Game theory literature largely lacks a generally accepted method, capable of transforming both cardinal and ordinal games or games where one player is cardinal and the other one is ordinal. We devised a new method to overcome this problem. We used propositional logic to represent our general argument. Afterwards developed basic inferences, conclusion is derived according to modus ponens, based on these inferences we derived biconditional statement and truth table. By adding and subtracting same figure to/from opposite expected outcomes (according to change in preference of one or both players) games having ordinal and/or cardinal payoffs can be transformed. We used the Notorious ?Prisoners Dilemma? as an example and transformed it under our new method. Our method will not only expand the available knowledge in game theory by including both ordinal and cardinal transformations but it can also be helpful for the potential development of new taxonomies and topologies.