You could probably write out an equation that would take the distribution of decisions (expressed in payoff for defection vs. cooperation), and compute the optimal probability distribution (as a function of expected value for defection, or ratio of cooperation/defection payoff, perhaps) to use for this strategy.
Bongo’s comment rightly implies that the result will depend on whether other players observe the probability you will betray them as a function of payoff, or just the probability overall.
You could probably write out an equation that would take the distribution of decisions (expressed in payoff for defection vs. cooperation), and compute the optimal probability distribution (as a function of expected value for defection, or ratio of cooperation/defection payoff, perhaps) to use for this strategy.
Bongo’s comment rightly implies that the result will depend on whether other players observe the probability you will betray them as a function of payoff, or just the probability overall.