Entrepreneurial Chess

Although the combinatorial game Entrepreneurial Chess (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 [x, y] 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.