Author: Uri Blass
Date: 02:51:41 01/11/03
Go up one level in this thread
On January 11, 2003 at 03:08:18, Dann Corbit wrote:
>{
>I just fiddled around to see what ought to be possible. Both without giving up
>any piece and with giving up only minor pieces, this is the best I can do. Is
>it possible to get more material than this?
>}
>[Event "Edited game"]
>[Site "DANNFAST"]
>[Date "2003.01.10"]
>[Round "-"]
>[White "-"]
>[Black "-"]
>[Result "*"]
>[ECO "A00e"]
>[Variation "Ware Opening"]
>
>1. a4 b5 2. a5 b4 3. a6 Bb7 4. axb7 b3 5. c4 Nc6 6. b8=Q a5 7. Nf3 a4 8.
>Nd4 a3 9. Nc2 bxc2 10. Nc3 a2 11. Rb1 a1=Q 12. b4 Ra6 13. Ba3 c1=Q 14.
>b5 Nd4 15. b6 h5 16. b7 Nf6 17. Qa7 g6 18. b8=Q Bh6 19. e3 Rb6 20. Bd3
>Nd5 21. Qa4 Ra6 22. c5 Nb6 23. cxb6 c5 24. b7 Qcb2 25. Ne2 c4 26. Qa7 c3
>27. b8=Q c2 28. Be4 c1=Q 29. h4 Bg5 30. hxg5 h4 31. Rf1 h3 32. Rg1 h2
>33. Rf1 h1=Q 34. Bf3 Rf8 35. Bh5 gxh5 36. g6 h4 37. g7 h3 38. g8=Q h2
>39. Qh8 Qg1 40. Qg8 h1=Q 41. g4 Qhh2 42. g5 Qhh1 43. g6 Qhh2 44. Qh7
>Qhh1 45. g7 Qh3 46. g8=Q Ne6 47. f4 Ng5 48. fxg5 Qhh2 49. Qgh8 Qhh1 50.
>g6 Qhh2 51. g7 Qhh1 52. g8=Q f6 53. Qah4 d6 54. Bc5 dxc5 55. d4 c4 56.
>d5 c3 57. d6 c2 58. Qad4 Qbb7 59. Qba7 Qaa5+ 60. Qd2 Qac7 61. Qad4 Qa3
>62. Qa1 Qac5 63. Qg2 Qgh2 64. Qg1 Qhe5 65. Qhd3 Qh3 66. Q8h7 Qhd7 67.
>Q7e4 Qd7c8 68. Qhh1 Kf7 69. d7 Qe8 70. d8=Q c1=Q 71. Q8d4 Q1a3 72. Q4b2
>Qc5d6 73. Qec4+ Qee6 74. e4 Qdd8 75. Nd4 Rh8 76. Nb5 Qg8 77. Nd6+ Kf8
>78. e5 exd6 79. Rf2 Qef7 80. e6 Rh5 81. Ke2 Qfg7 82. Qdf4 Qa4 83. Kd2
>Qad7 84. Qge1 Qg7f7 85. Qbd4 Ra8 86. Q3b3 Kg7 87. e7 Rg5 88. e8=Q Rg6
>89. Qdb2 Qh3 90. Kc2 d5 91. Q2c3 d4 92. Kb2 d3 93. Qa3 d2 94. Ka1 Qe5
>95. Qdc2 d1=Q 96. Qfe3 f5 97. Rg2 f4 98. Rg3 f3 99. Rg4 f2 100. Rg3 f1=Q
>*
>{
>[D]r1qqQ1q1/1q3qk1/6r1/4q3/2Q5/QQQ1Q1Rq/2Q5/KR1qQq1Q w - -
>}
>
>[Event "Edited game"]
>[Site "DANNFAST"]
>[Date "2003.01.10"]
>[Round "-"]
>[White "-"]
>[Black "-"]
>[Result "*"]
>[ECO "A00e"]
>[Variation "Ware Opening"]
>
>1. a4 a5 2. b4 b5 3. c4 c5 4. d4 d5 5. e4 e5 6. f4 f5 7. g4 g5 8. h4 h5
>9. axb5 axb4 10. cxd5 exd4 11. exf5 gxh4 12. Rh3 Nd7 13. Re3+ Ne7 14.
>Na3 Qa5 15. Qf3 Ne5 16. Kf2 h3 17. b6 h2 18. b7 h1=Q 19. b8=Q b3 20. d6
>b2 21. d7+ Kf7 22. d8=Q b1=Q 23. f6 Ke6 24. f7 Bg7 25. f8=Q d3 26. Re4
>d2 27. g5 d1=Q 28. Be3 c4 29. Qd2 c3 30. Qe8 c2 31. g6 Bf6 32. g7 Qd5
>33. Qb2 c1=Q 34. g8=Q+ Kd6 35. f5 Bh4+ 36. Qfg3 Bg5 37. f6 Qh4 38. f7
>Qhg4 39. f8=Q h4 40. Qgg7 h3 41. Qgg8 h2 42. Qgg7 h1=Q *
>{
>[D]r1b1QQ1r/4n1Q1/3k4/3qn1b1/4R1q1/N3B1Q1/1Q1Q1K2/Rqqq1BNq w - -
>}
1)It is impossible to improve the first game if you want more material.
Claim:if no pawn is captured then we need at least x captures to promote 2x
pawns and a private case say that we need at least 8 captures to promote 16
pawns.
proof:Denote number of white pawns in file i by wp(i) when white pawns include
promoted pawns from file i.
Define open pawn as a pawn that has no enemy pawn to block it from
promoting(open pawns also include promoted pawns).
Denote number of white open pawns in file i by wpo(i)
define for every file i sw(i)=max(wp(i)-1,wpo(i))
Do the same for black sb(i)=max(bp(i)-1,bpo(i))
my claim is that sw(a)+sw(b)+sw(c)+sw(d)+sw(e)+sw(f)+sw(g)+sw(h)
+sb(a)+sb(b)+sb(c)+b(d)+sb(e)+sb(f)+sb(g)+sb(h)
can be increased only by 2 by every capture that is not a pawn capture and
cannot be changed with no captures.
The value of this number is 0 in the beginning of the game so you need at least
x captures to get 2x promotions.
proof:
It is clear that every capture ixj from file i to file j and can influence the
number of opened
pawns and pawns only in file i,j
suppose without loss of generality white capture and the capture is cxd capture.
sw(c) is not increased by definition and the same for sb(d)
only sw(d) and sb(c) can increase the sum.
We always have
bp(c) -1<=sb(c)<=bp(c)
so by definition sb(c) can be increased only by 1 because bp(c) is not changed.
The only case when sw(d) can be increased by 2 is the case when
sw(d)=wp(d)-1 before the capture but in that case white has a pawn that is not
an open pawn in file d and this pawn cannot become an open pawn when the pawn
that blocked it to be an open pawn was not captured
so sw(d) continue to be wp(d)-1 after the capture and wp(d) is increased only by
one.
2)For the second case I can do better
[Event "Edited game"]
[Site "F3K9V7"]
[Date "2003.01.11"]
[Round "-"]
[White "-"]
[Black "-"]
[Result "*"]
1. a4 b5 2. axb5 d5 3. c4 e5 4. f4 exf4 5. cxd5 g5 6. h4 gxh4 7. g4 h3 8.
g5 h2 9. g6 a5 10. g7 a4 11. Nc3 a3 12. Rb1 a2 13. Nf3 a1=Q 14. Rg1 Nh6 15.
g8=Q h1=Q 16. e4 c5 17. Nd4 c4 18. d3 f3 19. b6 f2+ 20. Kd2 f5 21. Be2 f1=Q
22. b4 f4 23. b7 f3 24. b5 f2 25. b6 Qfh3 26. d6 f1=Q 27. e5 Qfg2 28. Ke1
Nf7 29. Na2 c3 30. Nc2 Nc6 31. b8=Q h5 32. b7 h4 33. Qa7 Qhg4 34. b8=Q h3
35. d4 h2 36. Rf1 Qhg1 37. d7+ Ke7 38. d5 Qc7 39. d6+ Ke6 40. d8=Q h1=Q 41.
d7 Ne7 42. Ne3 c2 43. Bb2 c1=Q 44. Qe8 Qf4 45. Nc2 Kf5 46. d8=Q Ng6 47. e6
Ng5 48. e7 Nf7 49. Qea4 Ng5 50. e8=Q
*
Uri
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Last modified: Thu, 15 Apr 21 08:11:13 -0700
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