Strategy
Stable discs in Reversi
The short answer
A stable disc can never be flipped again, whatever either player does. A disc is stable when every line through it is either full or backed to the board edge by its own colour. Stability starts at the corners and spreads along the edges, then inward. It is the only disc count worth trusting.
Most discs on a Reversi board are borrowed. Stable discs are the ones you actually own, and learning to see them is what turns a decent player into a good one.
The test for stability
A disc gets flipped when an opponent places a disc so that a line of your discs is trapped between two of theirs. So a disc is safe on a given line when that trap is impossible.
There are four lines through any square: the row, the column, and the two diagonals. Your disc is safe on one of those lines if either of these is true:
- The line is full. There is no empty square left on it, so nothing new can be placed to bracket anything.
- The disc is backed to the edge. Going one way along that line, there is an unbroken run of your own colour all the way to the edge of the board. There is no room behind you for an opponent's disc.
A disc is stable when all four lines pass that test. Fail one and it can still flip.
Watching it spread from one corner
Here is a real game with 9 squares left. Neither player has taken a corner yet, so neither player has a single stable disc. Every disc on the board can still change colour.
White plays h1. That is one disc, and it makes 7 discs permanent at once: h1, h2, h3, h4, h5, h6, h7. Every one of those discs is backed to the h1 corner by an unbroken run of White discs, so there is no longer anywhere to place a disc that could bracket them.
Two moves later White adds h8, and the right edge closes from both ends. Stable count: 8. Two moves after that White takes a8 as well and the left edge follows, giving 15 permanent discs with the score at 27 to 33.
Black has 0 stable discs at the end of that game and loses 22 to 42, with White holding 22 discs that could not have been touched.
Why stable discs beat disc count
A disc that is not stable is a disc that might belong to the other player in ten moves. Counting all your discs in the middle of the game measures something that has not settled yet, and it usually measures it backwards, because a big pile of discs normally means a lot of exposed frontier.
Counting stable discs measures what is already decided. In the game above, the moment White reached 15 stable discs the result was effectively fixed, even though the disc count was still close.
| What you count | What it tells you |
|---|---|
| Total discs, midgame | Almost nothing. Often the reverse of the truth. |
| Legal moves | Who is choosing and who is reacting. See mobility. |
| Frontier discs | How many targets you have handed over. |
| Stable discs | The part of the final score that is already fixed. |
Building stability on purpose
- Get a corner first. Nothing else produces stability early. Corner strategy.
- Build outwards from it along the edges. Each disc added to an unbroken run back to a corner is permanent on arrival. Edge strategy.
- Do not build edges towards a corner you do not own. That run is not stable, it is a target. X-squares and C-squares.
- Watch both edges from the same corner. A corner backs two edges, so a corner plus a few discs each way is worth more than a longer run in one direction.
Try it against the computer
Play the computer and after each of your moves count how many of your discs are backed to a corner. If the answer is zero after move forty, you are losing whatever the score says.
Next: corner strategy, edge strategy, endgame strategy, or back to the strategy guide.
Frequently asked questions
What is a stable disc in Othello?
A stable disc is one that can never be flipped again, no matter what either player does for the rest of the game. Corners are stable the moment they are played, and stability spreads out from them along the edges and then inward.
How do I tell whether a disc is stable?
Check all four lines through it: the row, the column and both diagonals. The disc is stable if, on every one of those lines, it is either backed all the way to the board edge by discs of its own colour, or the line is completely full. If any line has room to be bracketed, the disc can still flip.
Are edge discs automatically stable?
No. An edge disc still has the edge line running both ways, so it can be bracketed along the edge. It becomes stable when there is an unbroken run of its own colour back to a corner, or when the whole edge is full.
Should I count stable discs instead of total discs?
Yes, right up until the last handful of moves. Stable discs are guaranteed; everything else is on loan. A player with 18 stable discs out of 24 is usually beating a player with 38 that are all still flippable.
Can a disc be stable without a corner?
Yes, when the lines through it are completely full. In a filled row, nothing can be added to bracket anything, so those discs are locked. In practice, almost all stability before the very end of the game comes from corners. Corner strategy.