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Kelly: interpreting information rate through optimized logarithmic capital growth

Contribution grade

Mathematics and statistics · Mathematics and statistics

Reference score180,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Kelly connected mutual information to the optimal long-run logarithmic growth rate of repeated symbol-conditioned bets at fair odds, and treated unequal odds and a track take with separate formulas.

Scientific scope

Kelly connected mutual information to the optimal long-run logarithmic growth rate of repeated symbol-conditioned bets at fair odds, and treated unequal odds and a track take with separate formulas. The criterion maximizes expected logarithmic capital growth under a specified repeated-betting information and probability model. It does not maximize every utility, guarantee wealth on each path or remove drawdown and estimation risk. Correlation, transaction cost, changing probabilities and finite horizons need separate treatment. This historical contribution is not investment guidance.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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