I watched Polls vs Win Charts – Positional Heuristics. The video brings an interesting point regarding heuristics. There are strategic heuristics and positional heuristics.

Several years ago, I played a game called Imperial Glory (probably in high school). The game involve attacking and defending using armies that can move across the grand theater of war. Once a battlefield is chosen, the only thing that I can do is to determine what tactics I should use to maximize my chance for emerging victorious. But over the course of playing, I realize that what kind of battlefield that I chose ultimately puts the ceiling on the maximum effectiveness of any tactics I can use. Sometimes, choosing a favorable battlefield and is all I have to do to ensure victory (such as bringing a defensive fight to a mountainous region), even with doing below average tactics.

We can think of strategy and tactics in a surface analogy. Let’s say we have an XYZ graph where X and Y are the independent variable that produce the dependent variable Z. Let’s also say Z is the output that we seek to maximize, while X and Y are the factors responsible for that. Imagine that the surface is wobbly with different elevations.

Tactics are searching for that optimal point. The notion of gradient descent, local optima, tabu search, all applies here. Basically tactics is about “given our current position, how can we improve our situation?”

However, strategy deals with the very essence of the solution surface. Stragey is the actual shape of the surface in which the tactic operates. A tactic that has outstanding performance in a solution surface might be utterly useless in an entirely different setting because the underlying strategy has a very different “topography” of the solution surface.

Heuristics is usually used in the context of tactic. After some time, do we know how much we have progressed to the optimal point? Why or why not? Are there any improvements or corrections to increase the effectiveness of our current tactics?

However, the ability to sense the fundamental shift of the prevailing solution surface is even more important. This is where higher-order heuristics plays in. Even if our tactics has been optimized, are we actually operating in the assumed solution surface, or the surface has changed in such a way that we fail to recognize the change?

Even better, given enough resource, technical know-how, and initiative, we can even be the cause of that change. By tampering with the rules, setting constraints ahead, and anticipating the counterparty’s movement we can render their intelligence and experience useless.