Some resources for chess (and/or mathematics)
(Freshman Seminar 23j: Chess and Mathematics, Fall 2003)


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.] An alternative database (a.k.a. EGTB, for EndGame TableBase) is Ken Thompson's at Bell Labs. This query to this database reveals that in the diagrammed position White to move ``wins'' (mates or reaches a won 5-man ending) in 197 moves, only by playing Bg6+, whereas if Black has the move (is this possible?) he draws -- and clicking ``pass'' shows that his only drawing move is Ke7. [More precisely, that's the only move that prevents White from winning; the Thompson database only distinguishes White wins from non-wins.]

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 very good on the computer screen, but at least the .ps should print correctly on a PostScript printer. The same is true for the PostScript and PDF files for my presentation at the initial seminar meeting, which was extracted from the same article.


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 .)