Author: Eelco de Groot
Date: 19:24:12 08/03/05
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On August 03, 2005 at 19:16:13, Dieter Buerssner wrote: >I looked at this a while ago. I came to the conclusion, that "practical" (?) >positions of 2 minor pieces vs. queen are won in general for the queen (when >using TBs - some wins are very long, and might be impossible for an engine >without TB support). > >I might remember wrong, I might have interpreted wrong, ... > >Regards, >Dieter I just googled up queen vs two minor pieces and luckily there is a lot of material on the subject, 194000 hits. I found it surprising that two Knights can hold out against the Queen, from the position Gian-Carlo gave the majority of moves is good enough for a draw 14 moves hold a draw, 5 moves lose (I looked it up at Lokasofts tablebase server) I think there should be a bonus for the Knight-pair in these cases! Jan Timman wrote a book about it I believe.. What you two found seems to be correct, going by what Wikipedia has to say about it, http://en.wikipedia.org/wiki/Endgame The relevant paragraph reads: Endings with no pawns Besides the basic checkmates, there are other endings with no pawns. Some of these are: A queen wins against a rook, but the third rank defense by the rook is difficult for a person to crack, unless he knows how. A queen normally wins against a bishop and knight, but there is one drawing fortress position. A queen generally has a theoretical win against two bishops, but many ordinary positions require up to 71 moves (which is a draw under the rules of competition, see fifty move rule); and there is one drawing fortress position for the two bishops. Two knights can generally draw against a queen by setting up a fortress. A rook versus a minor piece (bishop or knight) is generally a draw. A rook plus a minor piece versus a rook is usually a draw; as is a queen and a minor piece versus a queen. A queen versus a rook and a minor piece is generally a draw. Of course, there are positions that are exceptions to these general rules. In his landmark book Basic Chess Endings, Reuben Fine inaccurately stated that in endgames without pawns, at least the advantage of a rook (or equivalent material) is required to win, with two exceptions in which less of an advantage is sufficient. The advantage of a rook corresponds to a five-point material advantage using the traditional relative value of the pieces (pawn=1, knight=3, bishop=3, rook=5, queen=9). It turns out that there are several exceptions, but they are endgames that rarely occur in actual games. A four-point material advantage is often enough to win in some endings without pawns. For example, a queen wins versus a rook (as mentioned above, but 31 moves may be required); as well as when there is matching additional material on both sides, i.e.: a queen and any minor piece versus a rook and any minor piece; a queen and a rook versus two rooks; and two queens versus a queen and a rook. Another type of win with a four-point material advantage is the double exchange - two rooks versus any two minor pieces. There are some other endgames with four-point material differences that are generally long theoretical wins, but the fifty move rule comes into play in competition because in general more than 50 moves are required: two bishops and a knight versus a rook (68 moves); and two rooks and a minor piece versus a queen (82 moves for the bishop, 101 moves for the knight). A three-point material advantage can also result in a forced win. For instance, some of the cases of a queen versus two minor piece are such positions (as metioned above). In addition, the four minor pieces win against a queen. Finally there are some long general theoretical wins with only a two- or three-point material advantage but the fifty move rule usually comes into play because of the number of moves required: two bishops versus a knight (66 moves); a queen and bishop versus two rooks (two-point material advantage, can require 84 moves); a rook and bishop versus a bishop on the opposite color and a knight (a two-point material advantage, requires up to 98 moves); and a rook and bishop versus two knights (two-point material advantage, but it requires up to 222 moves!). The number of moves given are the number of moves to convert the endgame to a simplier endgame (or checkmate), and are from Fundamental Chess Endings, by Müller and Lamprecht; and Secrets of Pawnless Endings, by John Nunn. I have Secrets of Pawnless Endings from John Nunn but not sudied it, if necessary I could look up some material? Endgames are fascinating but there is just so much to study. Eelco
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