Six 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: Six men’s Merrills, Sechsermühle, Sechs-Männer-Mühle.

Draw with perfect play. Strongly solved over all 42,372,745 reachable positions (standard ruleset: no flying).


Result	Draw
Strength	Strong
Method	Retrograde analysis, Brute-force enumeration
Year	2026
Solved by	Brian Liou (open-source game-solver engine, 2026)
Source	Liou 2026*
Board	Two concentric squares (16 points) joined by lines at the four side-midpoints; no diagonals. Equivalent to the nine men’s morris board with its outer ring removed. 6 men per player.
State space	42,372,745
Evidence	self-archived*

* Self-archived: the result is available only from its authors (a repository, a post, a deposit), not yet refereed, formally verified or reproduced by someone else. The mark comes off when one of those happens. It applies to this repo’s own results too.

Solution history

Date	Size or opening	Result	Strength	Credit	Source
2026-06-18	standard rules, no flying	draw over 42,372,745 reachable positions	Strong	Brian Liou	source

Superseded rows stay in the table.

References

Resources

Code

game-solver — generic retrograde-analysis engine (the game-solver repository); six men’s morris is a plugin, solved and tested in CI

Notes

Six men’s morris is played on the two-ring (16-point) board — the nine men’s morris board with its outer square removed — with 6 men per side and no diagonals. Standard capture rules: forming a mill (three in a line) removes one opponent man (one not itself in a mill, unless all are); a player loses when reduced below 3 men or left with no legal move. This solve uses the standard ruleset with NO flying (a man reduced to 3 is not granted free movement). Small rule choices can change perfect play (cf. Gasser’s rule-variations work on nine men’s morris), so the result is stated for this ruleset. RESULT — DRAW, strongly solved. The game-solver engine computed the game-theoretic value of every one of the 42,372,745 reachable positions by retrograde analysis; the initial position is a draw. This fits the morris family: the diagonal-free morrises (Nine Men’s, Lasker) are draws, and only Morabaraba — which adds diagonal mills — is a first-player win. PRIOR ART — six men’s morris does not appear in the morris-solving literature checked (Gasser 1996; Gévay & Danner 2014, which solved its larger siblings) or in the published work of the main German Mühle community (muehlespieler.de, which teaches the small variants but publishes no solved values). Those sources are not an exhaustive search and a private earlier solve cannot be excluded, so no priority is claimed. VALIDATION is internal: (1) two independent implementations — bitmask and a cell-array version with a programmatically-derived board — agree exactly on the reachable-state count, the win/loss/draw split, and the draw; (2) the capture rules pass unit tests (mill detection, capture targeting incl. the all-in-mills exception, slide-captures, attrition loss); (3) five men’s morris (same board, 5 men) solves to 17,844,721 positions and is also a draw, a consistent data point. There is no smaller solved morris to cross-check against; the external gold-standard would be reproducing nine men’s morris’s known draw (~10^10 states), which is deferred as a separate, larger build.