Ordered By Move, from Move 11 on: KRAMNIK 1111 MATCH, delta = 0.39 KRAMNIK 0001 MATCH, delta = 0.02 KRAMNIK 1111 MATCH, delta = 0.11 KRAMNIK 1111 MATCH, delta = 1.96, FORCED MOVE KRAMNIK 1111 MATCH, delta = 0.19, only 2 real choices. KRAMNIK 0000 NON-MATCH, delta2 = -0.04 KRAMNIK 0000 NON-MATCH, delta2 = -0.52 17. Ne4! KRAMNIK 0000 NON-MATCH, delta2 = -0.10 KRAMNIK 1111 MATCH, delta = 0.18 KRAMNIK 1111 FULL MATCH, delta = 0.02 KRAMNIK 1111 FULL MATCH, delta = 0.08 KRAMNIK 1010 PART MATCH, delta2 = -0.02 KRAMNIK 1111 FULL MATCH (forced move), delta = 3.95 KRAMNIK 0000 NON-MATCH, delta2 = -0.15 KRAMNIK 0000 NON-MATCH, delta2 = -0.04 KRAMNIK 0001 PART MATCH, delta = 0.01 KRAMNIK 0000 NON-MATCH, delta2 = -0.13 KRAMNIK 1000 PART MATCH, delta2 = -0.12 KRAMNIK 1111 FULL MATCH (forced move), delta = 0.91 KRAMNIK 1111 FULL MATCH (moderately forced move), delta = 0.67. KRAMNIK 1110 PART MATCH, delta2 = -0.09 KRAMNIK 0000 NON-MATCH, delta2 = -0.59 (at the winning moment!) KRAMNIK 0000 NON-MATCH, delta2 = -0.15 KRAMNIK 0000 NON-MATCH, delta2 = -0.15 KRAMNIK 0000 NON-MATCH, delta = -0.34 KRAMNIK TTTT FULL TIE MATCH, delta = 0.00 KRAMNIK 1111 FULL MATCH, delta = Big KRAMNIK TTTT FULL TIE MATCH, delta = 0.00 28 moves. "Hamming Metric" (which means, only care if match or not): -------------- 10/28 0000 total non-matches, 35.7% 13/28 1111 Full or Full Tie Match 5/28 ambiguous matches ----- 18/28 with any match at all, 64.3%, a far cry from Danailov's stated "86%" 15/28 matches at 12 ply (splitting ties) 13/28 matches at 13 ply 14/28 matches at 14 ply (== the method in my Game 6 & Sukhovsky files), 50% 14/28 matches at 15 ply Fair-weighted match rate: 1 for 12 ply, 2 for 13, 4 for 14, 8 for 15 ply: 11x15 + 2x7.5 (ties) + 8 + 5 + 8 + 1 + 7 = 209 / 420 = just under 50%! Danailov's letter, as noted at http://www.chessbase.com/eventarticle.asp?newsid=3401, has the typo(?) "46" for the number of remaining moves, making 56 in all. Even if the phantom 18 moves were all matches, that would be 36/46, = 78.3%. Now Danailov's "40/46" is 86.956%, which clearly rounds to 87% But 24/28 rounds to 86%. Let's order the 0000 non-matches by delta2: KRAMNIK 0000 NON-MATCH, delta2 = -0.04 KRAMNIK 0000 NON-MATCH, delta2 = -0.04 KRAMNIK 0000 NON-MATCH, delta2 = -0.10 KRAMNIK 0000 NON-MATCH, delta2 = -0.13 KRAMNIK 0000 NON-MATCH, delta2 = -0.15 KRAMNIK 0000 NON-MATCH, delta2 = -0.15 KRAMNIK 0000 NON-MATCH, delta2 = -0.15 KRAMNIK 0000 NON-MATCH, delta2 = -0.34 KRAMNIK 0000 NON-MATCH, delta2 = -0.52 17. Ne4! KRAMNIK 0000 NON-MATCH, delta2 = -0.59 (at the winning moment!) To claim 6 more moves as matches, Fritz would have to differ by 0.15, which is rather large. Now a summary of Topalov's moves: TOPALOV 0001 MATCH, delta = 0.03 TOPALOV 0000 NON-MATCH delta2 = -0.13 TOPALOV 1111 MATCH, delta = 2.12, FORCED MOVE TOPALOV 1111 MATCH, delta = 0.43 TOPALOV 0111 MATCH, delta = 0.04 ---among many near-equal choices! TOPALOV 1100 PART MATCH, delta = 0.24, delta2 = -0.02 TOPALOV 1111 MATCH (forced move), delta = 2.07 TOPALOV 1110 PART MATCH, delta2 = -0.02 TOPALOV 1011 PART MATCH, delta = 0.04 TOPALOV 0000 NON-MATCH , delta2 = -0.09 TOPALOV 1111 FULL MATCH (forced move), delta = 1.25 TOPALOV 0111 MATCH (but could be FULL MATCH since 12/12 was not caught exactly), TOPALOV 1111 FULL MATCH, delta = 0.06 TOPALOV 0000 NON-MATCH, delta2 = -0.15 TOPALOV 0000 NON-MATCH, delta2 = -0.23. TOPALOV 011T PART MATCH, delta = 0.00 TOPALOV 0001 PART MATCH, delta = 0.02. TOPALOV 0000 NON-MATCH, delta2 = -0.30 TOPALOV 0000 NON-MATCH, delta2 = -0.23 TOPALOV 0000 NON-MATCH, delta2 = -0.18 TOPALOV 1111 FULL MATCH (moderately forced move), delta = 0.45 TOPALOV 1111 FULL MATCH (delta = 0.72 TOPALOV 1111 FULL MATCH, delta = 8.45 TOPALOV 0111 MATCH, delta = 0.12 TOPALOV 1111 FULL MATCH (essentially forced move), delta = 1.16 TOPALOV 1111 FULL MATCH, delta = Big. TOPALOV 1111 FULL MATCH (only legal move!), delta = \infinity TOPALOV 1111 FULL MATCH (only legal move!), delta = \infinity 7/28 clear non-matches (25%) 12/28 full matches 9/28 partial matches ----- 21/28 with some matching---75%! Fair-weighted match scoring: 7x15 + 8 + 14 + 3 + 7 + 13 + 14 + 10 + 8 + 14 = 196 / 420 = 46.7% Not much different (lower, even) from Kramnik by "fair" weights, though with a "match at any ply" approach, that 75% would look damning!---? 15 matches at 12 ply 18 matches at 13 ply 18 matches at 14 ply (my method for Game 6 and Sukhovsky's win), 64.3% 18.5 matches at 15 ply, for 66.1% On my 14-ply method, Topalov matches significantly more than Kramnik. On "any match", ditto! Indeed, if you take up to a 0.15 difference on the non-matches as above, TOPALOV 0000 NON-MATCH, delta2 = -0.09 TOPALOV 0000 NON-MATCH, delta2 = -0.13 TOPALOV 0000 NON-MATCH, delta2 = -0.15 TOPALOV 0000 NON-MATCH, delta2 = -0.18 TOPALOV 0000 NON-MATCH, delta2 = -0.23 TOPALOV 0000 NON-MATCH, delta2 = -0.23 TOPALOV 0000 NON-MATCH, delta2 = -0.30 you get 24/28 = the cited "86%" figure applying also to Topalov! But on a fair-weighted scheme, both players are between 45% and 50% in "Hamming fidelity". An even better measure will come from "Shannon fidelity", i.e. taking the number and degree of nearly-equal choices the players had into account. Based on comparisons, the data do not support cheating at all. My chess-specific comments on some moves in the large file make this even more clear... But the data DO indicate that Danailov's letter is lacking not merely in scientific control, it shows a positive (documentable and likely reproducible) match for mendacity! Dr. Kenneth W. Regan, 10/10/06.