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    "title": "Kelly: interpreting information rate through optimized logarithmic capital growth",
    "summary": "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.\n\nInformation can be valuable even when no error-correcting code is used. Kelly considered a receiver who uses noisy information about an outcome to allocate a repeatedly reinvested stake. Maximizing expected capital can favor a strategy that eventually loses everything; maximizing logarithmic growth answers a different long-run question. For independent symbols and noise, fair odds and a fixed allocation for each received symbol, allocating according to the posterior probabilities makes the maximum growth rate equal to the channel’s mutual information. Unequal odds without a track take add a baseline growth opportunity; the value added by the information remains the mutual-information term. With a track take, holding back some capital is possible and the formulas change. The original explicitly leaves comparison with general time- or history-dependent allocations to future theorems. This is an information-theoretic result under a mathematical repeated-betting model, not guaranteed profit or universal portfolio optimality. The article builds on Shannon’s information theory and discusses the earlier expected-utility framework.",
    "boundary": "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.",
    "area": "Mathematics and statistics",
    "topic": "Information theory and logarithmic growth",
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        "description": "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.",
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          "citation": "Kelly: interpreting information rate through optimized logarithmic capital growth — complete assessed article text",
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      "statement": "# Kelly: interpreting information rate through optimized logarithmic capital growth\n\nKelly 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.\n\nInformation can be valuable even when no error-correcting code is used. Kelly considered a receiver who uses noisy information about an outcome to allocate a repeatedly reinvested stake. Maximizing expected capital can favor a strategy that eventually loses everything; maximizing logarithmic growth answers a different long-run question. For independent symbols and noise, fair odds and a fixed allocation for each received symbol, allocating according to the posterior probabilities makes the maximum growth rate equal to the channel’s mutual information. Unequal odds without a track take add a baseline growth opportunity; the value added by the information remains the mutual-information term. With a track take, holding back some capital is possible and the formulas change. The original explicitly leaves comparison with general time- or history-dependent allocations to future theorems. This is an information-theoretic result under a mathematical repeated-betting model, not guaranteed profit or universal portfolio optimality. The article builds on Shannon’s information theory and discusses the earlier expected-utility framework.\n\n## Scientific scope\n\nThe 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.\n\n## People and systems\n\nJ. L. Kelly Jr.\n\n\n\n## Original sources\n\n- [Kelly: interpreting information rate through optimized logarithmic capital growth — complete assessed article text](https://bpb-us-w2.wpmucdn.com/u.osu.edu/dist/7/36891/files/2017/07/Kelly1956-1uwz47o.pdf)\n- [Publisher metadata and abstract: A New Interpretation of Information Rate](https://onlinelibrary.wiley.com/doi/abs/10.1002/j.1538-7305.1956.tb03809.x)\n",
      "summary": "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.\n\nInformation can be valuable even when no error-correcting code is used. Kelly considered a receiver who uses noisy information about an outcome to allocate a repeatedly reinvested stake. Maximizing expected capital can favor a strategy that eventually loses everything; maximizing logarithmic growth answers a different long-run question. For independent symbols and noise, fair odds and a fixed allocation for each received symbol, allocating according to the posterior probabilities makes the maximum growth rate equal to the channel’s mutual information. Unequal odds without a track take add a baseline growth opportunity; the value added by the information remains the mutual-information term. With a track take, holding back some capital is possible and the formulas change. The original explicitly leaves comparison with general time- or history-dependent allocations to future theorems. This is an information-theoretic result under a mathematical repeated-betting model, not guaranteed profit or universal portfolio optimality. The article builds on Shannon’s information theory and discusses the earlier expected-utility framework.",
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    "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.",
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