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Gondolinian comments on A hypothetical question for investors - Less Wrong Discussion
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To be fair though, that's only because of the strict limitations of the OP's thought experiment. If you could bet say 1% of your cash on a stock with your specifications, then assuming the transaction fees aren't a problem you should do so every day.
Well, of course the given setting limits the solutions. For example, if you can invest only a part of your wealth, the Kelly Rule comes into play.