About Tetgame

What is Tetgame?

Tetgame is a three-dimensional strategy game built from tetrahedrons. Players place tets, claim sockets with tokens, capture paths between tokens, and work upward toward sub-tetrahedron and whole-tet ownership.

Unlike games played on a fixed board, Tetgame's field is part of the contest. Each new tet can create more places to play, more ways to block, and more future choices to evaluate.

Plain idea:
Chess and Go are deep games played inside fences. Tetgame is a deep game where the fence can move, grow, and become part of the strategy.

The game in one minute

Each turn normally gives a player two actions.
A player may place a tet, place a token, or, when legal, remove a tet or token.
Tokens placed on related sockets can capture paths between them.
Captured paths can combine into sub-tetrahedral regions.
Captured subs can combine into ownership of a whole tet.
Some token placements can auto-fill connecting midpoint sockets, creating sudden tactical swings.
A removed tet or token is treated as spent for the match so players cannot bounce the same piece in and out forever.

Why Tetgame scales differently

In Checkers, Chess, and Go, the board is fixed. The game tree may be enormous, but the container is known. Tetgame changes the problem: every expansion can create new future options, so the strategic burden is not only finding a good move, but shaping the future board itself.

Fixed vs. Dynamic:In Chess/Go, the board is a container that empties or fills. In Tetgame, the board is the product, adding ~5 new connection points every turn.

Dual-Action Multiplier:A single Tetgame turn is technically two moves. In game theory, this results in b² complexity for a single ply.

Dimensionality:3D tetrahedral clusters create more interdependent "scoring layers" than 2D networks, forcing AI to evaluate volume ownership rather than just path connectivity.

Comparative Complexity Analysis at a glance

A comparison of state-space complexity and branching factors between classic finite board games and the expanding recursive systems of Trigame and Tetgame.

Game	Board bounds	Growth character	Useful comparison	Avg. Branching Factor (b)	State-Space Complexity
Checkers	Fixed 8×8 board	Shrinking	Large but bounded; pieces leave the board over time.	~3	~10²⁰
Chess	Fixed 8×8 board	Finite	Vast search tree, but all play remains inside the same square field.	~10⁴⁶	Fixed (8x8) - Shrinking
Go	Fixed 19×19 board	Filling	Huge positional space, but legal placements generally decrease as the board fills.	~10¹⁷⁰	Fixed (19x19) - Filling
Trigame	Expanding 2D field	Recursive	Locally finite, globally explosive through tile and socket expansion.	Infinite	Expanding (Recursive 2D)
Tetgame	Expanding 3D field	Dual-action 3D	Combines recursive expansion with volumetric scoring layers.	Infinite	Expanding (Dual-Action 3D)

The “Go Horizon”

A useful way to describe Tetgame's scale is the Go Horizon: the point where an illustrative Tetgame move tree becomes comparable to, or larger than, the estimated state-space of a 19×19 Go board.

C(n) ≈ Product of expanding branch choices across two-action turns In plainer terms: as turns pass, each new tet can add future choices, and each turn may combine two choices.

This is why Tetgame AI cannot rely on brute force. A Rabbot must use priorities: where to grow, where to block, when to capture, when to deny a center, and when to sacrifice a small path to gain a larger volume.

The Complexity Equation

The state-space complexity of Tetgame ( $C$ ) at turn $n$ can be modeled by the product of its expanding branching factor across dual-action turns:

C (n) = \prod_{i = 1}^{n} {(b_{i})}^{2}

Where:

$b_{i}$ : The branching factor at turn $i$ . Because each Tet adds ~5 sockets, $b_{i} \approx 20 + 5 i$ .
The Exponent ( $x^{2}$ ): Represents the Dual-Action Multiplier. Since a player takes two distinct actions per turn, the possible outcomes for a single turn are squared.
$\prod$ (Product): Represents the cumulative growth of the game tree as the board expands.

Why Turn 42 is the "Go Horizon"

In Go, the branching factor ( $b \approx 250$ ) decreases as the board fills. In Tetgame, the branching factor increases. By Turn 42:

The average branching factor per action is ~230.
With two actions per turn, the turn-based branching factor is $230^{2} = 52,900$ .
Compounded over 42 turns, this reaches $10^{171}$ , exceeding the total atoms in the observable universe and the entire state space of a 19x19 Go board.

The Multi-Player Complexity Acceleration

Complexity in these systems is driven by the Rate of Expansion. In a 12-player Trigame, the board grows so rapidly that it surpasses the complexity of Go by turn 38. However, Tetgame remains the most computationally dense; even with only 2 players, its dual-action turn structure allows it to reach the 'Go Horizon' faster than a 6-player Trigame match.

Configuration	The Go Horizon (Turn)
Trigame (2 players)	102
Trigame (12 players)	38
Tetgame (2 players)	42
Tetgame (6 players)	26

Tetgame state-space complexity growth showing checkers, chess, and Go horizon markers. — State-space growth

State-space comparison chart for Trigame and Tetgame against classic game horizons. — Trigame vs. Tetgame

Log-log state-space growth chart showing Tetgame crossing the Go horizon. — Log-log growth

Multi-player complexity growth chart comparing Trigame and Tetgame configurations. — Multi-player acceleration

Tetgame Complexity Calculator

Enter the current turn number to see the estimated state-space complexity (C) of the game tree.

Player Turn Number:

Complexity: 10¹⁷¹

This exceeds the total state-space of a 19x19 Go board.

Rabbots and Warrens

Tetgame's computer players are Rabbots. Each Rabbot can have its own temperament, tactical preferences, voice, and scoring priorities.

A Warren is a group of twelve Rabbots. The Alpha Warren is currently being refined so each Rabbot teaches, tests, or stresses a different part of Tetgame strategy.

Current design idea:
Players are not only competitors. They can become engineers and trainers, tuning their Warrens to handle expanding 3D strategy.

Strategy snapshot

Set and spike

Use the first action to create an opportunity and the second to claim it before anyone else can interfere.

Growth control

Place tets to decide where the board can expand, or use corner tokens to block expansion from key faces.

Volume before vanity

A path is useful, but a sub or whole tet can outweigh several small local gains.

Adaptive forecasting

The strongest play often comes from seeing how today's tet changes the next several turns.

Where the project is now

Current: Alpha Warren tuning

Refining the first Rabbots, testing personality logic, improving game records, and documenting how tokens, paths, subs, and whole-tet captures work.

Next: broader multiplayer shape

Continuing toward richer human, Rabbot, and mixed-player matches, with better help, clearer records, and stronger Warren editing tools.

Plain summary: Tetgame is locally understandable but globally explosive. A single tet is a small puzzle; a growing match becomes a living 3D network of choices, blocks, captures, and future consequences.