Wealth is a much more complex utility than others because given the different levels of wealth you have the marginal benefit of having that wealth decreases.

That is, let \(A\) be the fact that you are given $50, and let \(B\) be there being \(0.5\) chance of winning $100.

- risk neutral: the utility is linear—therefore \(A \sim B\)
- risk seeking: utility is convex (derivative increases as reward increases), so \(A \prec B\)
- risk averse: utility is concave (derivate decreases as reward decreases), so \(A \succ B\)