The problem here is that in your original post, you state that the goal is not to have more points than the other person, just to maximize your own points. Meaning that it is not a competition, and so there is no intrinsic value in defecting unless it is going to increase your points. given the rules of the game it dictates mutual cooperation is the only way to ensure a highest possible score. Because if you decide to defect after 49 rounds you may end up with 51, but you may end up with 49. (if after 48 rounds its either 48 or 50). two masters would come to the conclusion that if they go for the 51st point it is equally likely the other would as well and then end up with 49 points. So the solution is to cooperate and be guaranteed of 50, instead of defecting and averaging to 50 if you are lucky (which you wont be, because the other guy is a master).