Isn't this just E(f(x)) != f(E(x))? The first part shows the expected value of the return function, which is positive (from the gambler's perspective). The se

Isn't this just E(f(x)) != f(E(x))? The first part shows the expected value of the return function, which is positive (from the gambler's perspective). The second part uses f(E(x)): the gambling function applied to expected number of heads and tails (50/50), which is a loss on average. But that's disingenuous because it silently thwacks off the outliers where a gambler wins almost every time or loses almost every time, which is hugely positive on average. Essentially any nonlinear return function would have the same inequality. It's just stated trickily here and the analysis is deliberately misleading.