In this paper, we will be proving mathematically that scoring play combinatorial game theory covers all combinatorial games. That is, there is a sub-set of scoring play games that are identical to the set of normal play games, and a different sub-set that is identical to the set of mis\`ere play games. This proves conclusively, that scoring play combinatorial game theory is a complete theory for combinatorial games, and that every combinatorial game, regardless of the rule-set, can be analysed using scoring play combinatorial game theory.
Categories: math.CO