, with the help of Taylor, was once again tirelessly exploring the KolyvaginFlack method..."...Well, what can I say! Of course I was! Who wouldn't be exploring the KolyvaginFlach of an evening? Eh?! Wait a minute Pedro, me amigo, I forgot to google myself. The problem is that there is a near infinite number of Richard Taylors. There is also one who works designing models for movies (e.g Lord of the Rings) but there are many others of various ilks and kinds...as well as my metaphysician, the antiFree Will man who troubled poor FosterWallace (I have his huge book but haven't "gotten" round to reading it)... [By the way, note the difference, Americans say "math" and in NZ etc we say "maths" or "mathematics". But a "polymath" is not someone who does many math(s) but someone of wide erudition and so on.] Anycase, this old fellow is tickled pink by your interest in his comment! 

May2319
  Richard Taylor: I see that one of my Richard Taylors denounced organised religion. I believe myself that it is impossible to logically prove or disprove, e.g., the existence of God...so here I differ with the, sadly, now deceased, Richard Taylor. It is sad that one of me has died. (2003). Apparently the Philosopher had a dry wit and was a great bee keeper. But is it possible to compute how many Richard Taylors there are? I mean, how many I am? 

Jul2319
  Messiah: Very game
Much amazing
Wow 



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