Many decisions in life involve the tradeoff between risk and reward. Perhaps one has to choose between a "low risk, low reward" course of action, that plays it safe, but does not achieve any big wins; or a "high risk, high reward" choice which could potentially give greater benefits, but also greater downsides.

Risk management is a complex task, but one can explore it initially with some very simplified models, always keeping in mind George Box's dictum that "all models are wrong, but some are useful". For this simple model, one can assume that each course of action comes with two numbers: the "reward", which is the average positive net gain (benefits minus costs) one expects to get from pursuing the action, and the "risk", which in this model can be thought of as a standard deviation of the fluctuation from the mean. For instance, a "safe" action might have a reward of 5 and a risk of 3, which I would represent as 5±3 in this model, the return would typically range anywhere from 2 to 8 units of net benefit. A "bold" action might have a reward of 9 and a risk of 10, which I would represent as 9±10; in this model, the return would typically range from -1 to 19 units of net benefit. Here we imagine that there is some sort of bell curve in effect; while a 5±3 action will *usually* give a net benefit between 2 and 8, there could be exceptional events that lead the return to be less than 2 or greater than 8. But I will gloss over these tail events for sake of this discussion.

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