Cognivo

Learn Nine Men's Morris

Place nine men, make mills, then slide them.

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Three in a line

Three of your men along one line is a mill.

Place a white man that makes three in a line.

The story

Cut Into a Roman Roof

Nine Men's Morris is one of the oldest games still played by its original rules. Boards are carved into Roman and medieval stonework across Europe, and Shakespeare mentions it in A Midsummer Night's Dream.

The whole story

Nine Men's Morris is one of the oldest board games still played by its original rules. Boards are scratched into the roofing slabs of the temple at Kurna in Egypt, into the steps of the Acropolis, into cathedral cloisters at Canterbury, Gloucester, Norwich and Salisbury, and into the decks of the Gokstad Viking ship. The Roman world played a version, and the game turns up across medieval Europe under a shelf of names — Merels, Mills, Nine Man Morris, Mühle, Molino. Shakespeare mentions it in A Midsummer Night's Dream: "The nine men's morris is filled up with mud." The dating of the Kurna boards is disputed and probably far later than the temple itself, but the medieval evidence is not in doubt: for several centuries this was a game people cut into whatever stone was to hand.

A Draw, With Perfect Play

Ralph Gasser solved Nine Men's Morris in 1993. With perfect play from both sides the game is a draw, the same verdict checkers received in 2007.

The whole story

Ralph Gasser solved Nine Men's Morris in 1993, working through retrograde analysis and an alpha-beta search over the placing phase. The result: with perfect play by both sides the game is a draw. That places it alongside checkers, solved in 2007 to the same verdict, and against Connect Four, where the first player wins. The proof required building endgame databases for every reachable position with few enough pieces, then searching backwards from them — the same shape of argument used for checkers a decade later, on a game small enough to finish in 1993.

The full notes

Everything above, and more, in words, to read or to listen to.

Rules3 sections

Three Phases, One Game

Each player has nine men. The board is three nested squares joined by four spokes, giving twenty-four points where a man may stand. Placing. Players take turns putting one man on any empty point until all eighteen are down. White places first. Moving. After that, a turn means sliding one of your men along a line to an adjacent empty point. You cannot jump, and you cannot move to a point your man does not touch. Flying. Once you are reduced to exactly three men, you may move a man to any empty point on the board instead of only an adjacent one. Three of your men in a line is a mill, and closing one lets you take an enemy man off the board immediately. You win by reducing your opponent to two men, or by leaving them with no legal move at all.

  • A line of three only counts along the drawn lines. Three men round a corner is not a mill.
  • There are sixteen mills: four on each of the three squares, and four along the spokes.

The Rule Everyone Misremembers

When you close a mill you take one enemy man — but not one that is standing in a mill of its own, unless every enemy man is in one. That exception matters more than it looks. Without it, a player whose men all sat in mills could never be touched and the game could not end. With it, a player who has carefully protected everything discovers that the protection evaporates the moment it becomes total. Taking is also the only permanent gain in the game. Men never come back. Everything else — a good point, an open line, a cramped opponent — can be undone next turn.

  • Check what is protected before you build the mill, not after.
  • If all your opponent's men are in mills, the protection lifts entirely — that is often the moment to strike.

How a Game Ends Without a Winner

Two players who each hold a solid position can shuffle men back and forth forever, because a slide is always reversible. The standard rule stops it: if fifty moves pass for each side with no man taken, the game is a draw. Cognivo counts that as a hundred plies and warns you when the count is close. A position can only repeat while nobody is capturing, so counting quiet moves catches the same shuffle that threefold repetition would — with the advantage that the count is visible to you while it runs.

  • If you are ahead on men, watch the counter — a draw throws away a won game.
  • If you are behind, the counter is a resource. Shuffling safely is a real plan.
Strategy3 sections

The Game Is Usually Decided While Placing

Beginners treat the placing phase as setup and the moving phase as the game. It is the other way round. By the time all eighteen men are down, the shape of the position is fixed and the moving phase largely plays out what placing decided. Two things matter while placing. First, the four midpoints of the middle ring — the points where a spoke meets the middle square. They touch four other points each, more than anywhere else on the board, so a man there has options while a man in a corner has two. Second, do not chase mills. A mill you close during placing takes one man, but if closing it hands your opponent the whole centre you have made a bad trade. Watch what your opponent is building at least as closely as what you are.

  • The four middle-ring midpoints have four neighbours each. Corners have two.
  • A mill that costs you the centre is usually a bad trade.

The Double Mill Wins Games

A double mill — sometimes a "running mill" — is two mills sharing a man, arranged so that moving that man out of one closes the other. It takes an enemy man every single turn, for as long as it stands, and the opponent can do nothing about it directly. Building one is the clearest winning plan in the game, and preventing one is the clearest defensive priority. The related idea is a double threat: a move that creates two open mills at once, only one of which the opponent can block. This is what the one-ply thinking of a beginner cannot see, and it is precisely what a search finds. If you play the hard opponent here and lose without understanding why, look for the move two turns earlier that made two threats at once.

  • Two threats, one blocker. That is the whole game in four words.
  • A running mill wins on its own — if you see one coming, spend a move to stop it.

Winning Without Taking Anything

You do not have to reduce your opponent to two men. Leaving them with no legal move wins outright, and against a player who has taken corners and edges without thinking about mobility it is often the faster win. A man on a corner has two neighbours; block both and it is frozen. Freeze them all and the game is over regardless of how many men they still hold. This is why the flying rule exists. A player down to three men can move anywhere, so they cannot be blocked at all — the rule stops the endgame from being a formality and gives the losing side genuine chances. It is also why "reduced to two" and "cannot move" are two separate ways to lose rather than one.

  • Count your opponent's available slides, not just their men.
  • A player on three men cannot be blocked — they fly. Beat them on count instead.