Three men's morris
Morris / mill family · all families · data
Part of the morris (mill) family — see the family page for the scaling table and a playable explorer.
Also known as: Smaller merels, Nine holes, Tapatan, Tant fant, Achi, Alquerque de tres, Tic-tac-toe with movement.
First player wins with perfect play, and only by opening in the centre: the centre is the unique winning first move; the four corners draw and the four edges lose. With the centre opening banned the game is a draw.
| Result | First player wins |
| Strength | Strong |
| Method | Retrograde analysis, Brute-force enumeration |
| Year | — |
| Solved by | Classical result (folklore). The first-player centre win is documented by H. J. R. Murray, A History of Board-Games Other Than Chess (1952), and the game is small enough to verify exhaustively. |
| Source | folklore |
| Board | 3×3 grid of 9 points (3 horizontal + 3 vertical + 2 diagonal lines), 3 pieces per side |
| Distance to result | At most 9 plies total; after the central opening the first player forces the win within 7 further plies. |
Solution history
Section titled “Solution history”| Date | Size or opening | Result | Strength | Credit | Source |
|---|---|---|---|---|---|
| — | standard game | first player wins | Strong | Classical result | source |
One row, derived from the record’s year, solver and primary source; no fuller history is recorded yet.
References
Section titled “References”- Three men’s morris (Wikipedia) — a winning strategy for the first player unless barred from the centre
- Three Men’s Morris (Cyningstan) — history, rules, and Murray’s classification as the ‘smaller merels’
- Enigmatic Code — Headscratcher #245: a Python solver of the centre line (New Scientist, 2023)
Resources
Section titled “Resources”Code
Three men’s morris is the “movement” extension of three-in-a-row (it is to tic-tac-toe what nine men’s morris is to a placement-only mill game). Each player places three pieces, then slides them; a player wins by getting all three on a line (or leaving the opponent with no move). This is a trivial game — well under 10^4 positions, strongly solvable by inspection — so its standing here is the same as tic-tac-toe’s: a classically known result, no solving credit claimed. The first player wins, and only by taking the centre: corners draw and edges lose; with the centre opening banned the game is a draw (which is why most informal rule-sets ban it). The first-player centre win has been understood as folklore for centuries (the board appears in the 1283 Libro de los juegos and in far older carvings); Murray (1952) is the classical reference. This project’s open solver (engine/, the Tapatan ruleset) reproduces the result and contributes the full opening classification (centre wins uniquely; corners draw; edges lose). It is listed only as a reproducible verifier — the game is too trivial to claim as a solve.