Chilled Domineering

Abstract

This paper introduces a new game named Chilled Domineering, together with its mathematical analysis. Chilled Domineering is modified from the Domineering game by allowing a player placing a 1x1 domino while unable to place a 2x1 domino at a position. After modifying the rule, each position in the game becomes an infinitesimal. Many interesting infinitesimals are found in this new game. This paper calculates the game values of all sub-graphs of 3x3 squares and presents a rule to determine the outcome of any sum of these positions.