In this talk I'll discuss the notion of "invariant random orders", and explain how it can be useful in studying actions of countable groups. In particular, we'll formulate a unified "Kieffer-Pinsker formula" for the Kolmogorov-Sinai entropy of measure preserving actions of amenable groups, and show how it can be used to prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman, and mention some related open problems. Based on joint work with Andrei Alpeev and Sieye Ryu.