Machine-aided decision-making in complicated situations is demonstrably superior to unaided, human decision-making. In addition to being consistent and unbiased, computers can perform the very complex calculations needed to design formal, self-validating decision-making systems. An important advantage to self-validating systems is that they provide statistics which allow the user to diagnose and compensate for difficulties associated with complexity. This paper contains examples of problem domains which seem similar, but for which the difficulty varies greatly. The absence of intuition would have made the design of decision-making algorithms risky, if not impossible, in these cases.