Combinatorial Game Theory Workbench

Hackenbush Lab

You play

You move first

A small graph can hide a surprisingly subtle game. Cut an edge, watch unsupported branches fall, and inspect the exact game value behind the move. Some positions are surreal numbers; others need the richer language of short games.

First visit · from a move to its mathematical explanation

Choose a small position from Numbers or Nimbers. Compare a red–blue number with a green impartial game.
Use Play to test a move, or Create to change one edge. Follow the board's cut rules and compare what remains.
Switch to Create for Position Analysis, then turn on Live reasoning. Compare the options with the reduced game form, then try a sum of components.

Finite positions are solved exactly when they fit the search budget. Stable anchors are a nonstandard extension; infinite and loopy references have separately stated support. What the engine supports →

Current Value -

Type -

Outcome -

Turn Blue

Status Ready

Blue cuts blue edges Red cuts red edges Green: either player Edges with no path to the ground fall.

Capabilities

Roadmap

What this Hackenbush Lab supports today, what's partial, and what's coming. For the full account of the theory and the honest limits, read the status & theory doc →

Value

Position Analysis

- Build or load a position to evaluate it.

Exact Form -

Exact Number -

Mean -

Temperature -

Strategic Outcome -

Current Turn Result -

Temperature

0

Theory

Deep Analysis

Extra Analysis

Structure & Reasoning

The same position read two other ways: as a ring of connections, and as the chain of steps that turns it into a value.

Moves

Best Replies

Blue Moves

Red Moves

Data

Position JSON

Session Setup mode

Play Status Choose a side, choose who starts, then start a match.

Self-Test Results

Roadmap

Position Analysis

Deep Analysis

Structure & Reasoning

Best Replies

Blue Moves

Red Moves

Position JSON

Best Replies

Blue Moves

Red Moves