Bridge across, or loop around. Someone always wins.
GYRE is an original abstract strategy game for two players. The board is a ring of hexagonal cells — concentric rings around an empty centre. One player (Spoke) wins by building an unbroken chain of stones from the inner rim to the outer rim: a bridge across the ring. The other (Gyre) wins by building a chain that wraps all the way around the hole: a loop around it.
On a ring these two goals are topological opposites. When the board fills, exactly one of them is satisfied — never both, never neither. Draws are not rare; they are impossible. That property is proven in the rules and brute-force–verified in the test suite.
GYRE is an engineering answer to the known failure modes of classic games, each closed with a specific piece of mathematics:
| Flaw in older games | How GYRE removes it |
|---|---|
| Draws / stalemates (Chess, Tic-tac-toe) | Impossible — a no-draw theorem guarantees a winner on a full board. |
| First-player advantage (Hex, Go pre-komi) | Neutralised by the swap rule (pie rule): the second player may take the first move. |
| Solvability (Tic-tac-toe, Connect-4, Checkers — all solved) | Generalised Hex-style connection games are PSPACE-complete; scaling the ring keeps it unsolved. |
| Luck dominance (Monopoly, Snakes & Ladders) | Zero randomness — no dice, no cards, no shuffles. |
| Cheatability (hidden hands, hidden scores) | Perfect information — the entire state sits face-up and is publicly auditable. |
| Kingmaking (3+ player games) | Strictly two-player, zero-sum. |
A fuller treatment — including the honest caveats about what is proven versus
merely engineered toward — lives in docs/RULEBOOK.md.
- The board is
Rrings deep andCcells around. Standard size is 7 × 14. - Players are Spoke and Gyre. They alternate placing one stone of their colour on any empty cell. Stones never move and are never removed.
- Spoke wins with a connected chain touching both the inner rim and the outer rim (a radial bridge).
- Gyre wins with a connected chain that encircles the hole (a full loop).
- Swap rule (fairness): Player 1 places the first stone (a Spoke stone). Player 2 then chooses to either keep their side (and play Gyre) or swap (take that stone and play Spoke). This removes first-player advantage.
- Cells are hex-adjacent: each touches up to six neighbours, and the ring wraps around, so each row is a closed circle.
Because draws are impossible, play simply continues until one victory condition appears — and on a full board one always does.
Play in a browser (no build step, no dependencies):
open web/index.html # macOS
# or just double-click web/index.html in your file manager
Hot-seat for two humans, or play against the built-in casual AI. Choose the board size in the top bar.
Run the test suite (Node ≥ 16, no dependencies):
node test/gyre.test.js
# or
npm test
Current status: 21 passed, 0 failed. The suite verifies hex adjacency, bridge/loop detection, mutual exclusion across tens of thousands of partial boards, the no-draw theorem brute-forced over 60,000 random full boards, the swap-rule mechanics, and 4,000 random self-play games (all terminate with exactly one winner).
Regenerate the print-and-play sheets (Python 3):
python3 tools/make_board.py
# writes docs/printable/gyre-7x14.svg and gyre-5x10.svg
gyre/
├── README.md ← you are here
├── LICENSE ← proprietary, All Rights Reserved
├── package.json ← npm metadata (private)
├── CHANGELOG.md
├── AUTHORS
├── src/
│ └── gyre-engine.js ← rules engine (Node + browser, no deps)
├── test/
│ └── gyre.test.js ← self-contained test runner (21 checks)
├── web/
│ └── index.html ← playable client + casual AI
├── docs/
│ ├── RULEBOOK.md ← full rules + the mathematics
│ └── printable/ ← print-and-play SVG boards
│ ├── gyre-7x14.svg
│ └── gyre-5x10.svg
└── tools/
└── make_board.py ← regenerates the printable boards
The engine is dependency-free and runs unchanged under Node (require) and in
the browser (window.GYRE). Every edge the web client draws corresponds to a
real adjacency in the engine, so what you see is exactly what the rules use.
The board is a hex grid wrapped onto a cylinder: R rings (radial axis, with
hard inner/outer boundaries) by C columns (angular axis, which wraps). A
bridge is a connected same-colour component touching both radial
boundaries. A loop is a connected same-colour component whose path
accumulates a full ±C winding around the hole — detected by lifting cell angles
to absolute coordinates and checking for a nonzero multiple of C.
The key fact (a cylindrical cousin of the Hex no-draw theorem): on a filled board, the Spoke colour forms a bridge if and only if the Gyre colour does not form a loop. A radial cut of one colour blocks any angular cut of the other, and vice versa — so exactly one condition holds. This is what makes draws impossible, and it is the property the test suite hammers on directly.
This places GYRE openly in the connection-game lineage of Hex and Y; the contribution is the annular topology, the dual asymmetric win conditions, and the no-draw guarantee carried onto the ring, packaged as a complete, tested, playable game.
Proprietary — Copyright © 2026 Ideatrino. All Rights Reserved.
See LICENSE.
This repository is source-available for evaluation and reference only. No right to use, copy, modify, distribute, or commercialise the Work (including the GYRE name, rules, design, code, and artwork) is granted without prior written permission. For commercial-licensing enquiries, contact ideatrino@proton.me.
Note: this license expresses an "all rights reserved" intent and is not legal advice. For enforceable commercial terms or trademark protection, have a lawyer review or adapt it to your jurisdiction.
Ideatrino · ideatrino@proton.me · 2026