We answer the question, what should we say about V when we want togamble on X, and what is it worth? If V=X, we show that every bit ofdescription at rate R is worth a bit of increase Δ(R) in thedoubling rate. Thus the efficiency Δ(R)/R is equal to 1. Forgeneral V, we provide a single letter characterization for Δ(R).When applied specifically to jointly normal (V,X) with correlationρ, we find the initial efficiency Δ'(0) is ρ2.If V and X are Bernoulli random variables connected by a binarysymmetric channel with parameter ρ, the initial efficiency is (1-2p)2. We finally show how much increase in doubling rate ispossible when the sender can provide R bits of information about V andside information S is available only to the investor
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