A Convergent Abstract Strategy Game is a perfect-information system in which optimal play necessarily produces structural compression, irreversible commitment, temporal tension, and structural inevitability. Depth not by design decree, but as inevitable consequence of minimal structure.
Perfect Information
Complete Observability
All game-relevant state is visible, explicit, and unambiguous to all players at all times.
Deterministic State Transition
Given a game state and a legal action, the resulting game state is uniquely determined.
State Sufficiency
Legality of actions and game outcomes depend only on the current game state, not on how it was reached.
Finiteness & Decidability
Bounded Reachable State Space
The total number of distinct game states reachable from the initial state is finite.
Non-Abusive Draws
Mechanisms must prevent a player from forcing eternal avoidance or perpetual cycling while in a losing position.
Forced Termination
If a player is in a losing position, optimal opposition must be able to force a terminal state.
Irreversible Progress
Permanent Consequences
Some player actions must have permanent, non-undoable effects that meaningfully reduce or reshape future strategic possibilities.
Structural Convergence
Inevitable Narrowing
The interplay of rules and irreversibility ensures that optimal play cannot indefinitely postpone decisive interaction, rather the space of viable continuations narrows over time.
Necessary Consequences
From these four defining requirements alone, the following properties must emerge under optimal play:
These are not designed features. They are inevitable consequences of the structure.