Rectangular chocolate games have already been studied by a mathematician. We created step choocolate games that are new in the field of mathematics.
In step chocolate, a vertical break can reduce the number of horizontal breaks. Therefore the reduction of the z-coordinate may reduce the y-coordinate. This is not the case when the chocolate is rectangular.
To study the winning stratedy of step chocolate games, Grundy number is important. Grundy number is used a lot in combinatorial game theory.