The central thesis of 4X strategy: each turn is an investment decision. Your production is capital; the available actions (economy, expansion, research, defense, offense) are competing investments; the right comparison metric is MIRR — return that is time-adjusted, risk-adjusted, and reinvested at your empire’s own growth rate. Rank the options by MIRR, fund the top, reassess as the state changes. This is not a metaphor — the mathematical structure is identical to a firm allocating capital, which is why it is Risk and Entrepreneurship applied to a game.
Links (up): Risk and Entrepreneurship (the economics parent — profit as the reward for bearing risk; time preference), Value and Profit, Insurance (hedging research bets) Sibling (cousin instrument): Monopoly Frontier-Trade Theory & Subgraph Investment Optimization — same capital-allocation root, a non-4X game; Markowitz frontier / EPT is the metric there, MIRR is the metric here.
A thesis page (portable, source-independent). The worked numbers, per-game tiers, and simulator results live in the specimens it cites below — this page states the claim; they are its evidence.
Optimal 4X play reduces to the same problem as optimal business management: allocate scarce capital (production) to the investment with the highest risk-adjusted return (MIRR) each period (turn), reassessing as conditions change. The player who sees each turn as a capital-allocation decision beats the player running cached heuristics (“always factories first,” “rush colony ships”) — the heuristics are the deontological cache; the MIRR calculation is the consequentialist test you run when the situation deviates from the default.
| Business concept | 4X equivalent |
|---|---|
| Revenue | Production per turn |
| Capital expenditure | Economy / expansion / unit investment |
| R&D spending | Tech or spell research |
| Market expansion | Colony ships / new cities |
| Defense / insurance | Missile bases / garrisons |
| Acquisitions | Conquest |
| Opportunity cost | What you didn’t build this turn |
| MIRR | The common currency for comparing all of the above |
| Metric | Measures | Blind spot |
|---|---|---|
| ROI | Return per unit invested | No time dimension — when do returns arrive? |
| NPV | Returns discounted to present | Requires an arbitrary discount rate |
| IRR | Rate making NPV zero | Assumes reinvestment at the IRR itself (unrealistic) |
| MIRR | Effective return assuming reinvestment at your actual growth rate | Requires estimating your empire’s growth rate |
MIRR = (FV_returns / PV_costs)^(1/N) − 1
FV_returns compounded at YOUR empire's current growth rate (the reinvestment rate)
N = turns
The load-bearing insight: the reinvestment rate is your empire’s growth rate, not the investment’s own return. A cheap immediate return (a factory) and a large delayed one (a colony) both get reinvested at whatever rate you’re compounding at — so MIRR normalizes every option to your actual situation and makes them apples-to-apples across categories.
Each turn:
1. Assess state (map, neighbors, tech/spell tree, current production)
2. For each investment category: estimate MIRR + attach a confidence level
(high for economy/expansion; lower for military/diplomacy)
3. Rank by MIRR
4. Fund the top option
— exception: mandatory minimums (some research, some defense)
— exception: if the top two are close, split (diversify against uncertainty)
5. Reassess next turn (state changed → re-rank)
You don’t need MIRR to the decimal — you need the ranking right. Order-of-magnitude estimates suffice for correct decision ordering, which is the whole game. Real constraints keep the non-dominated set small (≈2–3 live options per turn); the framework’s job is to prune, not to oracle.
The economics parent (Risk and Entrepreneurship) says profit is the reward for bearing risk correctly under uncertainty, with returns subject to time preference. A 4X opening is that problem with the noise removed — no market swings, no competitors in the single-player opening, deterministic mechanics. It is a clean test bench: the safe investment (factory) vs the entrepreneurial bet (colony) with a crossover where marginal safe return drops below marginal entrepreneurial return — the same structure as “should a business reinvest or expand?” If MIRR ranks correctly here, the framework earns trust for the messier domains it abstracts.
mirr.py). Contributes: empirical factory-vs-colony crossover turns per race (Klackon T8, Sakkra T13, Human/Psilon T25) and the counter-intuitive finding that a production bonus helps colonies more than factories (more growth headroom); plus the model-gap list.masterofmagic repo (external) — Contributes: the Markov battle simulator grounding tier dominance (T5 Great Drake wins 100% vs everything T3 and below), which is what makes “reach the tier first” a real return.