Mathematical Strategame Theory (MST) and Biomolecular Mediated Computing (BMC) is a self-developed and fulfilled cross-disciplinary research field, which made up of one theoretical work and one practical work. The theoretical work of the research is referring to as Mathematical Strategame Theory (MST). The objective of MST is set to investigate a mathematical counterintuitive phenomenon generated by Parrondo’s paradox and extend the existing framework to the generation of other paradoxical effects. Several key findings have been discovered through the investigation. The identical paradoxical effects cannot be simply reproduced by a relatively simple capital-dependent game. In reality, the paradox can be explained by placing all its game rules and associated parameters within a probability space. Based upon this finding, the analogous paradoxical effects can be generated by artificially manipulating parameters within the probability space. Although Parrondo’s paradox can be treated as an appealing demonstration, which reveals the importance of developing the fuzzy logic gate, its potential application in contemporary financial market, however, is very restricted due to its specific game rules and switching mechanisms. Turning two unfavorable conditions into a favorable one as claimed by Parrondo’s paradox, on the other hand, inspires the development of conceptual model of financial option insurance. Unlike the traditional way of hedging, which is achieved by introducing negatively correlated financial derivatives into an existing financial portfolio, financial option insurance can be issued by an independent institution, which is very alike to an insurance company dedicated in option market. In addition to that, a simple mathematical model is developed, known as business of matching, to enhance its executional ability. The practical work of the research is referring to as Biomolecular Mediated Computing (BMC). BMC is a relatively new computing paradigm as compared to electronic mediated digital computing. The objective of BMC is to develop the conceptual biomolecular devices to solve specific classes of mathematical problems, which maps out potentials for future development of biomolecualr mediated computer. Three conceptual apparatuses have been proposed throughout the entire research, namely, strategic assignment apparatus, optimal route selection apparatus, and normative decision making apparatus. DOCTOR OF PHILOSOPHY (MAE)