Author: Anthony Bailey
Date: 13:25:09 10/07/99
The "Kasparov vs World" game has taken another interesting turn that has relevance for the role of endgame tablebases. The World has sacrificed one of its pawns and we are now in a KQP vs KQP position. Here it is, in fact: +--------+ | . . . .| |. . . . | | . p K .| |. . . P | | Q . . .| |. . . . | | . . . .| |k .q. . | +--------+ Black to move 8/8/3p1K2/6P1/1Q6/8/8/k2q4+b (Also see http://www.zone.com/Kasparov/, and in particular the strategy BBS, for in depth discussion of the game.) The five piece KQPKQ tablebase has always formed a key part of the World Team's analysis effort in this ending. About a fortnight ago, the World Team came here hoping that we might persuade the tablebase experts amongst you to create a KQQKQQ tablebase for us. The challenge was taken up and conquered by two different individuals and the resulting kqqkqq has already proven very useful, and provided us with some interesting drawing variations. It would now be possible to generate specialised tablebases to completely solve the current position in this historic game. Would anyone like to try? I present this also as an opportunity to prototype a new way to tackle the next generation of tablebases. One way to tackle this next generation of tablebases is to wait for 64 bit addressing and huger machines, but I present what could be an interesting alternative approach; to break the problem of generating a six piece tablebase that includes pawns up into smaller less demanding subtasks/subtables that are generated one at a time. Pawns are considered to be problematic in egtb because they break position symmetries. But their restricted and sequential path up and down the board can work in the tablebase generator's favour. Note that we don't have to consider captures, since this reduces the position to known five piece positions; hence the pawns can only move straight forward. (Also we have no pesky en passant questions to consider since the pawns in this case are on the d- and g-files in this particular case.) I suggest that one should ignore underpromotion for this experiment. The result will thus not be authorative, but the differences will be irrelevant for the purposes of analysing "Kasparov vs World". It will also form a good "proof of concept" experiment, prototyping the approach that can be used once more six-piece tablebases without pawns start to appear. So, let us suppose that one has access to the following existing tablebases: kqqkqq, kqqkq, kqqkp, kqpkq, kqpqp. From these one can generate the following tablebase using entirely regular means, except for not generating underpromotions as possible moves. There is relatively little new coding required to do this. kqq vs kq + pawn on d2, either side to move I suggest naming this pair of tablebases as kqqkqd2.nbw and kqqkqd2.nbb; I'll use this naming convention in the remainder of the post. I would expect this pair of tablebases to have sizes similar to those of kqpkq.nbw and kqpkq.nbb. The encoding scheme could be e.g. exactly the same as that for kqqkq if using the older most straightforward encodings (i.e. without Nalimov's use of symmetries, which do not seem to offer any advantage here.) Having calculated this tablebase, one can go on/back to generate kqqkqd3.nbw kqqkqd3.nbb kqqkqd4.nbw kqqkqd4.nbb kqqkqd5.nbw kqqkqd5.nbb kqqkqd6.nbw kqqkqd6.nbb The Black pawn is currently on d6 in "Kasparov vs World", so this is sufficient. Similarly, in the other direction one can generate kqg7kqq.nbw kqg7kqq.nbb (i.e. kqkqq plus white pawn on g7) kqg6kqq.nbw kqg6kqq.nbb kqg5kqq.nbw kqg5kqq.nbb The White pawn is currently on g5 in "Kasparov vs World", so again I would suggest stopping here for now. Having generated these large (but definitely considerably smaller and surely much simpler to create than kqqkqq) tablebases, an array of smaller ones takes us to a solution for the kqpkqp cases required. These tablebases will be much smaller; the size of a four-piece kqkq tablebase without use of symmetries. They should thus be even easier to generate. kqg7kqd2.nbw kqg7kqd2.nbb (i.e. kqkq plus white pawn on g7, black pawn on d2) kqg7kqd3.nbw kqg7kqd3.nbb kqg7kqd4.nbw kqg7kqd4.nbb kqg7kqd5.nbw kqg7kqd5.nbb kqg7kqd6.nbw kqg7kqd6.nbb kqg6kqd2.nbw kqg6kqd2.nbb kqg6kqd3.nbw kqg6kqd3.nbb kqg6kqd4.nbw kqg6kqd4.nbb kqg6kqd5.nbw kqg6kqd5.nbb kqg6kqd6.nbw kqg6kqd6.nbb kqg5kqd2.nbw kqg5kqd2.nbb kqg5kqd3.nbw kqg5kqd3.nbb kqg5kqd4.nbw kqg5kqd4.nbb kqg5kqd5.nbw kqg5kqd5.nbb kqg5kqd6.nbw kqg5kqd6.nbb (The current game position is in the last tablebase generated.) Of course, the main reason I write is that I want to see the position solved (and I hope there is a draw here for Black!) Without this kind of help, it is probable that the World is likely to lose the game despite having done very well up until now because very precise play is now required. It is hard to get agreement on precise play from a crowd of patzers who don't read much analysis unless you can speak with certainty; and that's where most of the voting power is. I would like very much for us to prove the draw. But my own affiliations to the World Team aside, I think it might be one step in an interesting approach to generating six-piece tablebases without waiting for the next generation of hardware. Use symmetries to cope with the six-piece egtbs without pawns, and then use the limitations on pawn moves to counter the fact that pawns break symmetry in order to create the remaining positions with pawns more incrementally. What do people think about this general idea? And does anyone want to give this particular experiment a go? - Anthony.
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