Making uncertainty tractable

Today's wargames, heirs to the Kriegsspiel, are required in the professional military environment to have an architecture that makes it straightforward to extract the data they generate and to analyse both the decisions taken and their consequences. Hence the combat resolution algorithms, frequently based on stochastic assignment, which make playing out a scenario look like a mere exercise in computation: choosing one path among all the possible ones, where every branch is a decision and resolving that scenario successfully (an engagement, an operation or a battle) is simply finding the optimal path. Seen this way, a wargame would be a computationally tractable model and therefore a predictable one. What follows sets out to refute that premise.

01 · Tractable is not predictable

When a contested situation is formalised rigorously, the temptation is to build a simulator: a system that, given certain initial conditions, returns a result, and always the same one, since repeatability tends to be taken as a sign of rigour. That intuition is misleading and it is worth saying so from the outset. A deterministic simulator does not predict how the conflict will develop or resolve; it predicts what the simulator itself will do. That it always returns the same result says nothing about the world it formalises; it demonstrates that its rules are well defined. Nobody who has seen a real conflict expects the same deployment, executed twice, to unfold and conclude in the same way.

Three distinct properties live together beneath this confusion. Determinism, which is a property of the model: the same input always produces the same trace. Tractability, which also belongs to the model: it allows the model to be run, sampled and inspected, every result to be traced back to explicit rules, and the range of validity of those rules to be declared. Both depend on the design of the model and can be guaranteed. Predictability, by contrast, does not belong to the model but to the world. It requires the initial state to determine the evolution of the system sufficiently. In a contested environment that condition is not met: the initial state is never epistemologically complete, and beyond that, the evolution of the conflict itself generates information that did not exist at the initial instant. No modelling eliminates that uncertainty; it can only manage it within the declared limits of the model. Predictability, therefore, can never be promised.

From this follows the corollary that governs everything below: a model can be simultaneously deterministic, tractable and utterly unpredictable, with no contradiction whatsoever. Determinism and tractability depend on the engineer; predictability does not.

02 · The game is not computable

Having discarded the study of a single trajectory, intuition offers a second possibility: if one run is not enough, run them all. Branch at every decision, walk the complete tree, return the whole space instead of an arbitrary branch.

If we do the arithmetic, for a deliberately modest scenario, barely ten units where each has ten possible actions, a single turn contains 10¹⁰ decision configurations; eight turns chained together give 10⁸⁰ possibilities, the same order of magnitude as the estimated number of atoms in the observable universe.

That calculation has been generous to anyone defending enumeration as a solution. Only one side decides, the adversary is frozen, there is no chance in the resolution, no imperfect information, no simultaneous actions, no continuous space, no open-ended force allocations; everything that a model of a real scenario adds, and that multiplies this space by dozens of further orders of magnitude.

This is not a difficulty that next year's advance in computing power is going to solve; there is no universe large enough to hold the enumeration. Exhaustive enumeration stops being an algorithm and becomes a physical impossibility. Whoever promises to explore the complete space is not describing a capability; he is revealing that he has not done the arithmetic.

03 · Structuring uncertainty

We have already seen that the space cannot be enumerated. Nor would that be necessary in order to address the problem. Focusing on models of contested environments involving decision-making, particularly open conflicts or what is called the grey zone, although this proposal can also be extended to other contexts, we find that most of the volume of the space is irrelevant: continuations that no doctrine, no logistics and no rational adversary would produce. The probability mass sits in a concentrated region.

Consider a given initial state, a question, a declared range of validity; consider these values anchored. This anchor is not a renunciation of exploring, it is what allows us to explore and to draw out a meaning of any value. Without an anchor there is no exploration, only a random walk.

Starting from that anchored question and having explored the space, what we obtain is not a computational result but a measure: P(Y | anchor, decisions). And its uncertainty decomposes into three parts of different natures: that of the world (which is irreducible; it is represented, not eliminated), that of the model (epistemic; it is ours and is reduced by work), and that of the sampling (numerical; it decays with the number of runs). To predict would require σ²world to be small; that the world itself, once the initial question is anchored, barely dispersed. It does not, and no amount of work will change that, because that variance belongs to the phenomenon and not to the model. Tractability is a different demand and it is within our reach: it is making σ²model and σ²sampling known and bounded; the first by submitting the assumptions to refutation and declaring the range of validity, the second by raising the number of runs until their contribution is negligible.

It is sampling from the anchored initial question that explores the space of outcomes. And it is a viable solution, but there is a second space that no amount of arithmetic exhausts, because no prior model of it exists: the decision-making of the actors under pressure. That second space is not sampled. It is exposed and observed.

04 · Experiment, educate and exercise

The space of outcomes is sampled. An organisation's space of decisions under pressure is not sampled; it is exposed. How? By putting real people to decide inside the tractable model.

The three «E»s are the three uses of that exposure, and the same instrument serves for all of them:

To experiment is to try out courses of action, tactics and assumptions, and to see the distribution of what they produce. It is σ²model under scrutiny: the exercise refutes the assumption.

To educate is to build the capacity to decide under pressure, by exposing the decision-maker to situations where there is no optimal answer, because as we have seen the space is not computable. One learns to decide under irreducible uncertainty, not to get it right. Judgement is trained because there is no solution to memorise.

To exercise is to train teams and procedures under pressure in controlled environments and to observe when and how coordination and cohesion break down. The aim is not to memorise plans or templates, since courses of action are not repeatable.

This leads us to conclude that the key concept is exploration; not the exploration of the space, since that is impossible. What is done is to anchor the point of departure, and from that anchor to explore through experiment, education and exercise. The space is not explored; exploration proceeds from an anchor.