Blockbusting is a
solved combinatorial game introduced in 1987 by
Elwyn Berlekamp
Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Contributors, ''IEEE Transactions on Information Theory'' 42, #3 (May 1996), p. 1048. DO10. ...
illustrating a generalisation of
overheating.
The analysis of Blockbusting may be used as the basis of a strategy for the combinatorial game of
Domineering
Domineering (also called Stop-Gate or Crosscram) is a mathematical game that can be played on any collection of squares on a sheet of graph paper. For example, it can be played on a 6×6 square, a rectangle, an entirely irregular polyomino, or a ...
.
Blockbusting is a
partisan game In combinatorial game theory, a game is partisan (sometimes partizan) if it is not impartial. That is, some moves are available to one player and not to the other.
Most games are partisan. For example, in chess, only one player can move the white ...
for two players known as Red and Blue (or Right and Left) played on an
strip of squares called "parcels".
Each player, in turn, claims and colors one previously unclaimed parcel until all parcels have been claimed.
At the end, Left's score is the number of pairs of neighboring parcels both of which he has claimed.
Left therefore tries to maximize that number while Right tries to minimize it.
Adjacent Right-Right pairs do not affect the score.
Although the purpose of the game is to further the study of
combinatorial game theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the playe ...
,
Berlekamp provides an interpretation alluding to the practice of
blockbusting
Blockbusting was a business practice in the United States in which real estate agents and building developers convinced white residents in a particular area to sell their property at below-market prices. This was achieved by fearmongering the ...
by
real estate agent
A real estate agent or real estate broker is a person who represents sellers or buyers of real estate or real property. While a broker may work independently, an agent usually works under a licensed broker to represent clients. Brokers and agen ...
s:
the players may be seen as rival agents buying up all the parcels on a street,
where Left is a
segregationist
Racial segregation is the systematic separation of people into racial or other ethnic groups in daily life. Racial segregation can amount to the international crime of apartheid and a crime against humanity under the Statute of the Interna ...
trying to place his clients as neighbors of one another
while Right is an integrationist trying to break them up.
The operation of overheating introduced to analyze Blockbusting was later adapted by Berlekamp and
David Wolfe
to
warming to analyze the end-game of
Go.
[
]
References
Abstract strategy games
Combinatorial game theory
Solved games
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