Note on the KPK-table Size H.J. Messerschmidt Department of Applied Mathematics University of Witwatersrand Johannesburg, South Africa Ever since Clarke's memorable work on perfect chess endgames, (clarke, 1977) considerable attention has been given to constructing tables to play various basic endgames perfectly. Since these tables are quite large, it is obviously important to keep the size to the absolute practical minimum without complicating the construction or usage. As far as the KPK-endgame (white king and pawn against lone bTack king) is concerned, it seems that a significant reduction is indeed possible. By using sy~netry around the central vertical midline, Clarke uses a table of 7x4x4096 = 114688 entries. This can in effect be broken down into four different tables each of 7x4096 positions with the pawn on the a,b,c or d file. (The pawn can never change files.) If we now take cognizance of the fact that the king and the pawn are both two particularly short sighted pieces in chess (both can only influence squares in their immediate vicinity), it turns out that while the a and b files are different from each other and from the c and d files, owing to board geometry, (the disturbing influence of the edge of the board) the c and d file tables are very similar. In fact the only difference between them is the maximum distance between the pawn and the respective kings. With a little subtleness this problem can be overcome. Let us use an 8x9 chess board with the pawn in the middle file. Both c and d file positions from the normal board can be mapped onto this board with no difficulty. This method represents a saving of 2x7x4096 - 7x72x72, or 57344 - 36288, or 21056positions. Taken over the whole table 18.4% saving. this represents an board table is identical to that for the 8x8 board table, except for the factor 72 instead of 64. Clarke, M.R.B., "A Quantitative Study of King and Pawn Against King," in M.R.B. Clarke, ed., Advances in Computer Chess I, Edinburgh: Edinburgh University Press, 1977. JCIT Hosts Israel's First Major Computer Chess Tournament Monroe M. Newborn School of Computer Science McGill University, Montreal At the invitation of the organizers of the Jerusalem Conference on Information Technology and the Israel Chess Association, six chess programs and their progranmlers gathered in Jerusalem on August 6-8 for a special three round computer chess tournament. The event was won by Tom Truscott's DUCHESS who upset David Slate and Larry Atkin's World Champion program, CHESS 4.6. CHESS 4.6 tied for second place with CHAOS. Also participating were OSTRICH (Canada) TELL (Switzerland) and BS '66 '76 (Netherlands). The tournament was held at the Jerusalem Convention Center adjacent to the new Jerusalem Hilton Hotel. Computers located at Hebrew University, the Bank of Israel, and the Israel Office Mechanization Center were connected to the tournament site by telephone. A Data General Nova 3 and a Hewlett-Packard HP 2100 were live at the site. Tne event attracted large audiences including a number of Israel's top human chess players. International Master Shimon Kagan served as Tournament Director and his c(mmlentaries were in both Hebrew and English. Speed chess games after the regular sessions were very exciting with C ~ S S 4.6 and DUCHESS playing on an even footing with strong Israeli players. Kagan and CHESS 4.6 played a game of speed chess on Israel national television one evening around Ii p.m. The game was adjudicated a draw when the T V s h o w ran out of time. The event was organized by Yoram Alster (Israel) and Ben Mittman (USA). It was supported by the JCIT, the Israel Chess Association, IBM and CDC. [Ed. Note: The original information contained results, but the file we received contained only partial information for one program.] Even this can be improved upon. The 8x9 board is synanetrical around the middle column. We can therefore always rotate say the white king to the first 5 files, this gives: 57344 - 7x5x8x72, or 57344 - 20160, or 37184 positions. Taken over the whole 32.4% saving. table this represents a Since less positions are stored in the table, this not only represents a saving in storage space, but also in machine time for the construction of the table. Indexing the 8x9 i0

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