Author: Ed Trice
Date: 05:42:58 01/20/04
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Hi Marc, > >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. > It looks like NxM/2 is a good approximation then, since 10x8/2 = 40 and you have a longest win of mate in 39. >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... Actually I hacked together a primitive db generator to just get some quick and dirty results, I am not sure if my results are correct either. What I will do it set up Gothic Vortex to run with a 1 GB hash table and have it verify some of your positions if you like. So far it has a nominal search depth of 23 plies in 8:57 for your mate in 39. With check extensions, usually Vortex can find a forced mate in N at about nominal depth 2N/3 or sometimes even N/2. So, I expect soon to have an answer for you (I can also play into the line to reduce the time to find the mate, but it is more fun this way.) I will let you know how it turns out. Thanks for your post! --Ed
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