Author: Eugene Nalimov
Date: 13:56:55 09/01/98
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On September 01, 1998 at 14:43:03, Rémi Coulom wrote: > >On September 01, 1998 at 05:38:08, Ernst A. Heinz wrote: > >>You should probably be more careful with your public statements and re-read >>my article because these ideas are already mentioned. >> >> >>Sorry, but your math is wrong: 33 + 3*30 + 3*55 + 3*58 = 462. >> >I am sorry, I can not make additions correctly when it is early in the morning >:) > >> >>See Section 4.1 "The Two Kings" of my article. Because I confine the first >>Pawn to one half of the board, I get 3612 = 2*1806 legal placements of two >>Kings on an otherwise empty chess board. >> >>For KPK you get 1806 * 48 = 86688 and I get 3612 * 24 = 86688 which is >>exactly the same. >I apologize again. I compared my figures to your table without reading the text >carefuly and I noticed that for other endings I add a small improvement. This >was only because of the 48*47... and 62*61*60... tricks of course. I will post >more carefuly next time. > >> >>=Ernst= Ok, here are possible improvements: For KPK (and other tablebases that involve pawns), we can often restrict pawn not to 48 squares, but less. You can do that either by using large array (32x64x48), where all possible positions enumerated (unsatisfactory solution), or by using one array that is 1806 entries long and some comparison and arithmetic operations to enumerate all possible KPK positions. Doing so you can encode KPK not in 86688, but in 84012 different values - a 3.1% improvement. Also, for some tables you can exploit the fact that both kings cannot be simultaneously checked. If side on move has, for example, queens or kings, you can use two arrays - one is 1806 entries, and the second is 64*32 or 64*64 entries - to encode all legal poitions for both kings and one extra piece. For KQK, WTM, that gives us not 462*62=28644, but 26097 different values - almost 8% saving. Eugene
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