A common reason for giving research participants post-trial access to the trial intervention appeals to reciprocity, the principle, stated most generally, that if one person benefits a second, the second should reciprocate: benefit the first in return. Many authors consider it obvious that reciprocity supports PTA. Yet their reciprocity principles differ, with many authors apparently unaware of alternative versions. This article is the first to gather the range of reciprocity principles. It finds that: most are false. The most plausible principle, (...) which is also problematic, applies only when participants experience significant net risks or burdens. Seldom does reciprocity support PTA for participants or give researchers stronger reason to benefit participants than equally needy non-participants. Reciprocity fails to explain the common view that it is bad when participants in a successful trial have benefited from the trial intervention but lack PTA to it. (shrink)