Othello X-Squares and C-Squares: When They Cost You the Corner

An X-square is the square diagonally inside a corner (b2, g2, b7 or g7), and a C-square is an edge square right next to a corner (like b1 or a2). While the corner is empty, stay off them: in 2,000 games between Poozee's Medium computers, the opponent ended up with the corner after 86.5% of X-square moves and 60.8% of C-square moves. But the danger is the corner, not the square. A C-square that didn't let the opponent into the corner right away came out even, and when every move left is next to a corner, your best bet is one that keeps the corner shut.

Our Othello strategy guide showed that avoiding these squares did more than any other single rule it tested, and Othello openings for beginners measured what one costs in the first ten moves. This guide goes further: what actually happens to the corner, what the move costs at every stage of the game, when it is safe, and which version of the rule to follow.

The squares next to each corner

Each corner has one X-square and two C-squares:

A corner disc can never be flipped, because nothing can get on both sides of it. To take a corner, your opponent needs a line of your discs running out from it with one of theirs at the far end. A C-square disc can start that line along the edge, and an X-square disc along the long diagonal. That's the whole danger, so once their corner is taken (by either player) they are ordinary squares, and everything below is about X- and C-squares next to an empty corner.

How we tested

Everything comes from the engine behind Poozee's Reversi, with seeded randomness so every number can be repeated exactly:

1. Real games. We had two Medium computers play 2,000 games and followed the corner after every X- or C-square move.
2. The cost by stage. In each of 4,000 Medium games we picked a move number from 11 to 50 and took the first position from there on where the player to move could choose an X- or C-square or something else (a few came as late as move 58). From each one we played two games: one after the X- or C-square, one after the best other move (both picked by the Hard computer's judgment, 4 moves deep), with two copies of Medium, or of Hard, playing the rest. Corners were never on offer in these positions.
3. The exact endgame. On the 1,965 endgame positions from our Othello parity guide, with 10 to 14 squares empty, an exact search gave every legal move's final result with perfect play.
4. Rules of thumb. Simple players that follow different versions of the rule played Medium, and the same rules were scored against the exact search.

How often you lose the corner

Medium knows these squares are bad, so it played most of them late: of the 15,189 X- and C-square moves next to an empty corner in the 2,000 games, 78.1% came after move 40.

The two kinds of square are very different. An X-square let the opponent into the corner at once more than two times in three. A C-square did that less than one time in four.

What happened when the corner wasn't open right away is the most useful part:

• After the 6,576 C-squares that didn't let the opponent take the corner at once, the opponent got the corner 48.9% of the time and the player who made the move 50.1%. That's even.
• After the 2,080 X-squares that didn't open the corner at once, the opponent still got it 62.5% of the time, against 35.6% for the player who made the move.

So an X-square stays dangerous even when the corner looks shut. The corner then hangs on the whole diagonal behind it: if your opponent ever gets a disc on that diagonal past an unbroken line of yours, the corner is open. A C-square is mostly a question of right now: if your opponent can't take the corner after it, you're usually fine.

Pro tip: Before you play an X- or C-square, ask one question: after this move, can my opponent play in the corner? For an X-square, also look down the whole diagonal.

What it costs at each stage

Here is what playing the X- or C-square did to the score of the player who chose it, compared with the best other move. A draw counts as half a win, so 50% means an even game.

Each cell is the score after the X- or C-square vs after the other move, over 3,902 positions against Medium and 1,561 against Hard (from the first 1,600 games), about a quarter of them in each row.

Through move 40, the X- or C-square cost about 15 to 24 points of score, against either level. After move 40 the cost about halved, to 9.6 points against Medium and 8.4 against Hard.

Against Medium, X-squares cost far more than C-squares: 20.2 points against 11.8. Against Hard the two were close, 16.8 and 15.1 points, a gap well within the noise of a sample this size. For the first ten moves, see the mistake table in our openings guide.

In the endgame, the corner decides

With 10 to 14 squares empty, X- and C-squares are often all that's left. In 431 of the 1,898 endgame positions where the player to move had a choice, every legal move was an X- or C-square next to an empty corner, and only 59 had none. So "never play there" can't be the whole rule. Here is how each kind of move did against the exact search:

"Best move" is how often the move was as good as the exact search's choice, "Discs lost" is how many discs it gave away compared with the best move, and "Result thrown away" is how often it turned a win into a draw or loss (or a draw into a loss). "Opens the corner" means the opponent could take that corner right after.

Three things stand out:

• Next to a taken corner, these are some of the best squares on the board, about as good as a corner itself, whichever player owns the corner: 46.7% best moves next to your own corner, 46.3% next to your opponent's.
• An X- or C-square that keeps the corner shut was a best move about 30% of the time (32.1% and 29.4%), against under 18% for inside and other edge squares. It wasn't safer in every way, though: X-squares that kept the corner shut threw the result away more often (19.8%) than inside squares (15.8%) or other edge squares (13.8%).
• The ones that open the corner were the worst moves of all, by every measure in the table. A C-square that let the opponent in was a best move only 6.5% of the time.

A safe C-square

Black has three moves, and all of them are next to an empty corner. h2 flips h3, and then every disc from h2 to h7 is black, so White can't use the h column to take h1, and g1 and g2 are still empty. Black wins by 38 with best play, and in the line our search follows, White plays g1 next and Black takes h1. The two X-squares let White into a corner at once and lose by 54 (g2) and 48 (b7).

A safe X-square

g7 flips five discs, three of them along the diagonal (f6, e5 and d4), so from g7 back to c3 every disc is black and the next square, b2, is empty. White has nothing to flank with. Black wins by 40 with best play, and in the line our search follows, Black takes h8 itself later. Look at b7, though: it doesn't let White into a8 right away either, and it loses by 38. In our search's line after b7, White goes on to take both a1 and h8, and Black gets a8 only near the end. Keeping one corner shut doesn't make a move safe: count what it does to the rest of the board too.

Which rule to follow

We gave four simple players the same habits: take a corner when you can, otherwise leave your opponent as few moves as possible. They differ only in their rule about X- and C-squares next to an empty corner. Each played 4,000 games against Medium (the first 6 moves of each game random, each opening played twice with the colors swapped), and the same rules were scored on the 1,898 endgame positions (when a rule liked several moves equally, we averaged over them):

The plain rule more than doubled the score against Medium. But the version that only ruled out moves that open the corner did a little better in whole games and clearly better in the endgame, and the combination did best in whole games: avoid X- and C-squares, and when every move is one, pick one that keeps the corner shut. That player scored 50.2% against Medium while looking only one move ahead.

In the endgame the plain "never" rule added almost nothing (48.6% against 48.5%). What helped there was checking the corner. The rule from our parity guide that checks every move, not only the X- and C-squares, for a corner it gives away, then leaves the fewest replies, did a little better still: 54.6% best moves.

When giving up the corner is right

These are rules of thumb, and the exact search sometimes breaks them. Here White has six moves, and five of them let Black into a corner. The one that doesn't, a2, loses by 6. g7 opens h8, but taking it would flip only one disc, g7, and every one of Black's replies loses by at least 32, h8 included. When the corner would win your opponent little and your move wins you a lot, count before you rule it out.

A checklist for the squares next to a corner

1. Is the corner empty? If it's taken, by either player, the square is ordinary, and often a good one.
2. Can your opponent take the corner right after your move? If so, look for anything else first.
3. Is it an X-square? Then check the whole diagonal behind it, not just the next move. X-squares that kept the corner shut still lost it more often than not.
4. Is every move next to an empty corner? Play the one that keeps the corners shut, and of those, the one that leaves your opponent the fewest moves.
5. Near the end, count. With a dozen squares left, a corner that flips almost nothing can be worth giving away, as in the last diagram. Our Othello parity guide covers the other thing to count then: who gets the last move.

To practice, play the Hard level of Poozee's Reversi, which plays the last 10 moves perfectly. Before each move next to a corner, check the corner yourself, then use Hint (the Expert computer's choice) to see whether you agreed.

Keep playing

• Play Reversi against the computer or a friend
• Othello strategy: corners, mobility and the rules that matter most
• Othello openings for beginners: the first ten moves, tested
• Othello parity: odd regions and the last move
• How to play Othello: the rules, passing and scoring