Reversi strategy: how good players actually think

Reversi looks like a game about collecting discs. It is not. Almost every beginner loses for the same reason, and it is the opposite of what the board seems to be telling them.

The one idea everything else hangs on

A disc you own in the middle of the game is not a point. It is a piece of ground you have to hold. Every disc you place next to an empty square is a square your opponent can play beside, and every disc sitting out in the open can be flipped back later. Late in the game a single move can flip twenty discs at once, so the score at move thirty tells you very little about the score at move sixty.

Here is what that looks like on a real board. Black has played the greedy way, always taking the move that flips the most discs, against the Intermediate computer on this site.

abcdefgh

12345678

Black owns 18 discs against White's 6. That looks like a rout. It is the opposite. Black has 5 legal moves and White, if it were White's turn, would have 15. Black has 13 discs touching an empty square and White has 4. Every one of those Black discs is a target and a place for White to play next to. That game finished 0 to 64: Black lost every disc on the board.

It is not only greedy players who fall for it. Below is a quiet game between two copies of the same computer opponent. After 41 moves Black leads 30 to 15, twice the discs.

abcdefgh

12345678

Black lost that game 22 to 42. Nothing dramatic happened. White simply took the four corners near the end and every disc anchored to them stopped being flippable. The rest of this guide is about how that happens and how to be on the right side of it.

Corners: the only squares that are permanent

To flip a disc you have to trap it in a straight line between two of your own discs. A corner has no square beyond it in any direction, so no line can ever pass through it from both sides. A disc on a1, h1, a8 or h8 is yours for the rest of the game, no matter what happens.

That is worth far more than the one disc it looks like. Discs sitting next to a corner along an edge cannot be flipped either, once the run is unbroken back to the corner, and the effect spreads. By the end of the quiet game above, White owned 22 discs that no move on earth could flip.

You almost never take a corner by walking up to it. You take it because your opponent ran out of safe moves and had to open it for you. That is why corners and mobility are the same subject seen from two ends. Corner strategy in full.

X-squares and C-squares: how corners get given away

The four squares diagonally next to a corner are called X-squares: b2, g2, b7 and g7. Playing one while the corner beside it is still empty is the most expensive mistake in the game, because it usually gives your opponent a line straight into that corner.

Black to move below. Playing g2 looks harmless. It flips one disc and it reaches the top of the board.

abcdefgh

12345678

abcdefgh

12345678

The squares on the edge next to a corner, a2 and b1 beside a1 for example, are called C-squares. They are less deadly than X-squares but they cause the same kind of trouble, especially when they sit at the end of a run of your own discs. X-squares and C-squares, with diagrams.

Edges: useful, and easier to lose than they look

Edge discs can only be flipped along the edge or from inside the board, so they are harder to take back than middle discs. That makes edges attractive and it makes new players build them too early.

A long run of your discs along an edge with an empty corner at the end of it is not a wall, it is a queue. In the quiet game above, Black held five discs in a row on the top edge from b1 to f1 while a1, g1 and h1 stayed empty. When White finally played a1, every one of them flipped in a single move.

There is a good version of edge play as well: the wedge, where you drop a disc into a single gap between two enemy edge discs and it can never be taken back along that edge. Edge play, wedges and unbalanced edges.

Stable discs: the only count that matters

A stable disc is one that can never be flipped again, whatever either player does. Corners are stable the moment they are played. A disc is stable when, along all four lines through it, either the line is full or it is backed all the way to an edge by discs of its own colour.

Counting stable discs instead of total discs is the single biggest jump in playing strength most people ever make. A player with 15 stable discs and 20 total is beating a player with 40 total and none. How stability spreads from a corner.

Mobility: how many places you are allowed to play

Mobility is simply the number of legal moves you have. It is the plan that wins games. You are not trying to take discs, you are trying to reduce your opponent to a handful of choices, all of them bad, until they have to open a corner or an edge for you.

In the first diagram on this page, Black had 5 choices and White had 15. That gap is the whole story of the game. Moves that flip one or two discs, deep inside your own area, tend to be the good ones, because they take almost nothing and give your opponent almost nothing to work with. They are called quiet moves. Mobility, quiet moves and how to count them.

Frontier discs: your own worst enemy

A frontier disc is one that touches at least one empty square. Interior discs, completely surrounded, cannot be flipped and cannot be played next to. Every frontier disc you own is both a target and an invitation.

This is the mechanism underneath "fewer discs is better". Flipping a big line usually turns a row of interior discs into frontier discs, so the move that gains you the most discs is very often the move that hands your opponent the most squares.

Parity: who is forced to move last

Parity is about who has to move last into each empty region. The last disc played into a pocket of empty squares flips discs that the other player has no chance to flip back, so it is worth several free discs. With an even number of empty squares left, the player who moves second into a region generally gets the last word in it.

Late in a game the empty squares break into separate pockets, and each one has its own parity. Good players steer for the version where they fill the last square in most of them. Parity explained with a real endgame.

The endgame: where the discs finally count

With about a dozen squares left, the game changes character. Mobility stops mattering because there are hardly any moves left to have, and disc count starts mattering because there is no time for anything to flip back. This is the point where the patient player collects.

It is also the point where a mistake is unrecoverable, so counting beats instinct. Work out what the board looks like after the last square is filled rather than after the next move. How to play the last fifteen moves.

An order to think in

When you are choosing a move, run down this list. It is roughly the order the computer on this site uses too.

1. Is a corner available? Take it, unless taking it hands back something worse, which is rare.
2. Does this move give a corner away? If it is an X-square or a C-square beside an empty corner, look for something else.
3. How many replies does it give my opponent? Fewer is better. Count them if the position is close.
4. How many of my discs end up touching empty squares? Fewer is better.
5. How many discs does it flip? Last, and usually fewer is better until the final ten moves.

The opening

Black has exactly four legal first moves: d3, c4, f5, e6. Give the board a half turn, or flip it across either long diagonal, and one of them becomes another, so it genuinely does not matter which you pick. The marked squares below are all four of them.

abcdefgh

12345678

After that, the named opening lines start to diverge, and they are worth knowing mostly because they save you from working the first ten moves out every game. Why all four first moves are equal, opening strategy and the index of named openings cover that ground.

Every page in this guide

The board geometry pages explain which squares are worth what. The timing pages explain when to take them.

• How to win at Reversi: the whole plan from move one to the last disc.
• Corner strategy: why corners decide games and how to make someone give you one.
• X-squares and C-squares: the eight squares that lose games.
• Edge strategy: wedges, unbalanced edges and when an edge is a liability.
• Stable discs: the discs that can never be flipped, and how to count them.
• Mobility: keeping your options open and closing your opponent's down.
• Parity: who is forced to move last, and why it is worth free discs.
• Endgame strategy: the last fifteen moves, where counting replaces instinct.
• Tips for beginners: the short version, if you have just learned the rules.
• Common mistakes: the six errors that cost most games.
• The best first move: what the engine says when you actually ask it.

If you are still working out how the discs flip, start with the rules or how to play. The glossary defines every term on this page in one line each.

Try it against the computer

Reading about mobility does nothing. Counting it does. Play the computer on Intermediate, and before each move count your legal moves and then count the ones your move will give your opponent. Undo is free and unlimited, so when a game turns, step back to the move that turned it and take the other option.