A tiny universe that learned to play chess.

We gave chess its own physics. Pieces have mass and pull along the lines they can move. It learned the rest by playing itself.

Kepler's view
—
ku, pawn = 1
Field
White pulls harder Black pulls harder

Deeper tint, stronger pull.

Kepler
1abcdefgh2345678
You
White pulls harder Black pulls harder
Weights in this universe
Pawn1.0Knight2.7Bishop3.1Rook4.2Queen7.4
Area shows weight, pawn = 1. Light speed: pull travels at most 2 moves.
01 · How it works

Physics, rebuilt for a chessboard.

We wrote the laws. It found the constants itself, in 85,500 games of self-play.

Mass
17.4
Piece weight
Learned by the engine. Pawn = 1.
Gravity
Pull along its moves
Stops at the first piece in the way.
Light speed
12
2 moves
Pull reaches at most 2 moves.
Field
Who owns a square
Whoever pulls harder on it.
1abcdefgh2345678
Worked example The rook pulls up to its own pawn, and no further.

Named after Johannes Kepler, who found the planets' laws in observations. Kepler-64 finds its constants in its own games.

02 · What's inside

It knows space, not chess.

Not inside
  • Piece-square tables
  • King-safety rules
  • Pawn-structure rules
  • An opening book
  • A neural network trained on chess games
Inside
  • One field
  • About a dozen learned numbers
53%

Gen 3 scored 53% against Stockfish 19 limited to its 2100 setting, at 30 seconds plus 0.3 per move, over 200 games.

2100 is Stockfish's own setting, not a human rating. The opponent on this page plays a fixed search size; its strength isn't measured yet.

03 · The Law Ledger

Every law has to earn its place.

Each law played against a copy of the engine without it. Laws that helped stayed. The rest became alternate universes.

Kept
Pull follows the moves
Beats counting pieces alone, by far
Kept
Squares belong to the stronger pull
Control of space
Came back
Defenders hold pieces together
Cut at first, useful later
Rejected
Captures absorb weight
Better switched off
PNBRQ
Hunger
Rejected twice
A king torn apart by pull
Two designs, neither helped
PNBRQ
Roche
PNBRQ
Undertow

Open source, all of it.

The engine, the training runs and every number on this page are on GitHub.

Open problems
A crescent Earth rising over the grey, cratered horizon of the Moon, seen from Apollo 17 in lunar orbit.

Earth rising over the Moon, Apollo 17, 1972 · NASA