Ludologium
A computational atlas of play

Small rules.
Many possibilities.

A game is a system of rules that produces behavior. Explore what emerges—from a single decision to the structure of an entire game.

Compare two games ↓Explore the simulators ↗
BOARD GAMES · VIDEO GAMES · HISTORY · GAME THEORY
Game systems, made tangible.
About the imagery

Original AI-generated editorial illustrations made for Ludologium. These are illustrative compositions, not photographs of collection objects or historical records.

Image provenance · Rights & reuse

From objects to consequences

One move changes
what comes next.

The pieces give a game its form. Its rules give each decision a consequence. Try a small example.

A rule in motionTic-tac-toe / X to move
6

legal replies
for O

X plays top right. O has six legal replies, but must play bottom left to block X’s next-move win.

Tap an empty square to try another move. The dashed ring shows the threatened square.

20Indexed archetypes
42Mechanics
30Historical artifacts
18Patent lineages
6Simulators
10Data streams
Read the structure beneath the theme

The Game Genome Laboratory

Compare how two games handle information, resources, interaction and victory. Each dimension keeps its explanation.

Open full Genome Atlas ↗
COMPARATIVE STUDY10 SELECTABLE GAME RECORDS

Klaus Teuber · 1995 · 3–4 (Expandable to 6) players · 60–90 min

Variable hex topography with stochastic output and non-binding negotiation.

COMPLEXITY WEIGHT 2.30 / 5
Read game summary

Catan is an engine-building race where resource production is determined by stochastic bell-curve dice rolls upon a modular hex grid, driven by trade and network blocking.

Monopoly (The Landlord's Game)

Elizabeth Magie (1904) / Charles Darrow (1935) · 1935 · 2–8 players · 120–240 min (House rules: 360+ min)

Closed-loop circular track with rent extraction, capital concentration, and player elimination.

COMPLEXITY WEIGHT 1.65 / 5
Read game summary

Originally designed by Georgist Elizabeth Magie to demonstrate how monopolistic land ownership impoverishes society, commercial Monopoly turns rent extraction into an unconstrained zero-sum elimination mechanism.

Comparing Catan and Monopoly (The Landlord's Game) across ten dimensions.

Intensity: 0–10 · Existing atlas classifications, not quality ratings. The qualitative descriptions explain what each score represents.

InformationA / Catan: Partially Observable5 / 10B / Monopoly (The Landlord's Game): Perfect Information2 / 10

A / Catan: Public board position and dice probabilities; private development card hands and hidden victory points.

B / Monopoly (The Landlord's Game): All cash, deeds, mortgages, and board positions are fully public.

RandomnessA / Catan: Output Randomness (2d6 Gaussian)7 / 10B / Monopoly (The Landlord's Game): Stochastic Roll-and-Move (2d6)8 / 10

A / Catan: Stochastic resource generation governed by 2d6 probability distribution (peaks at 7, troughs at 2/12).

B / Monopoly (The Landlord's Game): Movement is entirely dictated by 2d6 rolls with jail doubling rule and Chance/Community Chest draw decks.

Spatial StructureA / Catan: Modular Hexagonal Network8 / 10B / Monopoly (The Landlord's Game): 1D Closed Linear Loop3 / 10

A / Catan: Variable hex terrain tiles with vertex settlements and edge road topology.

B / Monopoly (The Landlord's Game): 40-space perimeter track with fixed property groupings, railroads, utilities, and corner penalty nodes.

ResourcesA / Catan: Scarce & Differentiated8 / 10B / Monopoly (The Landlord's Game): Fiat Currency & Real Estate7 / 10

A / Catan: 5 discrete input commodities (Wood, Brick, Wheat, Sheep, Ore) with asymmetric tile distribution.

B / Monopoly (The Landlord's Game): Fixed nominal money supply, finite housing supply (32 houses, 12 hotels) enabling artificial house scarcity.

InteractionA / Catan: Barter Trade & Spatial Blocking8 / 10B / Monopoly (The Landlord's Game): Zero-Sum Rent Extraction9 / 10

A / Catan: Cooperative positive-sum trading mixed with zero-sum road network blocking and Robber taxation.

B / Monopoly (The Landlord's Game): Mandatory rent payment on landing; unconstrained property auctions and mortgaging.

Victory StructureA / Catan: Point Threshold (10 Victory Points)6 / 10B / Monopoly (The Landlord's Game): Last Player Standing (Total Bankruptcy)10 / 10

A / Catan: Non-elimination race to 10 victory points derived from infrastructure, longest road, and cards.

B / Monopoly (The Landlord's Game): Victory is achieved solely by bankrupting all rival players through compounding rent liabilities.

NegotiationA / Catan: Explicit & Non-Binding9 / 10B / Monopoly (The Landlord's Game): Unconstrained Asset Trading7 / 10

A / Catan: Active bilateral and multilateral trade bargaining during the active player's turn.

B / Monopoly (The Landlord's Game): Players can trade properties and cash at arbitrary prices to complete color monopolies.

Feedback LoopsA / Catan: Positive Compounding Engine8 / 10B / Monopoly (The Landlord's Game): Extreme Positive Runaway10 / 10

A / Catan: More settlements generate more resources, accelerating subsequent construction (mitigated by Robber hand limit).

B / Monopoly (The Landlord's Game): Capital concentration allows full house development, which increases rents by 400–1200%, bankrupting opponents exponentially.

Player EliminationA / Catan: Absent0 / 10B / Monopoly (The Landlord's Game): Present (Severe & Early)10 / 10

A / Catan: All players remain active until a victor reaches 10 VP, though runaway leaders can starve trailing players.

B / Monopoly (The Landlord's Game): Players who cannot satisfy debts are liquidated and forced out of the match.

Tempo StructureA / Catan: Discrete Sequential Turns4 / 10B / Monopoly (The Landlord's Game): Turn-Based Roll & Process3 / 10

A / Catan: Strict turn order with resource roll, trading phase, construction phase.

B / Monopoly (The Landlord's Game): Fixed clockwise turns with instant transaction resolution.

Catan

Mechanics

Modular BoardNetwork BuildingTrading / BarterDice RollingVariable Setup

Game-theoretic concepts

  • Non-Zero-Sum Bargaining
  • Holdout Problem
  • Tragedy of the Commons (Robber)
  • Pareto Efficiency

Monopoly (The Landlord's Game)

Mechanics

Roll and MoveAuction / BiddingSet CollectionPlayer EliminationIncome Transfer

Game-theoretic concepts

  • Monopoly Rent Extraction
  • Capital Accumulation
  • Zero-Sum Liquidation
  • Markov Chain Movement Probabilities
Keep investigatingExplore the mechanics graph ↗Open the Game Theory Lab ↗
Find your way through the atlas

The Architectural Pillars

Formal structures, dynamic simulations, historical artifacts and the systems surrounding play.

Compare two games ↓Understand a mechanic ↗Trace a game’s history ↗
I / 6 destinations

Structural Foundations

Understand what a game is made of, and how its rules relate to other systems.

Structure / tile & pawn
The Game Genome

10-dimensional system architecture decomposition

GenomeThe Mechanics Graph

40+ formal mechanics & neighborhood clusters

HypergraphThe Rule DNA

State transition grammar & emergent behaviors

GrammarRulebook Diff

Edition comparisons & incentive shifts

Version ControlGame Lineages

Typed genealogical trees with evidentiary links

PhylogenyConvergent Evolution

Independent structural convergence across history

Morphology
II / 6 destinations

Dynamics & Mathematics

Explore what rules produce: decisions, incentives, strategies and feedback.

Dynamics / chance
Monopoly Autopsy

Elizabeth Magie's Landlord's Game vs commercial Monopoly

Georgist LabGame Theory Lab

Executable Prisoner's Dilemma, Stag Hunt & Kuhn Poker

OpenSpielThe Strategy Space

Branching complexity, Minimax, MCTS & RL policies

Tree SearchChess Observatory & Simulator

Grandmaster literary move oracle & official rating distributions

Move Oracle & FIDECompetitive Meta Engine

MOBA balance perturbations & counter-topologies

Patch TelemetryThe Design Lab

Interactive rules modifier & sandbox simulator

Monte Carlo
III / 4 destinations

Archaeology & Culture

Follow games through their histories, interpretations and preservation.

Memory / board & stone
Archaeology Wing

The Table Through Time (Smithsonian & LOC open access)

1700–2000Preservation Wing

LOC preservation framework & hardware decay radar

EmulationScholarly Monographs

Peer-reviewed papers with APA 7th citations

5 TreatisesLudic Lexicon

Formal computational definitions & mathematical models

32 Terms
IV / 6 destinations

Industry, Telemetry & Law

Study the systems around games: players, updates, ownership and markets.

Industry / controller
Achievement Friction Map

Global milestone drop-off funnels & player attrition

Steam TelemetryThe Living Game

Active player pulses, patch cadences & service model

Live ConcurrencyPatch Genealogy

Downstream systemic mutations across patch histories

Rule EvolutionGame Patent Atlas

Controller & mechanics patent lineage trees

USPTO RecordsContent-Rating Graph

Ontological evolution of rating descriptors

ESRB 1994–2026The Business of Play

XBRL financial graph & publisher M&A networks

SEC EDGAR
Questions lead to questions

A closer look
at play.

Follow an explanation, examine its source, then take the next question.

What is Ludologium and how does it study games computationally?

Ludologium is a computational atlas of games, play, mechanics, and strategy that models games as formal state transition systems. Rather than operating as a subjective review archive, it deconstructs how explicit rules manufacture incentives, drive player behaviors, and produce emergent strategic equilibria across board games, video games, and historical artifacts.

INQ-LU-01 · Core Thesis

Salen, K., & Zimmerman, E. (2004) · View source

Salen, K., & Zimmerman, E. (2004). Rules of Play: Game Design Fundamentals. MIT Press.

The foundational design text formalizing how games operate as rule-based systems producing emergent experience.

How does the Game Genome decompose games across structural dimensions?

The Game Genome breaks games down across ten canonical architectural dimensions: information visibility, randomness type, spatial topology, resource scarcity, interaction models, victory conditions, negotiation rules, feedback loops, elimination constraints, and tempo structures. This enables structural system comparisons between disparate titles like Catan, Monopoly, and Chess regardless of superficial theme differences.

INQ-LU-01.A · Game Genome

Engelstein, G., & Shalev, J. (2019) · View source

Engelstein, G., & Shalev, J. (2019). Building Blocks of Tabletop Game Design. CRC Press.

Systematic classification of game mechanics into formal structural categories.

Why does Ludologium analyze Monopoly as a mathematical autopsy?

Monopoly was originally patented by Elizabeth Magie in 1904 as The Landlord's Game to demonstrate how unearned land rents concentrate capital and impoverish society. Computational simulations prove that casual house rules distort the game's termination probability, turning a 45-minute Georgist economic demonstration into a multi-hour war of attrition through artificial liquidity injections.

INQ-LU-01.B · Economic Systems

Magie, E. J. (1904) · View source

Magie, E. J. (1904). Game-board (U.S. Patent No. 748,626). U.S. Patent and Trademark Office.

Original patent establishing the anti-monopoly educational purpose of the Landlord's Game.

How does the Game Theory Lab utilize DeepMind's OpenSpiel framework?

The Game Theory Lab implements executable reinforcement learning and game-theoretic environments based on DeepMind's OpenSpiel framework. It allows users to simulate thousands of iterations across the Prisoner's Dilemma, Stag Hunt, Kuhn Poker, and Rubinstein Bargaining to observe how strategic cooperation, bluffing frequencies, and subgame perfect equilibria emerge under varying discount horizons.

INQ-LU-02 · Game Theory

Lanctot, M., et al. (2019) · View source

Lanctot, M., et al. (2019). OpenSpiel: A Framework for Reinforcement Learning in Games. arXiv preprint arXiv:1908.09453.

DeepMind's open-source library for research in game theory and multi-agent reinforcement learning.

Why does Tit-for-Tat outperform predatory strategies in repeated games?

Tit-for-Tat succeeds in repeated Prisoner's Dilemma tournaments because it satisfies four mathematical principles: it is nice by never defecting first, retaliatory by punishing immediate betrayal, forgiving by restoring cooperation instantly, and clear by being predictable. When the shadow of the future is long, mutual cooperation yields strictly higher cumulative payoffs.

INQ-LU-02.A · Cooperation Dynamics

Axelrod, R. (1984) · View source

Axelrod, R. (1984). The Evolution of Cooperation. Basic Books.

Axelrod's classic tournament showing the mathematical dominance of reciprocity over unconstrained predation.

What does the Chess Observatory reveal about global rating distributions?

The Chess Observatory analyzes official FIDE downloadable rating lists to track geographic player densities, title distributions, and rating inflation dynamics. It reveals a high statistical correlation between rapid and standard ratings, while charting the historic acceleration of grandmaster title attainment ages driven by modern engine preparation and digital training infrastructure.

INQ-LU-03 · FIDE Analytics

International Chess Federation (FIDE) (2024) · View source

International Chess Federation. (2024). Official Downloadable Rating Lists. FIDE.

The canonical global repository for standard, rapid, and blitz chess rating distributions.