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May0408
  al wazir: LoveThatJoker: you missed the critical tactical shot 35. Qxg6 which gives White a won game.> Right. Thanks. <Richard Taylor: 33...Qb5+> I missed that too, which is especially embarrassing since I had just confessed to having overlooked black's threats. 

May0408   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: 31. Ba4 Qe7 32. Qh1 Ng6 33. Qh6 Qf8 34. cxd4 Qxh6 35. Rxh6 Kg7 36. Rah1 Rh8 37. Nf5+ Kg8 38. Rxh8+ Nxh8 39. Ne7+ Kg7 A 22ply analysis of the resulting position evaluates the position at (+1.98). I run out the rest on autoplay at 20 plies per move. Some intermediate valuations are included (2122 plies deep, to confirm the correctness of the move chosen at 20 plies). 40. Rh5 Bxa2 41. Nf5+ Kg8 42. Rxg5+ Ng6 43. Rh5 a5 44. Bc2 c5 45. dxc5 Rd2 46.
Rh2 Rxh2 47. Kxh2 Nxe5 48. Kg3 Kf8 49. Nd6 Bd5 <+1.91> 50. Kf4 Nd7 51. Be4 Bxe4 52.
Nxe4 Ke7 53. Ke3 b6 54. Kd4 bxc5+ 55. Nxc5 Nb6 56. g5 Nc8 57. f4 Nd6 58. Kd5
Nc8 59. b3 Nd6 <+2.87> 60. Ke5 Ne8 61. Ne4 Nc7 62. Nd6 Na6 63. Nb7 Nb4 64. Nxa5 Nd3+
65. Ke4 Nb4 66. f5 Ke8 67. Nc4 Kf8 68. Nb6 Nc6 69. Nd5 Kg7 <+6.09  time to resign> 70. b4 Kf8 71. b5
Na5 72. Nb6 Ke8 73. Kd5 Nb7 74. Nc4 Nd8 75. Kd6 Nb7+ 76. Kc6 f6 77. g6 Nd8+ 78.
Kc7 Nf7 79. gxf7+ Kxf7 80. Ne3 Kg7 81. Ng4 Kh7 82. b6 Kg8 83. b7 Kf8 84. b8=Q+
Kg7 85. Qe8 Kh7 86. Qf7+ Kh8 87. Qf8+ Kh7 88. Nxf6# 10 A similar procedure for Bd3 produced:
31. Bd3 Nh5+ 32. Rxh5 dxe3 33. Qh1 Kf8 34. Rd1 e2 35. Bxe2 Qa4 36. Rxg5 Rxd1 37. Qxd1 Qxd1 38. Bxd1 Rd8 39. Bb3 Bxb3 40.
axb3 Rd2
A 22ply analysis of the resulting position evaluates the position at (+1.62). The 0.36 improvement for Ba4 is not a huge advantage. Here's the rest of the game: 41. Rf5 Ke7 42. b4 Rxb2 43. Rf4 b5 44. Rf6 Ra2 45. Kf4 a5 46. bxa5
Rxa5 47. Ke4 Ra4+ 48. Kd3 c5 49. g5 Rh4 <+1.68> 50. Rb6 Rf4 51. Ke3 Rc4 52. Rxb5 Ke6
53. Kd3 Rf4 54. Ke2 Kd5 55. Rb7 Ke6 56. Rc7 Rf5 57. Rxc5 Rxg5 58. f4 Rg2+ 59.
Ke3 Rc2 <+3.18>
60. Rc6+ Kd7 61. Kd3 Rc1 62. Rf6 Ke7 63. c4 Ke8 64. Kd4 Rd1+ 65. Ke4
Rc1 66. Kd5 Ke7 67. c5 Rc2 68. f5 Rd2+ 69. Kc6 Rf2 <+9.53, resignation overdue> 70. Kb7 Kf8 71. e6 Rb2+ 72.
Kc7 Ke8 73. Rxf7 Rc2 74. c6 Rxc6+ 75. Kxc6 Kd8 76. Rd7+ Kc8 77. Kb6 Kb8 78.
Rd8# 10
BOTTOM LINE: surprisingly, Bd3 appears to win a bit faster. Perhaps using other engines might reverse that result. Feel free to produce an argument to the contrary. 

May0408   znprdx: Plain and simple  Ba4 is incongruous...almost lame. Bd3 is pragmatic...almost too simple. However I remain confident that the immediate Nf5 is the best first move...the immediate Rh8+ (which I tried first before timing out)seems fine but I think less accurate...the key is the e7 square.... 

May0408   Terry McCracken: <znprdx: Plain and simple  Ba4 is incongruous...almost lame. Bd3 is pragmatic...almost too simple. However I remain confident that the immediate Nf5 is the best first move...the immediate Rh8+ (which I tried first before timing out)seems fine but I think less accurate...the key is the e7 square....> Lame? What is your rating? 

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
  chrisowen: Dufflogs fakeinho dikethou rh8soust harangues kg7soust gunghost rh7soust houndlob kg8soust gunghosts bd3soust dunkcost ng6soust guffloud keyinhod lucks its a 31Nh5+ rekeysoh kestrels aintuslo duckdown dufflegs hufflubs 0 1 oustlobs bg6soust guffloud qb5soust bondhuts lucks its div 33.cxd4 kestrels remikeoh remobile keyinhod dontbunt keyinhod 7 it ok oinkumus hikehour relovely it's vastlump jellobod hipmount wantlust barntask keyinhod bracey it's vastlump helmjilt whippets reletkey barnyins hilejump racybins ctrlhobs jimpwyns rh8soust harangues keyinhod pucklobs rh8soust houndhobs hutchlob huhslobs hunchhob glocklob gulchlob dunkslob dubslobs cluckfor punkshoh keyinhod umsumums it edictump idlekeys bandlump jocklust it mettleup fakeinho dufflogs rh8uphoh; 

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. 



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