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Physically Unclonable Functions are more and more important in the design of secure hardware, as they can ensure properties that conventional cryptography can not. In this paper we clarify the relations between strong PUFs and their unpredictability. For this purpose we first introduce an alternative definition for physical unpredictability, where the adversary can probe the physical responses of the Physical Function. We then illustrate physical unpredictability with a new instance of a PUF, based on the variability of the power consumption of a 65-nanometer chip. For this new PUF, we also evaluate the relation between robustness, unclonability and physical unpredictability. Our new definitions highlights the importance for designers to take into account if physical probing is possible or not (since the power of modeling attacks highly depends on this assumption). It also suggests that physical unpredictability is a generally useful tool for evaluating the unclonability of PUFs (since it can generate warning signals regarding the independence assumption that is frequently exploited for this purpose).