April 10, 2022 San Francisco

Failing to Calculate

The most common way I lose when playing a strategy game is by “failing to calculate”.

Most interesting strategy games are extremely hard to play optimally if you’re a human: In order to play perfectly, you’d need to consider astronomically many possible games. When we learn strategy games, we typically learn heuristics (for example, “what resources have I accumulated?”, or “How many pawns are worth a knight?”) that are easy to evaluate, and are correlated with winning. And learning a few of these heuristics puts you way ahead of people who haven’t learned them.

But there are (at least) two other important skills you need for winning strategy games.

The first is discovering new heuristics. You’ll do some of this without even thinking about it, as you play the game: “Heuristics”, as I’m using the term here, includes explicit ones like “how many pawns for a knight” as well as implicit ones, like “does this feel like a good move to me?”.

The second skill, which I find is the hardest, is noticing when to stop relying on heuristics, and buckle down and calculate the consequences of your actions. Once you have the heuristics, it’s extremely tempting to just play through games as quickly as you can using those heuristics. Calculating takes mental energy that good heuristics mostly avoid. But throughout the game, there are going to be chances to think concretely about consequences and incentives, and if you skip over those you’ll be missing the most important opportunities for getting an edge.

And if you’ve survived to the endgame intact, the first player to notice that it’s the endgame, and to start exploring the whole game tree, is going to win.

More generally, there are different levels of heuristics, where “higher-level” heuristics are extremely easy to calculate, but often less informatiave, and “lower-level” ones are harder to calculate and more informative. The generalized version of “buckling down and calculating” is “moving down the heuristic ladder”. At the bottom of this ladder are heuristics that are actually just memorized or compressed calculation.

This is important because the world is, from one perspective, made up entirely of games like this.