On Strategy

Thinking Out Loud About Dealing with Chance, Complexity, Choice, and Confusion

Over the years, I’ve read a number of authors’ works on strategy, ranging from ancient to modern, corporate to military to mathematical. Since I’ve been pondering the Gaza War lately, and its strategic implications, I thought it might be worthwhile to converse broadly about strategy as a whole. I’ll begin with my broad view on what strategy actually is, a concept that is as applicable to business as to war…

Strategy: The Art of Decision-Making in Conditions of Uncertainty

I define strategy as the art of decision-making in conditions of uncertainty. (In contrast, we might say logistics is the art of decision-making in conditions of certainty.) I define a strategist as someone who must make decisions in conditions of uncertainty. I classify situations which call for strategy as games (in homage to game theory). And I assume that in any game, the strategist aims to earn a payoff (reward) by beating the game, e.g. choosing correctly.

Since what separates strategy from logistics is uncertainty, we need to define uncertainty in, well, no uncertain terms. (Sorry.) There are four causes of uncertainty:

• Chance

• Complexity

• Choice

• Confusion

Uncertainty due to Chance

A strategist faces uncertainty due to Chance if the outcome of his choice is determined randomly. In a purely Chance-based game, without any other type of uncertainty, the strategist knows the possible outcomes and the probabilities of each; he simply does not know which outcome will occur.

Strictly speaking, true Chance only emerges in quantum mechanics but for most everyday uses, pseudo-random events can be treated as Chance by the strategist.

Games of Pure Chance: Roulette; Craps

In a purely Chance-based game, the strategist analyzes his payoff from each outcome and then makes a choice which is likely to maximize his payoff. The payoff must be broadly understood to include second- and third-order benefits and drawbacks.

For instance, the financial payoff from Roulette seems negative, but people still play Roulette. This suggests they are getting payoffs that aren’t accounted for by strictly financial considerations. I enjoy the experience of being at a Roulette table (it makes me feel like James Bond) so I tend to take a strategy that will minimize my expected loss on every turn of the wheel, letting me stay at the table as long as possible. Others might want the payoff of the Dopamine high from a big winning bet, and play accordingly.

Provided that the probabilities or payoffs of the choices do not change after each choice is made, playing one and many iterations of a Chance-based game will not affect the strategist’s decision-making.

Uncertainty due to Complexity

A strategist faces uncertainty due to Complexity if the outcome of his choice is determined by a series of deterministic processes that either (a) cannot be determined in advance even in theory or (b) cannot be determined in advance because of their susceptibility to “Butterfly Effects.” In a game of pure Complexity, the strategist’s choices are not affected by randomness nor by other player’s choices nor by lack of information.

Strictly speaking, pure Complexity never occurs because all processes are fundamentally quantum mechanical and hence stochastic at their base. At the macroscopic level of the strategist, however, such quantum processes can be ignored. (It is possible that the “b” in the Boggle tray might spontaneously transform into a “q” but it is so unlikely as to be irrelevant.)

Games of Pure Complexity: Mazes; Rubik’s Cubes; jigsaw puzzles

In a purely Complexity-based game, the strategist will typically take one of two approaches. First, he might utilize a heuristic known to efficiently address the complexity, and apply it iteratively until the game is beaten. Second, he might beat the game with a “flash of insight.” The former would be the equivalent of “always turning left” when solving a maze, the latter of somehow just “seeing” the way through the maze all at once. (Napoleonic strategists called this coup d'oiel, the act of the eye.)

Uncertainty due to Choice

A strategist faces uncertainty due to Choice if the outcome of his choice is determined by someone else’s choice. We will call this “someone else” the opponent, though it could in fact by an ally or neutral party. In a purely Choice-based case, without any other type of uncertainty, the strategist knows the outcome that will occur for any given choice he and his opponent(s) make; he simply does not know which choice his opponent will make.

Strictly speaking, true Choice only emerges if libertarian free will exists. If it does not, then what seems to be Choice is actually caused by either Chance or Complexity. However, if that is true, it is true of the strategist’s choices as well. Since it would be pointless for a strategist to strategize if his own choices were fully deterministic or stochastic, we assume the existence of libertarian free will for our purposes.

Games of Pure Choice: Prisoner’s Dilemma; Scissors Paper Rock

In a purely Choice-based case, the strategist analyzes his payoff from each choice he could make, given the choice(s) his opponent could make, and then makes whichever choice is likely to maximize his payoff. When playing many iterations of a Choice-based game, the strategist may develop an formal or informal model of his opponent.

Since we cannot prove libertarian free will, uncertainty from Choice can seem identical to uncertainty from Chance or Complexity from the perspective of the strategist. If the opponent’s free will turns out to actually be either random or deterministically complex, the strategist will adopt appropriate choices once that is discovered.

Uncertainty due to Confusion

A strategist faces uncertainty due to Confusion if the outcome of his choice is determined by information he does not possess. In a purely Confusion-based case, the strategist does not have the information to know the outcome that will occur for any given choice; but if he did have that information, his choice would be self-evident.

Case of Pure Confusion: Battleship; 20 Questions

In a purely Confusion-based case, the strategist typically adopts a heuristic that will, if iteratively applied, gradually increase the amount of information he possesses, until his choices become self-evident.

Mixed Games

Chess is a game where uncertainty arises from both Choice and Complexity. The number of potential interactions of chess pieces is so large that (to date) not even the world’s best supercomputers have been able to “solve” Chess, although they can play it very well.

Risk is a game where uncertainty arises from Choice, Complexity, and Chance. The number of different territories, the reward for owning each, the active opposition of the adversary, and the randomness involved in the outcome of each decision, make it a challenging strategy game.

Poker is game where uncertainty arises from Choice, Complexity, Chance, and Confusion. In Poker, you don’t know what you will draw (Chance); you don’t know what your opponent has already drawn (Confusion); you don’t know what your opponent will bet (Choice); and you can’t easily calculate the ramifications of all of the above (Complexity).

The real-life situations that confront strategists in business and war tend to be similar to Poker in that they involve all four causes of uncertainty.

Modeling Uncertainty

Whether formally or informally, consciously or subconsciously, strategists tend to guide their choices by modeling uncertainty using probability and statistics. This is obviously evident in games of Chance, but is true of all other types of games, as well.

For instance, let’s imagine that a strategist is playing chess. He sees an opportunity to make a bold move that will lead to a checkmate in 3 moves unless his opponent chooses to make an unorthodox response that is well outside the parameters of typical play. However, if the opponent does make the unorthodox response, the strategist will likely lose the game. To decide whether to make the move, the strategist would estimate (as best he can) the chance that the opponent will make the unorthodox move. A crude model would be to list all possible moves M the opponent could make, and then define the chance as 1/M. A better model would be based, perhaps, on evidence of past choices made by the opponent in similar circumstances, or an evaluation of time pressure from the chess clock, and so on.

However, the strategist must remember that just because he is modeling Choice, Confusion, and Complexity as if they were Chance, they are not actually due to Chance. Chance is merely a mathematical means of modeling other factors.

Meta-Strategy: The Art of Changing the Uncertainty

In some games, especially real-world “games” such as corporate takeovers or warfare, the strategist has the opportunity to change the uncertainty. He might choose to increase or decrease his own uncertainty, and/or increase or decrease his opponent’s uncertainty. This is meta-strategy.

Whereas strategy is the art of decision-making in conditions of uncertainty, meta-strategy is the art of changing uncertainty in conditions of decision-making. When people refer to people “playing 4D chess" often what’s meant is people applying meta-strategy. It is changing the rules of the game in your favor.

Where possible, a strategist will typically prefer to decrease his uncertainty while (if opposed) increasing his opponent’s uncertainty. One method of doing so is to create dilemmas. A dilemma is a problem that has no solution, only tradeoffs. For instance, imagine an infantry company commander is confronting a tank battalion. If the infantry company sets up in a forest, it presents the tank battalion with a dilemma: fight in unfavorable terrain, or bypass the forest and leave enemy troops in its rear. This creates uncertainty in the tank commander. He must consider:

• The Confusion presented by the forested terrain, capable of hiding his enemy

• The Complexity presented to logistical efforts if an enemy unit is in his rear

• The Choices that the company commander might make if bypassed

And so on and so on. Creating meta-strategic dilemmas is an important tool. However, often it won’t be possible for the strategist to decrease his uncertainty without the opponent enjoying a similar benefit. In this case, the particular characteristics of the strategist and his opponent will determine what he does.

• A strategist might be willing to increase his uncertainty in a category if it means increasing his opponent’s uncertainty by even more. A swordsman might suggest that he and his opponent duel blindfolded if he has great hearing and his opponent is partly deaf. A brigade commander might decide to have his reconnaissance force engage the enemy’s recon troops, possibly destroying both their recon forces, if he knows that he has satellite intel to fall back on and his opponent does not.

• A strategist might be willing to decrease his opponent’s uncertainty in a category if it means decreasing his own uncertainty by even more. A strategist might share valuable information with his opponent via a double agent, hoping to gain more valuable information from the now-trusted agent than he disclosed.

• If a strategist has a higher risk tolerance than his opponent, he might be willing to increase his uncertainty from Chance if it means increasing his opponent’s uncertainty from Chance by the same amount (or sometimes less). The opposite is true if his risk tolerance is low. In Poker, a player with a lot of chips might make a high bet to deter opponents who cannot afford losses of such magnitude.

• If a strategist has superior coup d'oiel than his opponent, he might be willing to increase his uncertainty from Complexity if it means increasing his opponent’s y the same amount, or vice versa. In Chess, a player who excels at (what chess aficionados call) tactical play might choose a very rare, complex, and under-studied opening in order to gain an edge over a player with greater command of traditional openings but less tactical skill.

• If a strategist knows his opponent better than his opponent knows him, he might be willing to increase his uncertainty from Choice if it means increasing his opponent’s by the same amount, or vice versa. In Rock Paper Scissors, some players tend to habitually throw the same play over time. When facing such an opponent, a strategist might ask for “best 3 out of 5” (e.g. more uncertainty from Choice) expecting that he’ll be better able to predict his opponent than vice versa.

In a future essay, we’ll examine attrition, maneuver, shock, OODA loops, and other strategic concepts from the perspective of this framework.