Author: José de Jesús García Ruvalcaba
Date: 12:07:43 09/16/00
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On September 16, 2000 at 14:33:51, guy haworth wrote: >Consider the following position from Ken Thompson's 6-man EGT site: > >8/8/7B/5B2/3K4/8/2k5/n6n b - - 0 1 > >It is a 'win' for White and also a maxDTC and maxDTM position. >DTC = 76 plies (38 moves) and DTM = 212 plies (106 moves). > >Black cannot protract the first phase beyond 50 moves and therefore might be >best advised to maximise DTM and (within that, should a choice occur) minimise >DTC. > >Similarly, White might be best advised to do the following in order: > keep the first phase down to 50 moves or less, > minimise DTM (Depth to Mate), and > maximise DTC (Depth to Conversion). > >These White/Black strategies leadd to what I call an SGM-C-_SM+C+ line. >However, White's (few) options and a Black defence along these lines can lead to > >[D] 6B1/1K6/1B6/8/8/8/3nk3/8 b - - 0 40 > >and a KBBKN 2nd-phase allowing a 50-move draw claim. > >So, the question is "Can this position be won under a 50-move rule, and if so, >how, given 'best play' by Black?". > >G The way to answer this question (and several others) is to produce a new set of tablebases, which are neither DTM nor DTC. For positions which are won but might (or might not) infringe the 50-move rule, two numbers are stored: the number of conversions needed to deliver mate and a new number, let's call it Marimar number. Now the way to compute the Marimar number for a given won (except posible for the 50-move rule) position X. If it is a mate, then the Marimar number is zero and the number of conversions is also zero. Otherwise, since the tablebases are computed by backwards analysis, this means that we have a position Y which can be reached by X and that is won (again, save the 50-move rule). If the move which leads to Y from X is not a conversion, then the number of conversions for X is the same as Y, and Marimar number for X is the Marimar number for Y plus one. If the move from X to Y is a conversion, then we have two cases: a) If Marimar number for Y is less than 100, then for X it is 1. b) If it is no less than 100, then for X it is 101. In either case increase the number of conversions by one. (It is needed a decision procedure when X leads to more than one winning position, and it is to follow the win with LOWER Marimar number). In these tablebases, won positions have a Marimar number lower than 100; while position which would be won without the 50-move rule but are a draw with it have a Marimar number no less than 100. Of course a special value for draws and a similiar reasoning for lost positions is also required. I am surprised nobody has tried this simple solution before. José.
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