Not if their probability of cooperation is so high that the expected value of cooperation remains higher than that of defecting. Or if their plays can be predicted, which satisfies your criterion (nothing to do with my previous plays) but not mine.

If someone defects every third time with no deviation, then I should defect whenever they defect. If they defect randomly one time in sixteen, I should always cooperate. (of course, always-cooperate is not more complex than always-defect.)

...I swear, this made sense when I did the numbers earlier today.