Author: Helmut Conrady
Date: 12:08:16 06/01/00
I have outplayed for every Nalimov 3 to 5 man-file one of the longest
sequences to mate. This file (30 KB), including a statistical overview
is after small corrections (thanks to Guy Haworth and others!)
downloadable again now. URL:
http://mitglied.tripod.de/ChessBits/index.html (Button "Tablebase
news").
Here some highlights (excerpt from the introduction text) with
interesting results:
1. The longest 3-man is KP–K (No. 110) with 56 plies, the longest 4 man
KR–KP (No. 46) with 85 plies and the longest ending in this database is
KPP–KP (107) with 254 plies to mate. The last endgame is the only one in
which the material balance changes five times and the longest at all.
2. The longest pawnless ending is KBN–KN (75) with 213 plies. Besides
KQP–KQ this ending might be one of the most difficult for human players
at all.
3. The ending with the latest capturing or promotion is KNN–KP (92). The
material balance changes just in ply 228!
4. In KQR–KQ (7) and KQR–KP (11) there is the longest series of checks
on the board (56 ones!). It is interesting to see that the stronger side
can win after this thunderstorm of checks.
5. Some endings are rather trivial, first because of the material
balance at the beginning or because of early capturing moves. But some
of them are indeed very subtle and seem to be studies. For example KR–KP
(46) comes near a study of Troitzy from 1895 (8/6k1/3PK3/8/6r1/8/8/8 w;
mate in 39 instead of mate in 42 in the tablebase-position) and KR–KQ
(37b) comes near a study of Rinck in 1916 (5q1k/1RR5/8/8/8/8/4K3/8 w; in
the tablebase-position white has to fight 7 moves longer to capture the
queen). In both examples the database-positions are (because the winning
sequences need more moves for the given theme) more interesting than the
studies.
6. Many of the winning-sequences add a number of moves to studies or
positions in endgame theory, for example in KBP–KP (82) and KRB–KR (
44). The real complexity of these endgames is shown since the
endgame-databases were computed.
7. 17 efforts for win would came in conflict with the 50-move-rule. Here
are the three with the greatest number of plies:
KRP–KQ (55) 152 plies
KBN–KN (75) 150 plies
KRP–KB (59) 149 plies
8. Many underpromotions are appearing in this database. Most interesting
are forced underpromotions (those, were the pawn move to the last
rank is the only winning move). Here are for each R, B and N the longest
distances from underpromotion to mate:
Rook: KPP-KB (105a) 85 plies (preventing from stalemate)
Bishop: KNP–Kn (97) 191 plies (preventing from stalemate)
Knight: KBP–KN (81) 199 plies (preventing from losing a
piece)
9. It is interesting that there is even a 4-man ending in which an
underpromotion is the only winning move: KBP–K (83).
10. The longest distance from a promotion to queen to mate appears in
KQP–KQ (29) and in KPP–KP (107) with exactly 243 plies.
Have many fun in discovering a part of the beauty of chess endings!
Helmut Conrady
conrady@knuut.de
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