Games Eternal - Games Entailed

• Published in: Winning Ways for Your Mathematical Plays Vol. 2; pp. 379 - 412
• Main Authors: Berlekamp, Elwyn R., Conway, John H., Guy, Richard K.
• Format: Book Chapter
• Language: English
• Published: Routledge 2003
• Edition: 2
• Subjects: Loopy Values; Smith's Rule; Loopy Components; Finishing Game; Loopy Games; Unmarked Option; Knight's Move; Orthogonal Moves; Bonus Move; Backward Analyses; Impartial Games; Dim; Varied Pairs; Legal Move; Ordinary Move; Heap Sizes; Ordinary Game; Loopy Positions; Subtraction Game; Loopy Option; Unequal Partners; Extra Move; Awful Game; Sunny
• ISBN: 9781138427570; 1138427578; 9781568811420; 156881142X
• DOI: 10.1201/9780429487323-4

This chapter talks about two main theories that are impartial games-C. A. B. Smith's for impartial loopy games, that might last forever, and authors' own new theory for games with entailing or complimenting moves. In fact it can be quite hilarious to watch an accomplished player spin the game round and round in several different circles before sneaking in the win. Great-Aunt Maude gave Jimmy and Ginny a compendium of games the Christmas, but most of the games were cheaply produced and not too interesting. Ginny soon noticed that when all the counters were on the top row it was what she called "that awful game with matches". Some positions admit circular chains of moves that need never arise in best play, even when you're adding them to other games. The theory of sums of games when such entailing moves are allowed appears for the first time in Winning Ways.