Entrepreneurial Chess

Original Paper

DOI: 10.1007/s00182-017-0580-z

Cite this article as:
Berlekamp, E. & Low, R.M. Int J Game Theory (2017). doi:10.1007/s00182-017-0580-z


Although the combinatorial game EntrepreneurialChess (or Echess) was invented around 2005, this is our first publication devoted to it. A single Echess position begins with a Black king vs. a White king and a White rook on a quarter-infinite board, spanning the first quadrant of the xy-plane. In addition to the normal chess moves, Black is given the additional option of “cashing out”, which removes the board and converts the position into the integer \(x + y\), where [xy] are the coordinates of his king’s position when he decides to cash out. Sums of Echess positions, played on different boards, span an unusually wide range of topics in combinatorial game theory. We find many interesting examples.


Combinatorial games Chess 

Mathematics Subject Classification


Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Elwyn and Jennifer Berlekamp FoundationOaklandUSA
  2. 2.Department of MathematicsSan Jose State UniversitySan JoseUSA

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