A useful frame is n-ply thinking.

How many layers, or plys, are you able to consider in your actions while still responding quickly?

An n+1 player can beat an n-player in ways the latter cannot understand.

This can be taken advantage of for bad ends!

Imagine a player who is clearly behaving in a morally good way for plys 0 to n. But in the n+1 ply they deploy an evil strategy to dominate.

This is similar to the "in the last round, defect" strategy in the iterated prisoner's dilemma.

If you think you're a 10-ply thinker but you're actually thinking 2-ply, you'll be operating recklessly in ways you don't understand.

The best way to get more plys is to have more experience and then reflect on that experience to abduct out an intuition.

Think of the ply beyond your current ability as a dimension you can't yet see.

All kinds of truly mind-blowing things will happen that are impossible for you to understand at that ply.

Similar to Flatland, or the 4D Toys iPad App or the Miegakure game.

With experience and practice, you can learn to see in additional dimensions.

The higher-ply thinker will look like they're breaking the rules, but in reality they're playing within a set of rules beyond your ability to comprehend them.