Digital watermarks, sparse dot patterns, and copy detection patterns are different types of copy-detectable images that have been used to protect documents and other physical objects against counterfeiting. There is a frequent claim about these technologies that they are ”virtually impossible to copy” or ”extremely hard to forge”. But can this claim be quantified? This paper investigates this question from a detection theoretic viewpoint, and shows that under certain conditions, a copy falsely detected as an original is extremely improbable.