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Evolutionary games have been extensively used to model and understand various complex real world situations, especially when investigating how cooperation evolve among self-interested players involved in strategic interactions. Many situations exhibit iterated interactions where players use past experiences (game history) to decide on their next actions. Cooperation evolves when a player trades the short-term benefits of being selfish with the long-term benefits of being cooperative, and this is only feasible if future interactions have sufficiently large discount factor (i.e., direct reciprocity settings). How do players decide on the discount factor is an interesting research question, it may depend on the player's personal experience or on public knowledge. In this study, we present novel models and investigate the cooperation levels in a coevolutionary environment of stochastic strategies. We extend the stochastic strategies' representation to allow players to evolve probabilities to terminate future interactions, and we show that this significantly decrease the levels of cooperation. We then show that the previous conclusion still holds when using global statistics as global (population-level) termination probabilities. We illustrate that enhancing the probability to cooperate in the game's initial round increases the levels of cooperation when termination probabilities are used by players.