Abstract
The combinatorial game theory is not only a new branch of modern mathematics but also an important subject of operations research. One basic combinatorial game can develop many different rules and different strategies to solve the problems, and both the rules and strategies follow the fundamental game theory to give the answer for the new version of the combinatorial game, such as the Nim game, one of the most basic combinatorial games, which has been researched for many years by a large number of researchers. This paper shows and extends the strategies of two combinatorial games, Tic-Tac-Toe and Green Hackenbush, based on the regular version which is connected with the combinatorial game theory.
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