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Strategic decision-making for sequential move games requires rationality and continuity of rationality to guarantee maximum payoffs at all nodes/stages/levels. Rationality and continuity of rationality in a player's behaviour are not often observed and/or maintained thus, leading to less optimal outcomes. More so, the belief in an opponent's rationality, on the other hand, co-determines the level of effort a player employs while making strategic decisions. Given irrationality and discontinuity of rationality in a sequential move game with mover advantages, there are strategic steps (algorithms) to convert and/or maintain the mover advantages of an irrational player. In this paper, the conversion strategy algorithms, as well as the optimal strategy algorithms, are developed using the Beta Limit Sum (BLS) strategy model and the game of strokes. The simulation exercises confirm that the BLS strategy model is an optimal solution for the finite sequential game of strokes. One of the key applications of these strategies is that of resource economics like environmental resources (clean water, air & land). These are public goods, as such, the optimal strategy entails that the community cooperates (as one entity) and takes the same actions or strategy to maintain a healthy and clean state of the communal environmental resources.