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Kelly's solution to allocating bets in a horse race, or other gambling games, maximizes the long-term growth rate, but is known to be risky. Here, I will describe optimal betting strategies that give the highest capital growth rate while keeping a certain low value of risk, that is, an optimal trade-off between the average and the fluctuations. This trade-off is also embodied in a general bound similar to thermodynamic uncertainty relations. Finally, I will discuss possible future applications in biology. This trade-off is also believed to operate in situations known generically in biology as "bet-hedging". Organisms may exchange a reduction of their present fitness for increased fitness in a possible future stressful condition. Some type of bet-hedging mechanism is believed to operate in the production of seeds by plants or in the resistance to antibiotics.
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