Reversi online

How to play reversi, and how a game ends

The board is eight by eight, and there is one piece for each of its sixty-four squares. Each piece is a disc with a black face and a white one, and black goes first. Two discs of each colour are already down when you sit, on the middle squares, one colour on each diagonal. A square is legal for you only if the disc you put there traps at least one unbroken line of your opponent’s pieces between itself and another disc of yours, along a row, a column or a diagonal. Each line it traps flips at once, and a move that flips nothing is not a move at all. That last rule is the one new players take longest to learn.

If nothing you could put down would flip anything, you do not get a turn at all: it goes straight back to your opponent, and you pick up again when something opens. The game ends when neither side has a legal square, which usually means a full board and sometimes does not. Then you count the discs. However many are showing, the larger number wins, and equal counts are a draw. No disc on this board belongs to anybody for long, because any of them can be trapped again on a later turn.

The turn that skips itself, and why there is no pass button

Reversi gives you no way to decline a turn, and the reason is the rule above rather than a missing feature: a placement has to flip something, so when nothing would flip for you there is nothing legal you could do, and the turn goes back. There is no pass button here, and no way to say you would rather not go. What the board does instead is say so out loud, naming the side that was skipped and whose turn it still is, and then marking every square the side to move may legally take.

This is not a corner case. We played 2,000 boards out at random against the shipped rules, and 610 of them, nearly a third, contained at least one skipped turn. One of them had it happen four separate times. Against the computer opponent the share goes past half: 161 games in 300. If you have sat down here a few times and never seen it, that is luck rather than observation.

Those same 2,000 playouts ran a mean of sixty moves, which is the board filling up: sixty empty squares at the start, sixty discs laid around the opening cross. Forty-two of them stopped short with a square still empty, because both sides ran out of legal squares before the board ran out of room.

Two Englishmen claimed it in 1883

Lewis Waterman and John W. Mollett both said they had invented reversi in 1883, and each called the other a fraud. Neither claim was ever settled. It travelled quickly all the same: Ravensburger began producing it in Germany in 1893, one of the first titles that publisher ever put out. Some accounts put the game earlier than either man, and no document has ever been produced for that. The 1883 dispute is attested. The older origin is a guess.

One game, two names, and a trademark on the newer one

The newer name belongs to a version patented in Japan in 1971 by Goro Hasegawa, a salesman who was 38 at the time and who borrowed it from Shakespeare’s play about a Moor of Venice among Venetians, black against white. Tsukuda Original began selling that edition in Japan in 1973 under his licence, and the rights outside Japan are now held by the toy company MegaHouse. The name is a registered trademark. The game under it is the 1883 one, which nobody owns.

So the two words are not two games. They are one game and two histories: an 1883 parlour game nobody owns, and a 1971 version of it that is somebody’s registered mark. More people search for the trademarked name than for the older one. This board says reversi because that is the older name and the one anybody is free to use, and free to use is what this collection is built out of. No product of that name is sold here, and nothing else is either.

The opening discs are the one rule that ever differed

Historic reversi began on an empty board. Your first two turns went into the middle squares, laid face up with nothing flipping, and you could decline to put both of your discs on the same diagonal, so the arrangement at the centre was something to compete for before the game proper began. The 1971 version took that choice away and fixed those discs as a diagonal cross before anybody sits down. That one rule is the difference between the two names.

The cross is what this board sets, as the rules above describe, so what you are playing here is the trademarked opening under the older game’s name. It is also the exact position that was solved in 2023, which is the section further down. If you came looking for one name and found the other, the board underneath is the one you wanted either way.

Black’s four openings are one square in disguise

Count the legal squares in the position this board starts from and there are exactly four for black, each of them flipping a single disc. Play them all out and the boards that result are the same position rotated or mirrored, so black’s opening is one square wearing several hats. Whichever of them black takes, white then has exactly three replies. Your first real decision is your second turn, and reversi is a game where the second turn is already a decision about a corner you will not reach for another forty of them.

Being ahead on discs is not being ahead

Across those 2,000 random playouts the disc lead changed hands a mean of 14.6 times. Nothing you take is yours for long, because every move you make opens squares for the other side, and each disc you flip is now sitting in a line your opponent can flip back.

What a lead is worth matters more than how big it is. The side holding more discs after thirty turns, however many more, went on to win 55 per cent of the random boards, which is barely better than a coin. In 300 playouts against our computer opponent the same lead was worth less than nothing: the side ahead on discs at that point won 41 per cent of the time. Random moves are not skilled ones and our opponent thinks only one turn ahead, so these are properties of the board rather than a theory of skilled play. What they do explain is a thing new players report: you think you are winning, and then you are not. Nobody arrives knowing that, and the people who enjoy reversi are the ones who have stopped believing the count.

What is worth holding is a corner. A disc flips only when it is trapped between two enemy pieces, and a corner has no square on its far side in any direction, so a disc in a corner can never be flipped again. By the same reasoning there is no such thing as a good square diagonally beside an empty corner. Our computer’s own table of square values puts numbers on both: a corner scores 120, no other square is worth more than 20, and the square diagonally next to a corner scores minus 40, because taking it is usually how a corner gets handed over. Winning is mostly holding corners and refusing the square beside them, which is where most reversi strategy advice starts. Everything after that is knowing when to break them.

What the computer opponent is doing

It plays one ply of minimax. For each legal square it has, it puts the disc down, looks at each reply you could make, and keeps the square whose worst reply leaves it best placed. What it is judging is the table of square values above, plus ten points for each legal square it holds over you, plus thirty points for each disc it leads by, and that last term stays switched off until fewer than ten squares are empty. So for most of a game it is playing for space and for corners rather than for discs, content to be behind on the count, and then it starts counting.

Over 300 boards a side against random opposition it won 281 as black and 290 as white. It is beatable, and the way to do it is in that paragraph: it never looks past your reply, so a trap you set two turns out is invisible to it. There is a second reason a computer sits on every board here, and it is not company. It is the seat the owner takes before a game is released: "I have play tested every game that ships." This one was met that way too, skipped turns and all.

If you came looking for a reversi bot, or for a hard one, that is all there is: one opponent at one strength, with no difficulty menu behind it. It is hard in one specific way and soft in another. It will not hand you a corner, and it will not see a plan two turns deep.

Solved in 2023, and the answer was a draw

In 2023 Hiroki Takizawa announced that the eight by eight game is weakly solved, in a paper titled Othello is Solved: with both sides playing perfectly from the opening position, the result is a draw.

Weakly is the load-bearing word there. What has been solved is play from the opening position with both sides perfect the whole way down, and that is not a machine that could tell you the right answer in the position you have actually made a mess of. Between two people at a reversi board it changes nothing at all. The lead will still swing a dozen times, and a game that is drawn at the bottom of a proof is still one you can lose on a Tuesday evening by giving away a corner.

Sitting down with a friend who is not in the room

To play reversi here you make a table, and the board hands back something to send on. Send it to the one person you want across the board from you, whatever country they are sitting in, and they are playing the moment it opens for them. Neither of you will need an account, and nothing installs. If they are in the room with you instead, the two of you can take turns at one screen. If nobody is free at all, the computer takes the seat, and the section above says how hard that seat is. Two seats and one link is the whole of multiplayer on this board.

There is nothing to download and nothing to keep track of. The squares open to you are marked before you click, the trapped lines flip on their own, and a skipped turn announces itself, which between them settle the arguments reversi is capable of starting. It is a quick game to set out and a long one to get right. Come and sit down, and do not be shy about the counting at the end.