Hi, > ... I have just been told by a colleague that Edouard Rodrigues > solved hex mathematically. I was very surprised because I had > never heard about it. > > The web site with the proof and optimal strategy is there: > http://jeudhex.com/?page_id=17
as I wrote before the claim by Edouard Rodrigues is poorly substatianted. However when I read his site, I stumnled about the second last paragraph, which reads: > Finally it will be noticed that the great number of analyses, carried out > without the help of a computer, of chess game positions, opposing a bishop > and a knight to a knight, has enabled us to finalize the method of analyse > used in this study. If he really has found something, Rodrigues should be able to give maximum number of moves until check mate for KBN-KN on boards of size m x n (the traditional size is 8x8). Such data would be interesting for Eiko Bleicher and me, because we had done brute-force backward analysis for the endgame KQ-KR on boards of size m x n. One of our findings are the maximum numbers of moves for n x n -boards: 17 on 5x5 23 on 6x6 29 on 7x7 35 on 8x8 44 on 9x9 54 on 10x10 69 on 11x11 85 on 12x12 108 on 13x13 132 on 14x14 205 on 15x15; Some more explanation can be found in our preliminary report (back from 2012) at www.althofer.de/chess-kq-kr.pdf Title: Maximum Lengths to Mate in the Chess Endgame King+Queen vs King+Rook on Boards of Size m x n Our main open question: are these max numbers for n x n boards growing about quadratically in n? Or even faster? For the simpler endgames KQ-K and KR-K it is easy to see that the max-to-mate numbers grow linearly in n. (cage technique) How are the numbers growing for KBN-KN on n x n boards? Perhaps even much faster than n^2? *************************************************** It would be nice when the findings by Rodrigues would give a clue (or a complete answer) here. However, I have severe doubts. Cheers, Ingo. _______________________________________________ Computer-go mailing list Computer-go@computer-go.org http://computer-go.org/mailman/listinfo/computer-go
