4. MATHEMATICAL GAMES
Aviezri S. Fraenkel. Selected Bibliography on Combinatorial Games and Some Related Material. Op. cit. in 3.B.
4.A. GENERAL THEORY AND NIM LIKE GAMES
Conway's extension of this theory is well described in Winning Ways and later work is listed in Fraenkel's Bibliography -- see section 3.B & 4 -- so I will not cover such material here.
4.A.1. ONE PILE GAME
See MUS I 145-147.
(a, b) denotes the game where one can take 1, 2, ..., or a away from one pile, starting with b in the pile, with the last player winning. The version (10, 100) is sometimes called Piquet des Cavaliers or Piquet à Cheval, a name which initially perplexed me. Piquet is one of the older card games, being well known to Rabelais (1534) and was known in the 16C as Cent (or Saunt or Saint) because of its goal of 100 points. See: David Parlett; (Oxford Guide to Card Games, 1990 =) A History of Card Games; OUP, 1991, pp. 24 & 175-181. The connection with horses undoubtedly indicates that (10, 100) was viewed as a game which could be played without cards, while riding -- see Les Amusemens, Decremps.
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