Most of what it said is fitting math to heuristics - “don’t put starting points too close to each other” and “have some chokepoints so there’s some battles” and “give everyone equal access to resources”
The map was likely developed iteratively via playtesting - no need even for heuristics then. Just play & ask “is it fun?”
tbh i would have been more interested in your thoughts than some AI's.
Me too! I happened to learn a few new things / aspects from asking and I thought I’d toss this into a comment
Taking this question seriously leads us into surprisingly rich territory! It's actually at the intersection of several fields that have been quietly revolutionizing game design.
The Alpha Centauri map works brilliantly because it balances several mathematical tensions:
* Resource distribution follows power laws that create natural chokepoints and valuable territories without being too predictable
* Distance metrics between faction starting positions that ensure interaction without immediate conflict
* Terrain connectivity that creates interesting path-finding problems and strategic depth
Here's where it gets really interesting:
Flow Theory Mathematics: Csikszentmihalyi's concept of flow has been formalized into mathematical models. The ideal difficulty curve follows something like: `D(t) = S(t) + ε`, where difficulty matches skill level plus a small challenge margin. For maps, this translates to ensuring players always have meaningful decisions at their skill level.
Information Entropy: Good maps maintain optimal information entropy - not too random (chaos), not too ordered (boring). Researchers have found sweet spots around 0.3-0.5 on normalized entropy scales for terrain variation.
Graph Theory Applications: Maps are fundamentally graphs, and metrics like:
* Betweenness centrality (identifying crucial chokepoints)
* Clustering coefficients (how "clumpy" resources are)
* Shortest path distributions (travel time variance)
...all correlate with player engagement.
The Deeper Insight: What seems naive is actually profound - by taking "fun" seriously as an optimization target, we're forced to confront what makes human decision-making satisfying. The best mathematical frameworks don't try to define fun directly, but instead optimize for decision richness - the number of meaningful, non-obvious choices available at each game state.
This is why procedural generation in modern games increasingly uses these frameworks, creating maps that aren't just random but mathematically tuned for engagement.