Author: Marc Bourzutschky
Date: 20:24:30 01/19/04
Go up one level in this thread
On January 19, 2004 at 20:53:03, Ed Trice wrote: >Hi Guy, > >> >>The 4-fold symmetry of (Gothic) Chess is factored out before Eugene starts >>counting. >> >>In fact, the positions usually go around in 8s, but not always. >> > >Yes, with the 80 square board, I cannot reduce the symmetry any further. I >contrain the white king to 20 squares, and the (usually) mated king, black, has >free roaming over all 80. > >>There's also usually a 'spike' of 'wins in 1' in EGTs, as the loser's men can be >>placed in many ways so that they are irrelevant to the next move. >> > >I had not thought of that, and it makes perfect sense. Cheron's triangle method implies that on an NxN board the longest mate should take about N^2/2 moves. Perhaps this generalizes to NxM/2 for a rectangular board. Cheron's method involves restricting the lone king to smaller and smaller right-angled triangles, where the right angle is one of the corners of the board, with the same color as the bishop. I modified Nalimov's code to work on a 10x8 board, which turned out to be a little more work than I had anticipated. For kbnk I obtain a maximum mate of 39 moves as shown below. Below also the .tbs file, where the symmetry factor of 4 has already been taken into account. This looks a little different from what Ed showed before, but there may well be bugs... KBNK on 10x8 board, maximal mate in 39 1N8/2k7/10/10/1B8/10/10/K9 w - - . N . . . . . . . . Won in 39 . . k . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . . . . . . . . . . . . . . . . . . . . . . . . . . . . K . . . . . . . . . w... 1. Na6+ Kb6 2. Nc5 Kb5 3. Ba3 Kc4 4. Kb2 Kd4 5. Kb3 Kd5 6. Kc3 Ke5 7. Kd3 Kf4 8. Nd7 Kf5 9. Bb2 Kf4 10. Nf6 Kf5 11. Ke3 Kg5 12. Ke4 Kh4 13. Kf4 Kh3 14. Ng4 14... Kh4 15. Bf6+ Kh3 16. Kf3 Ki2 17. Kg2 Ki1 18. Kh3 Kh1 19. Bd4 Ki1 20. Ni3 20... Kj2 21. Be5 Kj3 22. Bi1 Kj4 23. Ng4 Kj5 24. Kh4 Ki6 25. Ni5 Ki7 26. Be5 26... Kh6 27. Bf6 Ki6 28. Bg7 Kj5 29. Ng6 Ki6 30. Nf8 Kj5 31. Kh5 Kj6 32. Ng6 32... Kj5 33. Ni7+ Kj6 34. Kh6 Kj7 35. Nh5 Ki8 36. Ki6 Kj8 37. Bf6 Ki8 38. Nj6+ Kj8 39. Bg5# kbnk.tbs wtm: Draws: 22773 wtm: Mate in 39: 1 wtm: Mate in 38: 47 wtm: Mate in 37: 4708 wtm: Mate in 36: 71044 wtm: Mate in 35: 342449 wtm: Mate in 34: 717390 wtm: Mate in 33: 954448 wtm: Mate in 32: 944834 wtm: Mate in 31: 776582 wtm: Mate in 30: 602794 wtm: Mate in 29: 454627 wtm: Mate in 28: 345220 wtm: Mate in 27: 238410 wtm: Mate in 26: 200281 wtm: Mate in 25: 171199 wtm: Mate in 24: 177057 wtm: Mate in 23: 187337 wtm: Mate in 22: 166094 wtm: Mate in 21: 118827 wtm: Mate in 20: 71301 wtm: Mate in 19: 43839 wtm: Mate in 18: 46592 wtm: Mate in 17: 44036 wtm: Mate in 16: 46391 wtm: Mate in 15: 59358 wtm: Mate in 14: 74591 wtm: Mate in 13: 64586 wtm: Mate in 12: 45493 wtm: Mate in 11: 29032 wtm: Mate in 10: 17016 wtm: Mate in 9: 14259 wtm: Mate in 8: 15360 wtm: Mate in 7: 19263 wtm: Mate in 6: 15956 wtm: Mate in 5: 12777 wtm: Mate in 4: 4687 wtm: Mate in 3: 896 wtm: Mate in 2: 368 wtm: Mate in 1: 600 wtm: Broken positions: 741822 btm: Lost in 0: 133 btm: Lost in 1: 92 btm: Lost in 2: 77 btm: Lost in 3: 492 btm: Lost in 4: 2398 btm: Lost in 5: 3566 btm: Lost in 6: 5439 btm: Lost in 7: 4397 btm: Lost in 8: 4880 btm: Lost in 9: 4138 btm: Lost in 10: 7103 btm: Lost in 11: 14523 btm: Lost in 12: 21171 btm: Lost in 13: 29452 btm: Lost in 14: 24499 btm: Lost in 15: 18644 btm: Lost in 16: 20416 btm: Lost in 17: 19335 btm: Lost in 18: 18306 btm: Lost in 19: 24249 btm: Lost in 20: 43480 btm: Lost in 21: 72805 btm: Lost in 22: 100660 btm: Lost in 23: 97856 btm: Lost in 24: 95137 btm: Lost in 25: 105797 btm: Lost in 26: 133862 btm: Lost in 27: 200761 btm: Lost in 28: 289440 btm: Lost in 29: 417833 btm: Lost in 30: 591325 btm: Lost in 31: 835716 btm: Lost in 32: 1096698 btm: Lost in 33: 1221554 btm: Lost in 34: 1058394 btm: Lost in 35: 616039 btm: Lost in 36: 161943 btm: Lost in 37: 12785 btm: Lost in 38: 120 btm: Lost in 39: 5 btm: Draws: 1309156
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