We experimentally examine repeated prisoners' dilemma with random termination, where monitoring is imperfect and private. Our estimation indicates that a significant proportion of subjects follow generous Tit-For-Tat (g-TFT) strategies, straightforward extensions of Tit-For-Tat. However, the observed retaliating policies are inconsistent with the g-TFT equilibria. Contrarily to the theory, subjects tend to retaliate more with high accuracy than with low accuracy. They tend to retaliate more than the theory predicts with high accuracy, while they tend to retaliate lesser with low accuracy. In order to describe these results as unique equilibrium, we demonstrate an alternative theory that incorporates naivete and reciprocity.