Pillar 01 · 10-Dimensional Classification
The Canonical Game Genome Atlas
Compare games not by subjective ratings, but by formal architecture. Observe how Catan, Monopoly, Pandemic, and Chess differ in information observability, stochastic feedback, and spatial topology.
"Variable hex topography with stochastic output and non-binding negotiation."
SYSTEM DIFF
M
"Closed-loop circular track with rent extraction, capital concentration, and player elimination."
10-Dimensional Structural Decomposition
Information
5/10|2/10
Partially Observable
Public board position and dice probabilities; private development card hands and hidden victory points.
Perfect Information
All cash, deeds, mortgages, and board positions are fully public.
Randomness
7/10|8/10
Output Randomness (2d6 Gaussian)
Stochastic resource generation governed by 2d6 probability distribution (peaks at 7, troughs at 2/12).
Stochastic Roll-and-Move (2d6)
Movement is entirely dictated by 2d6 rolls with jail doubling rule and Chance/Community Chest draw decks.
Spatial Structure
8/10|3/10
Modular Hexagonal Network
Variable hex terrain tiles with vertex settlements and edge road topology.
1D Closed Linear Loop
40-space perimeter track with fixed property groupings, railroads, utilities, and corner penalty nodes.
Resources
8/10|7/10
Scarce & Differentiated
5 discrete input commodities (Wood, Brick, Wheat, Sheep, Ore) with asymmetric tile distribution.
Fiat Currency & Real Estate
Fixed nominal money supply, finite housing supply (32 houses, 12 hotels) enabling artificial house scarcity.
Interaction
8/10|9/10
Barter Trade & Spatial Blocking
Cooperative positive-sum trading mixed with zero-sum road network blocking and Robber taxation.
Zero-Sum Rent Extraction
Mandatory rent payment on landing; unconstrained property auctions and mortgaging.
Victory Structure
6/10|10/10
Point Threshold (10 Victory Points)
Non-elimination race to 10 victory points derived from infrastructure, longest road, and cards.
Last Player Standing (Total Bankruptcy)
Victory is achieved solely by bankrupting all rival players through compounding rent liabilities.
Negotiation
9/10|7/10
Explicit & Non-Binding
Active bilateral and multilateral trade bargaining during the active player's turn.
Unconstrained Asset Trading
Players can trade properties and cash at arbitrary prices to complete color monopolies.
Feedback Loops
8/10|10/10
Positive Compounding Engine
More settlements generate more resources, accelerating subsequent construction (mitigated by Robber hand limit).
Extreme Positive Runaway
Capital concentration allows full house development, which increases rents by 400–1200%, bankrupting opponents exponentially.
Player Elimination
0/10|10/10
Absent
All players remain active until a victor reaches 10 VP, though runaway leaders can starve trailing players.
Present (Severe & Early)
Players who cannot satisfy debts are liquidated and forced out of the match.
Tempo Structure
4/10|3/10
Discrete Sequential Turns
Strict turn order with resource roll, trading phase, construction phase.
Turn-Based Roll & Process
Fixed clockwise turns with instant transaction resolution.
Catan — Mechanics & Theory
Modular BoardNetwork BuildingTrading / BarterDice RollingVariable Setup
Game-Theoretic Formalisms
- Non-Zero-Sum Bargaining
- Holdout Problem
- Tragedy of the Commons (Robber)
- Pareto Efficiency
Monopoly (The Landlord's Game) — Mechanics & Theory
Roll and MoveAuction / BiddingSet CollectionPlayer EliminationIncome Transfer
Game-Theoretic Formalisms
- Monopoly Rent Extraction
- Capital Accumulation
- Zero-Sum Liquidation
- Markov Chain Movement Probabilities