Nine men's morris

Nine men's morris rules: how to play, in three phases

The board is twenty-four points. Three squares sit one inside the other, and four straight lines run through the midpoints of their sides to join them. Nothing crosses the centre and there are no diagonals here. Each side starts with nine stones in hand, and the object is to leave your opponent's side holding two stones, or holding no legal move. Jade and Ivory are the two sides at this table, and Jade goes first.

Phase one is placing. Take turns putting one stone from your hand onto any empty point, until both hands are empty. Eighteen stones cannot fill twenty-four points, so the position is never full, and more than six points stand bare by the time all eighteen have been placed, because mills start closing long before the hands run out.

Phase two is moving. Slide one of your stones along a line to an adjacent empty point. One step a turn, no jumping over anything, and still no diagonals.

The mill belongs to both phases. Fill one of the board's marked lines with three of your own stones, and the moment you close it you take one of your opponent's stones off before your turn passes. You may not take a stone standing inside a mill of its own while any other enemy stone is available; if every last one of them is in a mill, then any of them can go. Closing two mills with a single stone still takes one stone rather than two.

Breaking a mill and rebuilding it is allowed, and most games here are decided by it. Move a stone out of a completed mill this turn, move it back next turn, and the mill counts again and takes another stone. Nothing here remembers that those three points were already filled once.

Phase three is flying. A side reduced to exactly three stones stops walking: any of its three may go to any empty point anywhere. The other side, if it still holds four or more, keeps stepping one point at a time. Flying belongs to whoever is down to three and to nobody else, so for a stretch of the game the two sides are moving under different rules. Some boards in this family leave flying out altogether, and two of them are named further down.

Games end in four ways here. Once both hands are empty, drop below three stones and you have lost, since two stones can no longer form mills. Keep your stones but run out of legal moves and you have lost as well. Either player may resign. And a game going nowhere is stopped: fifty consecutive moving turns between you, twenty-five each, with no new mill closed in any of them, ends it as a draw. That fifty is this table's adjudication rather than a rule of the game. Placement does not count towards it, and the count returns to zero whenever a mill closes.

A board cut into a temple roof, and a date nobody can hold

The oldest thing anyone points at when this game comes up is a set of boards cut into the roofing slabs of the temple at Kurna in Egypt. R. C. Bell assumed a date of roughly 1400 BCE for them, and that number has travelled a long way since. It is why you will read that nine men's morris is three and a half thousand years old. Look at what the Kurna diagrams are before the number even comes up: they carry diagonal lines, which makes them boards for the twelve piece version of the game rather than for this one.

The number does not hold. Friedrich Berger looked at the same diagrams and found Coptic crosses cut among them, which puts at least some of that stonework many centuries the other side of 1400 BCE. His conclusion was blunt: certainly they cannot be dated. A pattern scratched into a roof has no layer to be dug out of and no rubbish heap beside it, so the slab can be ancient while the scratch is young. Keep the find, drop the number. Boards exist at Kurna, and nobody can say who cut them or when.

The earliest date that does hold is a written one, and it is a good deal later. In book three of the Ars Amatoria, around 8 CE, Ovid describes a game with three pieces a side, won by getting them into a straight line, and adds that it is a bad thing for a woman not to know how to play, because love often begins over a board. Three a side is the small version of this game rather than the nine stone one, so that passage attests the family and not the board on this page. Roman buildings carry the pattern all over the empire and they are undatable for the same reason Kurna is: those walls have stood open ever since, and anybody with a blade and a free afternoon could have cut one.

Cloister seats, a cathedral pillar and the back of a ship's plank

Medieval Europe is where the record stops being arguable, because the game is cut into furniture that can be dated around it. Boards survive in the cloister seats at Canterbury, Gloucester, Norwich, Salisbury and Westminster Abbey, and another sits in the base of a pillar in Chester Cathedral. Those cloister boards use holes rather than lines, which is where the old English name nine holes comes from, and on them a diagonal row counted for nothing. A twelfth century board from Novgorod is in the Kremlin museum there. A brick from a medieval site near Wisbech had been used as a board by the brickmakers before it went into the kiln, which pins the scratch in time more tightly than most of this evidence can: it had to be cut before the brick was fired.

The game travelled north as well. A wooden gaming board came out of the Gokstad ship burial, dated to roughly the year 900: a thirteen by thirteen tafl grid on one face, and this game cut into the other. One plank, two games. Further back than any of that, a fragment of clay tile from Mycenae carries a pattern that appears to be a morris board, though appears is the right word for it and nothing firmer has been established.

Read the find spots and you can infer the players, which is as close as this evidence comes to naming anybody. Masons, brickmakers, monks sitting through a long service, sailors with a plank and a knife. The pattern is portable as an idea rather than as an object, which is why its archaeology turns up on roof slabs, church seats and the backs of other things.

Shakespeare, and where the name does not come from

Giant boards were sometimes cut straight into the turf of a village green, and one of those is the reason the game turns up in Shakespeare. In A Midsummer Night's Dream, in the second act, Titania is listing everything that has gone wrong with the summer while she and Oberon quarrel, and among the drowned fields and the rotted corn she says that the nine men's morris is filled up with mud. The line works because an English audience in the 1590s knew what that looked like: a board cut in the ground, unplayed, filling with rain.

The name is a separate puzzle, and the dance has nothing to do with it, however much the sound of the word suggests otherwise. Daniel King puts the derivation at the Latin merellus, a counter or gaming piece, and the same root shows through the game's other names: merels, merrills, merelles, marelles and morelles. English also had ninepenny marl. North America has called it cowboy checkers, and its board is still sometimes printed on the back of a checkerboard. Mill, mills and the mill game point at the only thing that matters. We have not found a document that closes the etymology either way, so take the Latin as the best supported reading rather than a settled one.

The board is perfectly even in one way and lopsided in another

There are 16 mills here, eight lying one way and eight the other, with no diagonal among them. Sixteen lines of three is 48 places to stand, spread across 24 points, and the spread is exact. We counted it off the file that runs this table: every point lies on exactly two mills and not one lies on three. Measured by the mills it can form, each point on this board is worth the same as every other.

Movement is nothing like so fair. Count the lines leaving each point and the twenty-four split three ways. Twelve have two neighbours each and those are the corners of the three squares. Eight have three neighbours, the midpoints of the outer square and the inner one. Four have four neighbours, and those are the midpoints of the middle square, where the joining lines meet the ring at the centre.

So the strong squares are not the ones sitting on more mills, since no such square exists. They are the ones you can leave. A stone parked on a corner has two ways out and two enemy stones shut both; a stone on one of the four junctions has four ways out and shutting it costs twice as much. That arithmetic sits under the usual opening advice to spread your stones rather than chase the first mill you can see. Versatility here is measurable, and it is measured in exits.

The double mill, and the thirty-two ways to build one

A mill you can open and close at will is the strongest structure in the game, and it costs five stones. Arrange two mills so that each is one short, with their two gaps side by side. A single stone then shuttles between the pair: it lands, a mill closes, a stone comes off, and next turn it goes back and does it again. Players call it a running mill, or a double mill. Once it is built and cannot be interfered with, it strips the other side at one stone a turn.

We counted how many this geometry allows. Thirty-two pairs of adjacent points where one mill completes on the first and a different mill completes on the second, with no stone shared between them, which is the arrangement that lets the shuttle run without disturbing the four stones standing still. The count comes out of the same adjacency and mill tables the reducer uses, so it describes this board rather than a general one.

A running mill has no clock on it either. The fifty turn counter above returns to zero whenever a mill closes, and a shuttle closes one every second turn, so the draw rule will never rescue anybody from it. The answer is to stop it before the fifth stone lands, which means treating two enemy stones on an otherwise bare line as more urgent than two of your own.

Nine men's morris is a solved game

Ralph Gasser solved it at the Institut für Theoretische Informatik at ETH Zürich and published the result in 1996. The method was retrograde analysis: start from positions with few enough stones left that the outcome is obvious, record won, lost or drawn for each, and work backwards until the endgame databases cover something in the order of ten billion positions. An eighteen ply alpha-beta search run on top of those databases then carried the value back to the empty board. The empty board is a draw. Two players who never once err will not beat each other at this game.

The way it was done is the part that made the paper matter. The games solved before it had mostly been cut down with knowledge, pruning the tree using things people already understood about the game. Nine men's morris would not be cut down that way, so almost the whole state space had to be walked. It was the first nontrivial game solved on those terms, and it ran on a personal computer. Those figures come from the paper's published abstract rather than from its body, which would not extract.

Adding one rule can change the answer, which is worth knowing before anybody decides the whole family is drawn. Lasker morris, the ten stone variant Emanuel Lasker devised in which you may either place a stone or move one during the opening phase, comes out drawn as well. Morabaraba, the twelve stone board with diagonals played competitively in South Africa, does not: by the extended solutions Gábor Gévay and Gábor Danner computed, its standard opening position is a win for the player who moves first. Three closely related boards, two answers.

More than one board on these shelves has had its last word spoken by a machine, and the settlements are not the same shape. This one is written out and readable: the drawn game can be handed to you move by move. Hex has a proof that whoever opens holds a winning strategy, and no way of saying what a single move of it is. A result you can read and a result you can only trust are two different objects, and solved covers both.

How to win nine men's morris every time

You cannot, and that is the theorem above rather than a dodge. Against somebody who never errs this game is a draw. The useful version of the question is how to beat somebody who does err.

Place for movement in the opening rather than for mills. The four junctions and the eight three way midpoints are where a stone keeps its options, while a mill formed early in one corner buys a single stone and leaves the rest of your army in a heap. Build threats that cross instead. One line holding two of your stones and a gap is a single threat and it gets blocked; two lines crossing at the same empty point are two threats and only one can be answered.

Watch your opponent's freedom as closely as your own, because running out of legal moves loses the game outright and a player concentrating on mills will not see it coming. And spend your removals with a reason. Take the stone about to complete something, or the stone whose absence opens a line for you, rather than whichever one your hand is nearest.

Flying turns the last phase into a different game, and most advice stops before it. A side down to three stones reaches any empty point on its turn, and three of its own stones plus at most nine of yours never fill twenty-four points, so a flyer always has somewhere to go and cannot be shut in at all. Immobility stops being a way to win there. The third stone has to be taken, and that is harder than it sounds, because your opponent's flyer can drop onto any single gap you leave. Two open lines at once is the one thing it cannot cover, since it still lands on one point a turn.

The computer here plays to numbers that can be read straight off the file, so you can work against its habits rather than guess at them. Material is worth 100 a stone. A completed mill on a line carrying no enemy stone scores 220, and two of its own stones on such a line score 45. Two of your stones on a line clear of its own costs it 60. Standing with a capture owed to it is worth 300, and owing you one costs the same. Its search is exactly one move deep and stops there.

The 45 against the 60 is the pair to use. It values blocking you a shade above building for itself, so it will spend a turn spoiling a line of yours more readily than a person would, even with a mill of its own half made. Open two lines at once and a single ply of search cannot answer both. It has no difficulty settings, and taking the first seat or the second is your own choice rather than a level.

The rest of the morris family, and where the game turns up now

The pattern scales. Three men's morris is played on a three by three grid with three pieces a side and is a close relative of tic-tac-toe. Six men's morris drops the outer square, gives each player six pieces and has no flying at all; it was popular in Italy, France and England through the Middle Ages and was obsolete by 1600. Twelve men's morris adds four diagonals and twelve pieces, which is the board South Africa plays as morabaraba, where the pieces are called cows and the game is a recognised sport. Shax, from Somalia, uses our board with twelve pieces a side and its own rules. Lusalos, in the Philippines, uses our board and our nine stones and leaves flying out.

Nine men's morris in Assassin's Creed III and Black Flag

The game turns up where nobody went looking for it. Assassin's Creed III put a morris board in its colonial taverns as something a stranger can challenge you to, and Assassin's Creed IV: Black Flag did the same across the Caribbean. The minigame is the same in both, and so is what happens afterwards: people lose to a bartender and go looking it up, searching nine men's morris ac3 for the older game and nine men's morris ac black flag for the newer one.

What they are usually after is why the opponent kept taking a stone every single turn. That is the running mill described above, and it is the one pattern that turns a close game into a rout. Nothing about the board changes between the two games or between either of them and this one. Nine stones, twenty-four points, three phases.

A solver, a simulator, and the nine men's morris cheat that cannot exist

Type the name into a search box and much of what comes back is machinery. A nine men's morris solver, a nine men's morris simulator, a best move calculator, a nine men's morris cheat. Being solved is what attracts all of it, and they are not the same tool at all.

A solver does the arithmetic. It reads the position out of the same kind of database Gasser built and returns its true value, and a solver playing its own advice from the start cannot be beaten, only drawn with. A simulator is a board with nobody on the other side of it, useful for setting a position up and pushing stones around until a shape makes sense. A nine men's morris cheat has nothing behind it, because there is nothing to cheat towards. The best result available against faultless play is the draw, which is free, so the only thing a cheat can win is a game against somebody who was not faultless, which is the same thing practice wins.

There is none of that here. The opponent on this board is the one described above, a single ply of search and a page of arithmetic, which makes it a sparring partner rather than an oracle. It can be beaten, and losing to it teaches you something that an engine holding the entire drawn game could not.

Playing nine men's morris online, free

One press opens a table here and mints a private link for it. Hand that link to the person who ought to have the other nine stones, and their seat is live the moment they follow it. No account is created at either end, nothing is downloaded, and the pair of you can be on separate continents. Together in one room, share a single screen and pass it across as each stone goes down. Alone, take Jade or Ivory and the computer will play whichever you left.

The table keeps the bookkeeping, which matters more in this game than in most. It counts the stones each of you has standing and the stones still in hand, it lights the points you are allowed to use, and when a mill closes it lights the stones you are allowed to take. That last one is the rule people get wrong most often at a wooden board, since the protection a mill gives lapses the moment every last enemy stone is inside one, and nobody wants to recount the whole position mid argument.

We play every game here against that computer opponent before it ships, which is what it is there for. Everything rebuilt on this site is a game nobody owns, and morris has been common property for as long as anybody has been able to scratch it into a step. Nine stones each. Come and take a seat, and do not worry about not knowing the rules, since almost nobody arrives knowing them.