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orthonormal comments on Decision Theories: A Semi-Formal Analysis, Part III - Less Wrong
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Won't that let the opponent steal utility from you? Consider the case where you're going up against another TDTer which is willing to consider both the strategy "if they cooperate only if I cooperate, then cooperate with 99% probability" and "if they cooperate only if I cooperate, then cooperate." You want your response to the first strategy to be defection and your response to the second strategy to be cooperation, so it's in their interests to play the second strategy.
You've made it into a bargaining game with that mixed strategy, and indeed the version of TDT we introduced will defect against an opponent that outputs the mixed strategy (if that opponent would output a pure cooperate if that were the only way to get its adversary to cooperate). But bargaining games are complicated, and I'm saving that for another post.