Play checkers

The rules this board plays

Eight squares by eight, and only the thirty-two dark ones are ever used. Nothing stands on a light square all game. Twelve pieces fill the three rows nearest each player. Cream opens on this table, where tournament English draughts gives the first move to the darker side instead. The opening position is a mirror of itself, so the only thing that changes is the name of whoever starts. Exactly seven moves are legal at the start: four pieces can step, and between them they have seven empty squares to step to.

An uncrowned piece is called a man. It moves one square diagonally forward onto an empty square and never backwards. It captures by jumping: an enemy piece on the next diagonal square with an empty square directly beyond it, and the jumped piece leaves the board. If the same piece can jump again from where it lands, it must, and the whole chain counts as one move: two jumps in a row are a double jump, and nothing stops a chain at two. This table sends a jump sequence as a single action, so a chain cannot be abandoned halfway through.

Capturing is compulsory. If a jump exists anywhere in the position, jumps are always all you are offered. What you keep is the choice of which one: two chains that take different numbers of pieces are both legal here, and you may take the shorter. That is the American rule, and it is the first of two places where this board parts company with the ten by ten game, where the maximum capture is the only legal capture.

A man that reaches the far row is crowned, and a king moves and captures one square diagonally in any direction, backwards included. A man that crowns in the middle of a chain stops there. The crown ends the move even when the new king can see another jump from the square it has landed on, and anything further waits for your next turn. We set the position up and checked it against the shipped rules: a man jumping into the king row is offered exactly one move, one capture long, with the crown on it and nothing after it.

There are two ways to lose and the second is quieter than the first. You lose when your last piece is taken. You also lose when you still have pieces and no legal move at all, so a side that has been blocked has lost. Draws are counted rather than agreed. Let eighty consecutive turns pass with no capture and no man moved, and this board calls the game drawn on its own. Tournament play uses the same threshold from the other end: the American Checker Federation’s forty move rule gives each player forty moves, and there a draw has to be claimed rather than arriving by itself.

Games rarely go near that. We ran a thousand of them through the shipped rules with both sides playing legal moves at random: the middle game ran fifty-four turns, nine in ten finished inside a hundred and twenty, and the longest reached two hundred and fifty-one. Random play is not your play, so read those as the shape of the game rather than a clock. What they do settle is that the eighty turn counter is a backstop and not a thing you will meet.

Checkers is solved, and the answer is a draw

In 2007 a team at the University of Alberta led by Jonathan Schaeffer announced that eight by eight checkers is solved. Not usually drawn, not drawn in practice: perfect play by both sides, from the position you are looking at when the board is first set out, ends level every time. Neither side has anything better available. The paper is called Checkers Is Solved and Science published it on 19 July 2007.

Checkers has roughly 5 x 10^20 legal positions, five hundred billion billion of them. Four in a Row, the other solved board on this site, has about 4.5 x 10^12, which makes checkers around a hundred million times the larger problem. That board fell in 1988, twice in the same month, to two people working separately. Checkers took another nineteen years, and it came out a draw where Four in a Row is a win for whoever goes first.

The proof did not visit every position. It worked from both ends and met in the middle. Endgame databases were computed for every position with ten pieces or fewer, thirty-nine trillion of them, each labelled a win, a loss or a draw. A search then ran forward from the opening until it dropped into those databases, following only the lines that could change the answer. Around 10^14 positions were evaluated in all. The program was Chinook, the work began in 1989, stalled in 1997, restarted in 2001, and finished eighteen years after it started.

Solved is a precise word here, and this is the weaker of its two meanings. A weak solution settles the value of the starting position and supplies a strategy that guarantees it. A strong solution would settle every position the board can reach, and nobody has that for checkers. The draw was proved across nineteen tournament openings, which covers the game as it is played on this table, where your first move is your own to choose. The tournament variant that deals the first three moves from a deck is a separate question and was not the one answered.

None of it reaches a game between two people. Perfect play is not available to you and it is not available to whoever opens your link. What the proof settles is the value of the position when neither side ever errs. What is left to you is every turn on which the rules offer a choice, and across the thousand games we measured that was a little over five moves a turn, each one of them yours to get wrong. Chess has never been solved and people still lose it in four moves.

Marion Tinsley, and the record the proof caught up with

The proof closes a story that belongs to one man. Marion Tinsley held the world championship from 1955 to 1958 and again from 1975 to 1991, and he never lost a world championship match. Between 1950 and his death in 1995 he lost seven games of checkers in total. Two of the seven were to Chinook.

The program played him twice. In August 1992 Tinsley took the match four wins to two, with thirty-three draws alongside them. In August 1994 they sat down again, drew six games, and Tinsley withdrew because he was ill. Pancreatic cancer killed him on 3 April 1995. The title passed to a program without a game being lost.

Set his record beside the proof and the two point the same way. If perfect play draws, a draw is the most anyone could ever take from a perfect opponent, and a draw is what Tinsley handed almost everybody who sat down opposite him for forty-five years. One career of playing suggested it. Eighteen years of computing settled it, twelve years after he had died.

Which checkers this is, and which it is not

Checkers and draughts are two names for one family, and the family is not one game. This board plays the eight by eight version: twelve pieces a side, men capturing forwards only, kings that move one square, and a free choice among the captures on offer. North America calls that checkers, or American checkers. Britain calls it English draughts. Those are the rules this table runs and the only rules it runs, and there is no variant picker anywhere on it.

The other big one is international draughts, and nearly everything in it is different. The board is ten by ten, each side has twenty pieces, men capture backwards as well as forwards, and kings fly: a king slides any distance along a diagonal and takes a piece standing well away from it. The capture that takes the most pieces is the one you must play, however many that is. The light side opens. That is the game of the Dutch, French, eastern European and west African clubs, and across much of Europe it is simply what the word draughts means. The 2019 world championship was played in Yamoussoukro, in Ivory Coast.

So whether checkers is solved depends on which board is in front of you. The 2007 proof is about the eight by eight game and nothing else. International draughts is a far larger problem and nobody has solved it. Italian draughts will not let a man take a king. Turkish draughts moves its pieces straight instead of diagonally. The same pieces on the same squares, and results that do not transfer between them.

The players knew about the draws a century early

Nobody inside the game was surprised in 2007. Strong checkers had been drawing itself to a standstill for a hundred years, and the game’s own tournaments were rebuilt around the problem long before anybody proved there was no way out of it. From 1900 the American championship used a two-move restriction, in which the first two moves were drawn at random rather than chosen, to push both players off the lines they had memorised. In 1934 that became the three-move restriction, and the United States championship has been played that way ever since. The British Isles kept the two-move version into the 1950s.

That is a century of evidence collected the expensive way, by people who kept not being able to win. The restriction did not make the game deeper. It made the openings unfamiliar, which is a different thing to ask for. This table deals nothing. Your first move is your own, which is the go-as-you-please game, and go-as-you-please is the game the proof is about.

There is no luck in this game anywhere

Checkers is a two player game with no dice, no shuffle, nothing face down and nothing hidden. Both of you see the whole position at all times. The rules module behind a game here takes no random input of any kind and the server contributes nothing to the board, so every position that appears came out of a move that one of you chose.

What is true, and what makes people reach for the word luck, is how often the rules take the turn out of your hands. We counted it. A thousand games of random legal play, run through the shipped rules: not quite a quarter of all turns, 24.1 per cent, were turns on which a capture existed and therefore had to be made. One turn in five, 20.5 per cent, offered exactly one legal move and no alternative to it, and nearly all of those were forced captures. Eight in ten capture turns had nothing left to decide. The average turn offered a little over five and the busiest offered eighteen.

So a fifth of a game of checkers plays itself, and that is the feeling behind the word. It is still not luck. The rule that takes your turn away takes your opponent’s away on the same terms, and both of you can see it coming several moves out. The other four fifths are yours. The computer on this board looks three turns ahead and no further, and across forty games against random legal play it won all forty.

Playing checkers, and what the phrase has come to mean

Two questions arrive at this page together. One is how to play checkers, and the rules above answer it. The other is what playing checkers means, because the phrase has a second life outside the game: somebody is playing checkers while somebody else is playing chess, meaning blunt against subtle, reacting against planning. That meaning is usually attributed to Kobe Bryant, and we have not found a first source for the attribution, so take it as folklore rather than a quotation. The comparison underneath it can be checked, and half of it holds.

Checkers is the smaller game on every measure anybody uses. Seven moves open a game of checkers where twenty open a game of chess. A man has two directions and a king has four, where chess has six kinds of piece and a separate set of rules for each. Checkers is solved and chess is not.

The half that does not hold is the one the phrase is making, and Tinsley is the argument against it. The small game took eighteen years of computing to settle, and the man who played it best lost seven games in forty-five years of people trying to beat him. Smaller is not shallower.

How long a jump can get

The shortest step on this board can turn into the longest move in the game, so we went looking for the ceiling. We generated 400,000 random positions and put them through the shipped rules. The most one move took was seven pieces, all of them taken by a single king. The longest an uncrowned man produced was three, and the crowning rule is what holds it there, because a chain that arrives in the king row ends on arrival.

Ordinary games look nothing like that. Across the thousand random games, 2,121 turns took more than one piece and not one of them took more than three. Seven needs a board arranged for it, and we make no claim that seven is the true maximum, only that it is what a long search turned up. A chain is built several moves in advance by giving a piece away, because your opponent’s next move stops being theirs the moment you offer it, and that is how you know where their pieces will be standing when your turn comes back.

Where the game came from, as far as anybody can show

The likely ancestor is alquerque, a capture game played on a five by five grid of intersecting lines, and much older than the chequered board. Somebody moved those pieces onto a chess board and the game we have is what came out. The usual account has it being played in 1100, probably in the south of France. Crowning is attested by 1243, in the rhymed chronicle of Philippe Mousket, where the game is called fierges, which was then the French word for the chess queen. French still calls the game dames and the crowned piece a dame. English says king.

Compulsory capture arrived later and split the family. France added the rule and the forced version took the name jeu forcé, and that is the branch this board sits on. The earliest book in English about the game was written by William Payne in 1756, with a foreword by Samuel Johnson. Both names are literal once you look: checkers is named after the chequered board, and draughts after the verb to draw, in the old sense of drawing a piece across a surface.

Anything older than that is a guess. Boards with a checkered pattern have come out of burial chambers in Egypt and are sometimes presented as early checkers, but no rules came out with them, and the most an honest account can say is that the pattern is old and the game is not shown to be. What is attested is the crowning in 1243 and the book in 1756. The 1100 date is the account everybody repeats, and it rests on less.

Playing checkers online, three ways to open a board

You do not need an account for any of the three, and none of them puts anything on your device. Open a table here and a link comes back with it. Send that link to one person and they have the second seat as soon as they follow it, from the next room or from the far side of an ocean. If the person you want is already beside you, one device does the job for both of you: make your move, then turn the screen round. With nobody to send a link to tonight, try the computer, which looks three turns ahead and never tires of you.

That computer opponent doubles as a test instrument. Every game here is play tested before it ships, a whole game through against the machine, which is why one waits on every board on this site. Checkers is here because its rules belong to nobody and always have, so digitising it and handing it out costs nothing but the work. The collection runs from boards you have never heard of to the classic ones everybody already knows, and they arrive on the same terms.