This paper explores contributions made by Jule Eisenbud pertaining to the substantive interrelationship of psi functioning to probabilistic behavior. It is argued that Eisenbud came very close to articulating a construct that may prove very useful to psi theoreticians and researchers. That construct is “smias”, which was first articulated by researchers examining the foundations of probability theory in connection with an investigation of the gambler’s fallacy. It is shown that the smias construct fits Eisenbud’s theorization very well indeed, and that (...) the construct offers psi researchers and theorists an account of the law of large numbers that can: (1) incorporate psi as a universally operative influence, or set of influences on probabilistic outcomes; (2) avoid the gambler’s fallacy while accomplishing (1), and (3) at the same time offer an account of why psi can be difficult to detect and/or replicate. (shrink)