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Solved Games

Morris — the mill family

The morris, or mill, family is a line of placement-and-movement games: each player places stones, then slides them along the board’s lines; completing a mill — three in a row — lets you capture an opponent’s stone, and you lose when reduced below three men or left without a legal move. The family scales from a trivial 9-point board up to the 24-point boards of nine men’s, Lasker, and Morabaraba, whose solution databases run to ~10¹¹ positions.

A clean pattern runs through it: the diagonal-free morrises — six men’s, nine men’s, Lasker — are all draws under perfect play; adding diagonal mills (Morabaraba, the twelve men’s morris) tips the game to a first-player win. The tiny three men’s board, which has diagonals, is also a first-player win.

This project’s contribution is six men’s morris: it was absent from the morris-solving literature — which had solved its larger siblings but skipped it — so this is its first published strong solution (a draw, over all 42,372,745 reachable positions).

The family

Section titled “The family”
Game Men Board Positions Result Solved by
Three men’s morris 3 9 pts (diagonals) trivial First player wins folklore (Murray, 1952)
Six men’s morris 6 16 pts 42,372,745 Draw this project (2026)
Nine Men’s Morris 9 24 pts 7,673,759,269 Draw Gasser (1993)
Lasker Morris 10 24 pts 136,476,472,674 Draw Stahlhacke (2003)
Morabaraba 12 24 pts + diagonals ~112,000,000,000 First player wins Gévay & Danner (2014)

All five are strongly solved. Positions count the reachable / database size under each solve’s ruleset; Morabaraba’s is the approximate figure reported by Gévay & Danner.

Play the solver

Section titled “Play the solver”

The explorer plays four, five, or six men’s morris on the 16-point board (switch with the toggle) from a precomputed perfect-play tablebase — six men’s is this project’s result. Every move is labelled win, loss, or draw under perfect play.

More

Section titled “More”