The Confirmation Bias refers to the problem of searching for, and therefor finding, only evidence that supports your preferred conclusion. This is likely to occur when using anecdotal evidence.

The Positive Bias on the other hand, refers to the problem of testing your beliefs about what your theory allows, but not about what it disallows. In terms of formal logic, two predicates P (corresponding to your theory of awesome triplets) and Q (corresponding to the actual rule) are logically equivalent if and only if for all x in the domain, P(x) implies Q(x) and Q(x) implies P(x). The Positive Bias is only testing samples of the form "P(x) implies Q(x)" but not of the form "Q(x) implies P(x)", or equivalently "not P(x) implies not Q(x)". This bias is likely to occur when designing an experiment.