## Abstract

We answer the question, what should we say about V when we want to gamble on X, and what is it worth? If V = X, we show that every bit of description at rate R is worth a bit of increase Δ(R) in the doubling rate. Thus the efficiency Δ(R)/R is equal to 1. For general V, we provide a single letter characterization for Δ(R). When applied specifically to jointly normal (V,X) with correlation ρ, we find the initial efficiency Δ′ (0) is ρ^{2}. If V and X are Bernoulli random variables connected by a binary symmetric channel with parameter p, the initial efficiency is (1 - 2p)^{2}. We finally show how much increase in doubling rate is possible when the sender can provide R bits of information about V and side information S is available only to the investor.

Original language | English (US) |
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Number of pages | 1 |

State | Published - 1995 |

Event | Proceedings of the 1995 IEEE International Symposium on Information Theory - Whistler, BC, Can Duration: Sep 17 1995 → Sep 22 1995 |

### Other

Other | Proceedings of the 1995 IEEE International Symposium on Information Theory |
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City | Whistler, BC, Can |

Period | 9/17/95 → 9/22/95 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics