We demonstrate that XOR Arbiter PUFs with an even num-ber of arbiter chains have inherently biased responses, even if all arbiterchains are perfectly unbiased. This rebukes the believe that XOR Ar-biter PUFs are, like Arbiter PUFs, unbiased when ideally implementedand proves that independently manufactured Arbiter PUFs are not sta-tistically independent.As an immediate result of this work, we suggest to use XOR ArbiterPUFs with odd numbers of arbiter chains whenever possible. Further-more, our analysis technique can be applied to future types of PUFdesigns and can hence be used to identify design weaknesses, in partic-ular when using Arbiter PUFs as building blocks and when developingdesigns with challenge pre-processing. Finally, we discuss consequencesfor the parameter recommendations of the Interpose PUF.Investigating the reason of the systematic bias of XOR Arbiter PUF, weexhibit that Arbiter PUFs suffer from a systematic uniqueness weakness.