Here is a new example. I was thinking about strategy as a pro golfer playing in a 72-hole tournament. Generally, you want to minimize expected value, get the

Here is a new example. I was thinking about strategy as a pro golfer playing in a 72-hole tournament. Generally, you want to minimize expected value, get the lowest average score on each hole. It is obvious that near the end of the tournament, if you're behind, you want to play riskier golf, and if you're in the lead, you want to play less risky golf. That maximizes your chance of winning. This means instead of optimizing for expected value, you sacrifice expected value in exchange for higher or lower variance, respectively. What I realized a couple of days ago is that even earlier in the tournament, you don't want to optimize expected value -- you always want to give some of that for higher variance. Why? Because in the variance/EV trade-off curve, the slope of the curve is zero at the maximum value, which means to add h units of variance, you give up o(h), realistically, O(h^2), expected value. So there is some value of h where the trade-off is worth it. (Concrete example: Golf tournaments could be modeled as a coin-flipping contest, where you get +1 point for flipping heads, -1 point for flipping tails, with 72 coin tosses. Suppose you could pay a 0.01 point cost to double the point value, i.e. you get +1.99 or -2.01 as a result of the coin toss. Then you should, because doing so on the first coin tosses will increase your chance of winning.)