Some resources for chess (and/or mathematics)
(Freshman Seminar 23j: Chess and Mathematics, Spring [2005-]2006)


Complete endgame analyses. There are several Web interfaces to the databases that give the outcome of every position with at most 5 men on the board, and many pawnless positions with at most 6. This site [now back in order :-)] gives various information, including DTM (distance-to-mate) and DTZ (distance to zeroing the 50-move count). [in FEN, a.k.a. Forsyth notation, the position is entered by scanning the board left to right, top to bottom; e.g. the full-point mutual Zugzwang White:Kb2,Pc2,Pc3,Black:Ka4,Ra3 is entered as 8/8/8/8/k7/r1P5/1KP5/8.]

We shall explain in the seminar how such databases are created; here is one early (1979) explanation in English. [In EG (Roycroft's EndGame monthly), "*C*" means computer-related material, and "GBR class 0103" is Rook vs. Knight -- and in turn GBR stands for Guy, Blandford, and Roycroft, creators of the GBR code for chess endings and diagrams.]

More game reconstruction puzzles. Francois Labelle's ``Chess Problems by Computer'' contains many remarkable results and example of game reconstruction puzzles obtained by exhaustive computer search. There are also many remarkable puzzles with entirely unique solutions, some of which you can find on the Web by asking Google for ``proof games". (For an explanation of why they're called ``proof games'', see the entry on ``Legal position'' in the chess glossary for the Seminar.

Chess and combinatorial game theory. Here are links to my first and second articles on chess positions that illustrate and can be explained by the combinatorial game theory of Winning Ways (see below).

The mathematical knight: an article by Richard Stanley and myself that appeared in the ``Mathematical Recreations'' section of the Mathematical Intelligencer, Vol.25 (2003), #1, pages 22-34. We'll cover much of this material in the course of our seminar. You can download the paper as either a PostScript or a PDF document; unfortunately neither format looks perfect on the computer screen, but at least the .ps should print correctly on a PostScript printer.


All of these are on reserve at the Cabot (a.k.a. Science Center) Library:

D. Hooper, K. Whyld: The Oxford Companion to Chess, 2nd ed. (1992) (Hollis #002646059, WID-LC GV1445 .H616 1992); 1st ed. (1984) (Hollis #000254071, WID-LC GV1445 .H616 1984).

This is a wonderful one-volume encyclopedia; particularly good for us are the extensive treatment and well-chosen illustrative examples for chess terminology from Alfil to Zugzwang. I put both editions on reserve because they give different examples for the same terms.
E.R. Berlekamp, J.H. Conway, R.K.Guy: Winning Ways, for Your Mathematical Plays (2 Vols.; Hollis #001036312, Cabot Science QA95 .B47, Hilles QA95 .B446 1982, Lamont QA95 .B446 1982)
The canonical reference for the ``combinatorial game theory'' invented by the three authors. For the most part we'll use material from the first part of Volume 1.
J. Levitt, D. Friedgood: Secrets of Spectacular Chess (Hollis #005553758, Depository HNE354; Widener GV1449.5 .L48 1995x)
A pioneering discussion of the esthetics of chess, particularly of chess problems/studies.
J. Morse: Chess Problems: Tasks and Records (Hollis #005238140, Depository HNELT7)
Note particularly the last few chapters, which address tasks such as ``What's the longest Mate-in-N problem in which White has only the King and one Pawn?''. Mate-in-2 specialists will also learn a lot from the first dozen or so chapters. Some of the records have been since superseded, but Morse has published periodic updates in The Problemist; copies of these updates will also be on reserve at the library.
T. Krabbé: Chess Curiosities (Hollis #000418971, WID-LC GV1447 .K73x 1985)
For the most part this is not directly connected with our Seminar topics, but directed at similar sensibilities. For instance, some actual games in which one player castled after move 40. (For more along these lines, see Krabbé's chess site; for instance, the castling records and many others such as a 269-move game are on this page .)