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The structure of the paper is as follows. Section 2 introduces notation. Section 3 introduces the main definitions and gives a simple example using one-way functions. Section 4 shows the parallel between properties of optimal predictors and classical probability theory. Section 5 discusses behavior of optimal predictors and reductions and shows $\textsc{SampNP}$ has a complete problem under appropriate reductions. Section 6 discusses existence and uniqueness of optimal predictors. Section 7 discusses applications to AGI. Section 8 discusses possible avenues for further research. Appendix A reviews relevant theorems from complexity theory. about one-way functions.  Appendix B reviews the Kakutani-Glicksberg-Fan fixed point theorem.