Strategy
Parity in Reversi
The short answer
Parity is who is forced to move last. The final disc played into a pocket of empty squares flips discs the other player can never flip back, so it is worth several free discs. With an even number of empty squares and no passes, the second player to move gets the last one.
Parity is the last thing most players learn and the first thing that starts winning them close games. It is arithmetic, not judgement.
The basic idea
Every move you make can be answered. Your opponent replies, and some of what you just flipped comes back. The one exception is the move that fills the last empty square in an area: there is no reply, so everything it flips stays flipped.
A Reversi game starts with 60 empty squares and Black moves first. Black plays odd-numbered moves, White plays even ones, so White plays move 60 and fills the last square. That is why parity is said to belong to White at the start. Every pass flips it over to the other player.
Regions, not one big count
The whole-board count is only the start. Once the middle fills up, the empty squares break into separate pockets that do not touch each other, and each pocket has its own parity.
Below is a real game with 19 empty squares in 5 pockets.
| Size | Odd or even | |
|---|---|---|
| a1, a2, b2, a3, a4 | 5 | Odd |
| g1, h1, h2 | 3 | Odd |
| h4 | 1 | Odd |
| a7, b7, a8, b8 | 4 | Even |
| g7, d8, e8, f8, g8, h8 | 6 | Even |
3 of those pockets have an odd number of squares. An odd pocket is one the player who moves into it first also finishes, if both players keep answering inside it. An even pocket goes to whoever moves into it second. Nobody wants to be the first to touch an even pocket.
Why the last disc is worth so much
Take the same game eleven moves further on. There are 8 empty squares left in 4 pockets and the score is 23 to 33.
Six moves later Black is down to 1 legal move and the score is 29 to 33. There are only 2 pockets left, each of a single square: a1 and b2.
Black plays b2 because it is the only legal move. White plays the last square, a1, and it flips 9 discs: b1, c1, d1, e1, f1, g1, b2, c3, d4. Black cannot answer, because there is nothing left to play. The game ends 22 to 42.
White had the last move in every remaining pocket. That is what parity buys, and it is why a game that looks level with twelve squares left can finish twenty discs apart.
Playing for parity
- Do not open a new pocket for nothing. The first person into an even pocket usually loses it.
- Count from about fifteen squares left. Before then, the pockets are still merging and the count changes every move.
- An odd pocket is a free move. If you move into it first, you also finish it, so odd pockets are where you spend your turn when you do not want to touch anything else.
- Passes flip everything. If either player is going to be forced to pass, redo the count. How passing works.
Try it against the computer
Play the computer and when about fifteen squares are left, stop and map the pockets. Count the size of each. Then decide which one you want to be second into, and play everywhere else first.
Next: endgame strategy, mobility, stable discs, or back to the strategy guide.
Frequently asked questions
What is parity in Othello?
Parity is about who is forced to move last. With an even number of empty squares and no passes, the player who moves second fills the last one. Playing the final disc into a pocket of empty squares flips discs your opponent has no chance to flip back.
Why is moving last an advantage?
Because nothing can answer it. Every earlier move can be flipped back by the reply; the last move into a region cannot. It is normally worth several free discs, and in a close game it is worth the game.
Does Black or White have parity in Othello?
White, in a game with no passes. There are 60 empty squares at the start and Black moves first, so White plays the 60th and last disc. A single pass flips that around, which is one reason forcing a pass can be worth doing.
What is region parity?
Late in a game the empty squares break into separate pockets. Each pocket has its own parity: a pocket with an even number of squares tends to fall to whoever does not move into it first. Good endgame play is choosing which pocket to open and when.
How do I use parity in a real game?
From about fifteen squares left, count the empty pockets and their sizes. Try to be the one who moves second into each even pocket, and avoid opening a fresh pocket for nothing. Endgame strategy works through it.