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H. G. Muller wrote on Sat, Mar 3, 2012 07:57 PM UTC:

Rook vs Waffle also has a very unusual distribution of the DTC (distance to conversion):

Usually a won end-game has only a single pronounced peak close to maximum DTC.
E.g. for KBN.K (where DTC = DTM, as there is nothing to capture):

The maximin game is (W = WA):

[Event 'Computer Chess Game']
[Wite 'CHEWW_LAPTOP']
[Date '2012.03.03']
[Round '-']
[White 'EGTgen 1.2.4']
[Black 'hgm']
[Result '1-0']
[TimeControl '40/60']
[Variant 'fairy']
[FEN '3K4/1R6/2k2w2/8/8/8/8/8 w - a6 0 1']
[WetUp '1']

{--------------
. . . K . . . .
. R . . . . . .
. . k . . w . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
white to play
--------------}
1. Kc8 {M74/1} We6 2. Kb8 {M73/1} Wd6 3. Ka7 {M72/1} Wd5 4.
Rh7 {M71/1 0.1} Wc5 5. Ka6 {M70/1 0.1} Wc4 6. Ka5 {M69/1}
Kd5 7. Rc7 {M68/1 0.1} We6 8. Kb5 {M67/1 0.1} Wd6 9. Re7
{M66/1 0.1} Kd4 10. Re1 {M65/1 0.1} Wd5 11. Rd1+ {M64/1 0.1}
Ke5 12. Kc4 {M63/1 0.1} Wf7 13. Re1+ {M62/1 0.1} Kd6 14. Kd3
{M61/1 0.1} Kd5 15. Rf1 {M60/1 0.1} Wg7 16. Rg1 {M59/1 0.1}
We5 17. Rg5 {M58/1 0.1} Ke6 18. Kd4 {M57/1 0.1} Wf5 19. Rg8
{M56/1} Wd7 20. Rh8 {M55/1 0.1} We7 21. Ke4 {M54/1 0.1} Kd6
22. Rh6+ {M53/1 0.1} Kc5 23. Ke5 {M52/1 0.1} Wd7 24. Rh7
{M51/1 0.1} Kc6 25. Kd4 {M50/1} Wc7 26. Rg7 {M49/1 0.1} Wb7
27. Kc4 {M48/1 0.1} Wd5 28. Rg6+ {M47/1 0.1} Wd6 29. Kd4
{M46/1 0.1} Kd7 30. Ke5 {M45/1} Wf8 31. Ra6 {M44/1 0.1} We8
32. Ra7+ {M43/1 0.1} Kc6 33. Ke6 {M42/1 0.1} Wg6 34. Ra8
{M41/1 0.1} We4 35. Rc8+ {M40/1 0.1} Kb6 36. Rc4 {M39/1 0.1}
We3 37. Kd6 {M38/1 0.1} Kb5 38. Rc3 {M37/1 0.1} We2 39. Kd5
{M36/1 0.1} Kb4 40. Rc2 {M35/1 0.1} We1 41. Rc4+ {M34/1 0.1}
Kb3 42. Kd4 {M33/1 0.1} We2 43. Rc6 {M32/1 0.1} Wf2 44. Ke3
{M31/1 0.1} Wh4 45. Kd3 {M30/1 0.1} Wg4 46. Rg6 {M29/1 0.1}
Wf4 47. Rb6+ {M28/1 0.1} Ka4 48. Kd4 {M27/1 0.1} Wg4 49. Kc5
{M26/1 0.1} We2 50. Rb2 {M25/1} We1 51. Rb4+ {M24/1 0.1} Ka3
52. Re4 {M23/1 0.1} Wc3 53. Re3 {M22/1 0.1} Kb2 54. Kb4
{M21/1 0.1} Wc2 55. Re2 {M20/1 0.1} Kc1 56. Kc4 {M19/1 0.1}
Wd2 57. Rg2 {M18/1 0.1} Kd1 58. Kc3 {M17/1 0.1} Wf4 59. Rf2
{M16/1 0.1} Wg4 60. Kd3 {M15/1 0.1} Ke1 61. Rg2 {M14/1 0.1}
Wh4 62. Re2+ {M13/1 0.1} Kf1 63. Ke3 {M12/1 0.1} Wg4 64. Rf2+
{M11/1 0.1} Kg1 65. Rc2 {M10/1 0.1} Wg3 66. Rc5 {M09/1 0.1}
Wg4 67. Kf3 {M08/1 0.1} We6 68. Rc1+ {M07/1 0.1} Kh2 69. Rc2+
{M06/1 0.1} Kg1 70. Re2 {M05/1 0.1} Wc4 71. Rg2+ {M04/1 0.1}
Kh1 72. Rg4 {M03/1 0.1} We6 73. Re4 {M02/1 0.1} Wd6 74. Kf2
{M01/1 0.1} Wf4 75. Rxf4 1-0 {black resigns}

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