Blockbusting is a two-player game in which players alternate choosing squares from a line of squares, with one player aiming to choose as many pairs of adjacent squares as possible and the other player aiming to thwart this goal. Elwyn Berlekamp introduced it in 1987, as an example for a theoretical construction in combinatorial game theory.[1][2]
Rules
editBlockbusting is a partisan game for two players, meaning that the roles of the two players are not symmetric. These two players are often known as Red and Blue (or Right and Left); they play the game on an 
Although the purpose of the game is to further the study of combinatorial game theory, Berlekamp provides an interpretation alluding to the practice of blockbusting by real estate agents: the players may be seen as rival agents buying up all the parcels on a street, where Left is a segregationist trying to place clients as neighbors of one anotherwhile Right is an integrationist trying to break up these segregated groups.
Theory
editIn introducing the game of Blockbusting in 1987, Elwyn Berlekamp also introduced overheating, an operation for analyzing the theory of combinatorial games, and used Blockbusting as an example for that operation.[1]
The operation of overheating was later adapted by Berlekamp and David Wolfeto warming to analyze the end-game of Go.[3]
The analysis of Blockbusting may be used as the basis of a strategy for the combinatorial game of Domineering.[4]
References
edit- ^ a b Berlekamp, Elwyn R (1988-09-01). "Blockbusting and domineering". Journal of Combinatorial Theory, Series A. 49 (1): 67–116. doi:10.1016/0097-3165(88)90028-3. ISSN 0097-3165.
- ^ Berlekamp, Elwyn R.; Conway, John H.; Guy, Richard K. (January 1, 2001). "Blockbusting". Winning Ways for Your Mathematical Plays, Vol. I (2nd ed.). A K Peters. p. 186. ISBN 1-56881-130-6.
- ^ Berlekamp, Elwyn; Wolfe, David (1994). Mathematical Go Endgames. Ishi Press. p. 52. ISBN 0-923891-36-6.
- ^ Siegel, Aaron N. (2013). Combinatorial game theory. Graduate Studies in Mathematics. Vol. 146. American Mathematical Society, Providence, RI. p. 490. ISBN 978-0-8218-5190-6. MR 3097920.